RAILROAD  ENGINEERING 
By  WILLIAM  G.  RAYMOND 


Railroad  Field  Geometry  (Without  Tables) 

i6mo.     242  +  ix  pages,  138  figures,  leather, 
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Elements  of  Railroad  Engineering 

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pages,  1 10  figures,  18  plates.   Cloth,  $3.25  net. 

Railroad  Field  Manual  for  Civil  Engineers 

vii  +  398  pages,  4%  by  7, 31  figures,  83  tables. 
Morocco,  $3.00  net. 


Railroad  Field  Manual 

for 

Civil  Engineers 


BY 
WILLIAM  G.  RAYMOND,  C.E.,  L.L.D. 

Professor  of  Civil  Engineering  and  Dean  of  the  College  of  Applied  Science 

in  the  State  University  of  Iowa.    Member  of  the  American 

Society  of  Civil  Engineers  and  of  the  American 

Railway  Engineering  Association 


FIRST  EDITION 

FIRST  THOUSAND 


NEW  YORK 

JOHN    WILEY    &    SONS,   INC. 

LONDON:  CHAPMAN  &  HALL,   LIMITED 

1915 


4.* 


COPYRIGHT,  1915, 

BY 
WILLIAM   G.  RAYMOND 


Stanhope  ipress 

F.    H.  GILSON   COMPANY 

BOSTON,  U.S.A. 


PREFACE 

THIS  book  is  for  field  use  rather  than  for  office  use,  though  it  is  adapted 
to  a  large  percentage  of  office  work.  It  is  made  on  a  new  plan  which 
is  not  expected  to  gain  immediate  favor  but  which  it  is  hoped  will 
eventually  appeal  to  railroad  engineers  as  sensible  and  worthy  of 
adoption,  because  its  use  will  save  time  and  lessen  the  liability  of  error. 
The  degree  is  divided  decimally  instead  of  sexagesimally. 

When  the  author  was  a  young  man  engaged  on  railroad  location  he 
knew  one  or  two  engineers  who  had  one  vernier  of  their  transits  gradu- 
ated to  read  hundredths  of  degrees  for  greater  convenience  in  setting 
out  curves.  They  would  have  done  all  their  work  in  decimals  if  tables 
had  been  available. 

When  the  author  was  planning  this  book  he  gave  much  thought  to 
the  question  of  the  division  of  the  degree  and  the  forms  of  the  tables 
that  would  be  most  convenient  and  time  saving  for  the  field  men  who 
might  use  the  book.  He  remembered  that  in  practically  every  curve 
problem  it  is  necessary  at  some  stage  of  the  solution  to  transpose  from 
minutes  and  seconds  to  decimals  of  a  degree  or  vice  versa.  He  re- 
membered that  to  lay  out  subchords  would  require  much  less  mental 
effort  if  the  transit  were  divided  to  read  decimals  of  degrees  rather 
than  minutes.  He  wrote  to  a  half  dozen  of  the  leading  instrument 
makers  to  learn  what  would  be  the  cost  of  changing  the  verniers  on  an 
old  transit  to  read  decimals  of  a  degree  and  to  know  whether  there 
would  be  any  difference  in  price  between  two  instruments  ordered  new, 
one  to  be  divided  in  the  usual  way  and  the  other  divided  to  read  deci- 
mals of  a  degree.  All  but  one  of  the  makers  gave  a  price  in  the  neighbor- 
hood of  $20  for  changing  the  verniers  on  an  old  instrument,  and  no 
difference  in  cost  for  new  instruments.  The  author  then  wrote  to  about 
fifty  engineers,  chief  engineers  of  railroads,  independent  practicing 
engineers,  and  professors  of  railroad  engineering  in  colleges  and  asked 
their  opinions  as  to  the  desirability  of  a  change  in  practice  from  sexa- 
gesimal to  decimal  division  of  the  degree,  and  whether  or  not  a  table 
book  based  on  the  decimal  division  would  help  to  bring  about  the 
change,  if  desirable.  All  but  one  of  these  engineers  replied  that  the 
change  is  desirable.  The  one  was  a  professor  of  railroad  engineering. 
Of  the  others  all  but  two  thought  it  doubtful  if  the  change  could  be 

iii 

3O8538 


iv  PREFACE 

brought  about,  owing  to  the  conservatism  of  the  craft.  Two  chief  engi- 
neers of  prominent  eastern  roads  discussed  the  matter  with  their  assist- 
ants and  were  so  favorably  impressed  with  the  plan  as  to  say  that  they 
would  adopt  it  if  they  had  the  tables  to  make  it  possible.  Those  who 
thought  it  unlikely  that  the  change  could  be  brought  about  cited  the 
difficulty  with  the  introduction  of  the  metric  system  as  an  argument. 
To  this  the  author  replies  that  the  adoption  of  the  metric  system  in- 
volves a  change  of  unit.  The  adoption  of  the  decimal  division  of  the 
degree  involves  no  change  of  unit  and  merely  does  for  angle  work 
what  American  engineers  long  since  did  for  their  linear  work.  The 
book  still  retains  the  90°  quadrant.  To  be  sure,  minutes  and  even 
seconds  have  become  a  sort  of  unit,  but  so  were  inches,  chains,  and  links. 
These  are  practically  done  away  with  for  surveyor's  use  and  there  would 
seem  to  be  as  good  reason  for  doing  away  with  minutes  and  seconds. 
Practically  every  computation  involving  trigonometric  logarithms  re- 
quires less  work  by  the  decimal  system  than  it  does  by  the  sexagesimal 
system.  Instruments  will  be  graduated  to  read  to  hundredths  of 
degrees  directly  or  0.6  of  a  minute. 

Although  the  author  believes  that  the  "degree"  of  a  curve  should  be 
the  angle  subtended  by  an  arc  of  one  hundred  feet  instead  of  a  chord 
he  has  not  adopted  that  definition,  but  has  adhered  to  the  definition 
approved  by  the  American  Railway  Engineering  Association. 

Five-place  tables  have  been  adopted  as  representing  as  high  a  degree 
of  precision  as  is  warranted  by  the  field  work.  Computations  of  tables 
and  some  few  other  calculations  require  more  extended  tables  but  these 
practically  always~arise  in  connection  with  office  work  where  it  is 
assumed  that  there  are,  or  may  be  if  necessary,  six-place,  seven-place, 
and  even  ten-place  tables.  The  author  has  used  seven-place  tables, 
and  occasionally  ten-place  tables,  for  the  computation  of  the  tables  of 
this  book.  Persons  do  not  always  realize  it,  but  considerable  additional 
time  is  required  to  use  six-place  tables  over  that  required  for  five-place 
tables.  In  his  "Plane  Surveying  for  Classroom  and  Field,"  the  author 
discusses  this  question  at  some  length  and  works  examples  to  show  the 
relative  precision  of  four-place  and  five-place  tables.  The  conclusions 
of  the  discussion  are  as  follows: 

"i.  It  is  useless  to  make  linear  measurements  with  a  precision  of 
more  than  I  in  3500  if  angles  are  to  be  read  to  the  nearest  minute  only. 

"2.  It  is  useless  to  use  tables  of  more  than  four  places  for  angles  read 
to  the  nearest  minute  only. 

"  It  is  difficult  for  many  persons  to  bring  themselves  to  use  the  smaller 
tables  because  they  seem  to  see  a  greater  precision  in  the  use  of  tables 


PREFACE  V 

giving  results  that  are  true  to  five  and  six  significant  figures,  and  fail 
to  realize  that  the  field  work  on  which  the  computations  depend  does 
not  warrant  any  such  degree  of  precision,  which  is  therefore  only  a 
seeming  precision  that  is  misleading  and  does  not  exist  in  fact.  It  is 
true  that  linear  measurements  can  in  general  be  made  with  greater  pre- 
cision than  the  angle  work  gives  and,  hence,  it  is  the  angle  work  that 
fixes  the  precision  and  the  tables  to  be  used.  The  following  rules  may 
be  formulated: 

"  For  angles  read  to  the  nearest  minute  use  four-place  tables. 

"  For  angles  read  to  less  than  o°  oo'  30"  use  five-place  tables. 

11  For  work  in  general  requiring  certainty  in  the  third  significant  figure 
use  four-place  tables,  in  the  fourth  significant  figure  five-place  tables, 
and  in  the  fifth  significant  figure  six-place  tables. 

"  But  it  must  be  remembered  that  no  ordinary  surveying  work  is  pre- 
cisely enough  done  to  warrant  results  certain  to  more  than  four  signifi- 
cant figures,  and  that  five-place  tables  are  as  extensive  as  are  warranted 
by  any  land,  topographic,  railroad,  or  other  surveys  except  the  most 
refined  city,  bridge,  and  geodetic  surveys. 

"  Computation  labor  is  increased  about  50  per  cent  by  using  five-place 
tables  instead  of  four-place  tables,  and  about  one-third  by  using  six- 
place  tables  instead  of  five-place  tables." 

Before  using  the  logarithmic  tables  even  persons  somewhat  familiar 
with  the  use  of  logarithms  should  read  the  explanatory  text  preceding 
the  tables. 

The  text  concerning  spirals  and  the  spiral  tables  are  based  on  the 
American  Railway  Engineering  Association's  ten-chord  spiral.  The 
author  is  indebted  to  Mr.  Jenks  B.  Jenkins,  Valuation  Engineer  for 
the  Baltimore  and  Ohio  Railroad  and  Chairman  of  the  Track  Committee 
of  the  A.R.E.A.,  and  who  devised  the  ten-chord  spiral,  for  assistance 
with  this  part  of  the  work. 

The  author  has  endeavored  to  include  beside  bare  tables  —  many 
of  which  have  been  computed  for  this  book  and  are  not  found  in  other 
books  —  just  so  much  of  explanation  of  common  field  problems  as 
would  seem  necessary  to  refresh  the  memory  of  young  engineers  who 
have  not  had  these  drilled  into  them  by  long  experience. 

A  few  tables  have  been  taken  from  other  books.  Acknowledgment 
is  due  Mr.  Shelby  S.  Roberts  for  courteous  permission  to  use  tables 
from  his  "Track  Formulae  and  Tables"  and  to  the  American  Book 
Company  for  permission  to  use  plates  from  the  author's  "Plane  Sur- 
veying for  Classroom  and  Field  "  for  Tables  I,  XXIV,  and  LXXXIII, 
and  to  use  the  matter  of  Tables  LXX,  LXXI,  and  LXXVII. 


vi  PREFACE 

Great  care  has  been  taken  with  the  computations  and  the  proof- 
reading but  it  is  incredible  that  so  many  new  computations  should  have 
been  made  and  the  results  printed  without  error.  The  author  will 
esteem  it  a  favor  if  persons  will  report  any  errors  that  may  be  discovered 
to  him  or  to  the  publishers. 

This  book  may  be  used  about  as  conveniently  as  other  books  based 
on  the  sexagesimal  division  of  the  degree  by  those  who  do  not  care  to 
have  their  instruments  changed  or  to  adopt  the  decimal  division  for 
their  final  records,  and  it  has  some  features  not  found  in  existing  field 
books  that  may  commend  it  to  field  men.  Therefore,  it  is  put  forth 
under  the  hope  that  it  may  find  immediate  approval  in  a  few  places; 
that  it  may  be  tried  in  some  other  places;  and  that  familiarity  and 
experience  with  it  will  convince  users  that  the  author  is  not  a  mere 
faddist  but  has  contributed  something  of  real  use  to  the  fraternity. 

WILLIAM   G.   RAYMOND 
STATE  UNIVERSITY  OF  IOWA, 
IOWA  CITY,  IOWA, 


CONTENTS 


CHAPTER   I  PAGE 

SIMPLE,  COMPOUND,  AND  VERTICAL  CURVES i 

CHAPTER   II 
THE  SPIRAL 39 

CHAPTER  III 
LOGARITHMS  AND  TRIGONOMETRIC  FUNCTIONS 70 

CHAPTER   IV 
LOCATION  THEORIES  AND  TABLES 249 

CHAPTER  V 
ESTIMATING  AND  CONSTRUCTION  TABLES 262 

CHAPTER  VI 
TURNOUTS  AND  CROSSOVERS 297 

CHAPTER  VII 
AZIMUTH,  LATITUDE,  AND  TIME 305 

CHAPTER  VIII 
TABLES  FOR  METRIC  CURVES 314 

CHAPTER   IX 
MISCELLANEOUS  TABLES 320 

CHAPTER  X 
ADJUSTMENT  OF  INSTRUMENTS 333 

CHAPTER  XI 
SEXAGESIMAL  TRIGONOMETRIC  FUNCTIONS 337 


Vll 


RAILROAD    FIELD    MANUAL 


CHAPTER   I 

SIMPLE,   COMPOUND,  AND  VERTICAL   CURVES 

SIMPLE  CURVES 

Fundamental  notations  and  equations.  —  The  curve  running  from 
A  to  B  in  Fig.  I , 


A  =  T.  C.  (tangent-curve). 
B  =  C.  T.  (curve-tangent). 
V  =  P.  I.  (point  of  intersection  of  tangents). 
I  =  central  angle  or  deflection  angle  of  tangents. 
T  =  tangent  distance     =  R  tan  5  7. 
C  =  long  chord  =  2  R  sin  1  7. 

M  =  middle  ordinate      =  R  vers  5  7. 
E  =  external  distance    =  R  exsec  5  7. 
E  =  r  tan  *  7. 


C  =  2 


§  sec 


RAILROAD  FIELD   MANUAL 


Definition.  —  The  "degree"  of  a  curve  in  American  practice  is  the 
angle  subtended  at  the  center  of  a  circular  arc  by  a  chord  of  100  feet. 
In  Latin  American  states  where  the  metric  system  is  used  the  "degree" 
is  the  angle  subtended  by  a  chord  of  20  meters.     If  R  be 
the  radius  and  D  the  degree  of  a  curve,  then,  in  American 
practice, 

7?  =      50 
sinfZ?' 

Table  I  gives  R  and  its  logarithm  for  various  degree 
curves. 

C2 
Tangent   offset  /  =  R  vers  /  =  ^  .     The  tangent   offset   for  one 

station  is  tabulated  in  Table  I.     For  a  subchord  c  the  tangent  offset  is 

c2 

/c~/100T^o" 

Approximate  Fundamental  Relations.  —  Approximately,  radii  are  in- 
versely as  the  degrees  or 

R       D'  . 

-^>  =  -p   (approx.). 

Radius  of  a  i°  curve  is  5729.65  =  5730  (approx.). 


RD 


5730 


(approx.). 


Tangent  distance  for  a  D°  curve  of  central  angle  7  is 
TD  =  -—•  (approx.). 

Table  II  gives  tangent  distances  for  a  i°  curve  and  various  values  of 
/,  and  Table  III  gives  corrections  to  TD  =~^~  for  more  precise  re- 


D 


suits.  Values  of  C,  M,  and  E,  for  D°  curves 
are  also  found  approximately  by  dividing  the 
values  for  a  i°  curve  for  a  given  /  by  D. 
Table  IV  gives  values  of  E  for  a  i°  curve. 

A  curve  departs  from  a  tangent  approxi- 
mately thus:  O  =  |  n*D,  n  being  the  number 
of  stations  from  the  tangent  point  and  D  the 
degree  of  curve.  Two  curves  of  degrees  D 


T.C. 


FIG.  3. 


and  A  depart  from  each  other  by  the  same  approximate  law,  sub- 
stituting the  difference  of  degrees  D  —  A  or  D\  —  D  of  the  D  of  the 
foregoing  formula. 


SIMPLE,   COMPOUND,  AND   VERTICAL   CURVES  3 


The  deflection  angle  A,  for  a  chord  of  100  feet  is  |Z);    for  a  sub- 
chord,  c,  it  is  given  by 


or,  with  sufficient  exactness  for  all  curves  under  about  8°, 
-  0.5  cD,  in  hundred 

2 

5  =  0.3  cD,  in  minutes. 


5  =  —  X  -  -  0.5  cD,  in  hundredths  of  degrees, 

IOO          2 


The  ordinate  from  a  chord  at  any  point  given  by  its  distance  from 
the  center  is 


K  = 
or,  approximately, 

Whence,  for 


-  a) 


16 

a  =  lc,    K  =  ^ 
4 


(approx.). 


If  the  point  is  given  by  the  distance  from  one  extremity, 

„      QXS 

K  =  (approx.) 


Approximately 


=  872  Q  X  S  X  D 
10,000,000 

O_  =M 

8R  4 


RAILROAD   FIELD  MANUAL 


Location  by  Offsets  from  Long  Chord.  — 


AG 
BF 
Ab 


2  R  sin  -  D,     n  =  number  stations  A  to  G, 


D, 
AG^-BF 


CE  =  100  or  2  R  sin 

BF-CE 
—2 ,  etc. 


Bb 


be  =  ef  =  Be'  =  e'F 
Ff  =  Hh-  Hh"  =  R  (vers \nD  -  vers \(n  -  2)  D),  etc., 


c      h     e 

FIG.  6. 


or 


Ab  —  fG  =  IOOCQS D. 


Be'  =  e'F 
Bb  =  Ff  •- 
Cc'  =  Ee' 


IOO  COS 

100  sin 
100  sin 


-3 

2 

n  —  i  . 


D,  etc. 


Use  natural  functions  and 
move  decimal. 


In  the  particular  figure  Hh'  =  50  tan  j  D  because  «  is  odd. 

If  the  number'of  chords  is  not  more  than  8  or  the  degree  more  than  20 
and  of  an  even  number  of  tenths,  the  long  chords  and  middle  ordinates 
may  be  taken  from  Tables  V  and  VI,  thus: 

AG  =  long  chord  of  n  stations. 
. ,  _  .„_  long  chord  of  n  stations— long  chord  of  (n—2)  stations   etc 

Bb  =  Ff  =  middle  ordinate  for  n  stations  — 
middle  ordinate  for  (n  —  2)  stations,  etc. 
Location  from  Chord  Produced.  — 
Bb  =  R  vers  D,  or  100  sin  ^  D  for  natural 
functions. 

Bb  =  tangent  offset  of  Table  I. 
AV or  XA  gives  line  of  tangent. 

FIG.  7.  Stretch  the  tape  from  A   to  B  so  that  Bb 

shall    measure  as   above.     Produce  AB   to  c', 

one  tape  length,  and  swing  about  B  until  c'C  =  2  Bb.    Produce  BC  to 
e'  and  swing  about  C  until  e'E  =  2  Bb,  etc.     If  the  curve  begins  with 


SIMPLE,   COMPOUND,   AND   VERTICAL  CURVES  5 

a  subchord,  /,  swing  /  feet  above  A  to  B  (Fig.  8)  until  Bb  —  I  sin — • 

Swing  100  —  /  about  A  to  F  until  Ff  =  (100  —  /)  sin  IO°  ~ .  Pro- 
duce FB  to  cf,  100  feet,  and  swing  about  B  until  c'C  =  2  X  100  sin 
£  D,  or  twice  the  tangent  offset  of  Table  I.  Produce  BC,  etc.,  as 


FIG.  9. 


before.  For  ending  use  the  same  method  reversed.  Supposing  the  curve 
to  be  running  from  C  to  B  to  A,  locate  F  by  producing  CB,  measure 
over  Ff  and  Bb,  and  establish  A  between  /  and  b  at  /  feet  from  B. 

Problems.  —  Suggestions  for  passing  obstacles.     If  TC  only  is  in- 
accessible: 

(a)  Run  to  V  to  C T  and  run  curve  backwards. 

(b)  Assume  a  point  on  the  curve  beyond  the  obstacle;  compute  the 
tangent  distance  for  the  point,  as  TC  —  K\ 

run  to  K-,  deflect  angle  at  K  and  run  to  P 
and  run  the  curve  backward  and  forward. 
If  CT  is  inaccessible  the  same  methods 
with  obvious  modifications  may  be  used. 

To  pass  an  obstacle  on  a  curve  one  of  the 
methods  suggested  by  the  figure  may  be 
used.  The  line  AbC  is  run  as  ABC  would 
be  run  only  with  the  center  on  the  opposite 
side. 

To  change  TC  or  CT.  First  method: 
Assume  or  know  the  necessary  change  in 

tangent  distance  and  compute  a  new  degree  of  curve.  Second  method : 
Assume  a  new  D  a  round  number,  probably  such  as  to  accomplish  the 


O  RAILROAD   FIELD   MANUAL 

desired   result;  change  in   CT  or  TC  =  change  in  tangent  distances, 
or  m  =  T2  -  Ti  =  (R2  -  RJ  tan  \  I. 


/I 


FIG.  ii. 


FIG.  12. 


A  curve  ends  in  VB  or  V'B' ;  required  to  end  in  V'B'  or  VB.     Degree 
does  not  change.     It  is  necessary  to  find  change  in  A . 

K 


A  A'  =  VV  =  BB'  =  00' 


sin  / 


J 


o'.o    o" 


FIG.  13. 


1   FIG.  14. 


A  curve  ends  in  VB;  required  to  end  in  V'B'  or  V'B"  without  changing 
A .     Degree  changes. 


Rr  = 


K 


vers  / 


that  is,  change  in  R 


K 


vers  / 


A   curve  ends  in    VB;  required  to  end  in   V'B'.     A  and  D  change. 

•gr 

R'  =  R  db ; ,   according  as   B'   is  inward   or  outward   from  B. 

exsec  / 


SIMPLE,   COMPOUND,   AND   VERTICAL  CURVES 


A  A'  =  (R  —  R')  tan  /,  or  K  cot  \  7,  A  being  moved  ahead  or  back 
according  as  R'  is  less  or  greater  than  R. 

A   curve  ends  in   VB;  required  to  end  in   VB'.     Without  changing 
degree  A  A'  =  R  (tan  |  I  —  tan  \  /'), 
and  A  is  moved  forward  or  back  accord- 
ing  as   1'   is  less  or   greater   than   /. 
Changing  degree  and  keeping  A  fixed, 

T 
T    is    unchanged.       .*.    R'  = 3—77 

or  T  cot  \  I'. 

A  curve  ends  in  VB;  required  to  end 
in  V'B.     Fig.  16.     D  and  A  change. 

7?'       p  vers  7 

"*»     •*  1C  77 

vers  / ' 

yl^4  =  (R  sin  7  —  R'  sin  /')  and  ^4  is  moved  forward  or  back  accord- 
ing as  /'  is  greater  or  less  than  /. 

A  curve  ends  in  VB;  required  to  end  in  V'B'.     Fig.  17. 

i.   Assume  new  R'  <  R  according  as  B'  is  inside  or  outside   VB. 
Then 

K  K 


cos  a  =  I  — 


R-R' 


or     i  — 


R'  -R 


n  stations  =  -= 


Begin  at  n  stations  from  B  and  run  in  curve  of  D'  for  n'  stations  = 


!&».-.. 


FIG.  1  6. 


FIG.  17. 


2.   Or,  retaining  A  and  letting  n  be  total  number  of  stations  A  to  5, 

K 


D' 


approx. 


8 


RAILROAD  FIELD   MANUAL 


D'  will  be  greater  or  less  than  D  according  as  V'B'  lies  inside  or  outside 
of  VB.     Take  D'  nearest  round  number  that  will  be  sufficiently  exact 

and  run  the  curve  Dr  for  n'  stations  =  ~-,  • 

3.    Or,  assuming  a  new  degree  less  or  greater  than  the  original  accord- 
ing as  the  tangent  is  to  be  thrown  out  or  in,  find  n  of  Method  I  by 


t/ 
V 


V  7  (£>-£')' 

(D  —  D')  is  to  be  taken  as  the  difference  of  degrees,  subtracting  the 
smaller  from  the  larger,  a  =  nD,  «'  =  — ,  to  make  the  tangents  par- 
allel. Run  curve  of  degree  D'  from  C.C. 


FIG.  1 8. 


FIG.  19. 


COMPOUND  CURVES 

Given  RI,  R2,  AI,  and  A2;  required  7\  and  T2.     Fig.  18. 

FiF2  =  /i+*2. 
Solve  triangle  FFiF2  for  FiFand  F2F. 


Given  I,  7i,  T2,  and  RI;  required  R2,  AI,  and  A2.     Fig.  19. 
T2  -f  Ti  cos  /  -  Ri  sin  7 


cot  \  A2 


TI  sin  /  —  RI  vers  / 
/-A2, 

TI  sin  I  —  R2  vers  I 
vers  A2 


(a) 


SIMPLE,   COMPOUND,  AND  VERTICAL   CURVES 

Given  I,  7i,  T2,  and  Rz;  required  RI,  AI,  and  A2. 

RZ  sin  I  —  T\  —  Ti  cos  / 


l          *2  vers  7-T2  sin/ 
A2  =  I  -  Ai, 


C0t 


Rl  =  Rt  _  l^J^  !ili_i.  (b) 

vers  AI 

Given  7,  7\,  J?i,  and  AI;  required  A2,  JR2,  awJ  J"2. 

A2  =  7  —  AI. 
Rz  is  given  by  equation  (a)  above. 

7"2  =  (Rz  —  RI)  sin  A2  +  RI  sin  7  —  T\  cos  7. 
Given  7i,  7"2,  .R2,  and  A2;  required  AI,  7?i,  awd  7\. 

AI  =  7  —  A2. 
/?  is  given  by  equation  (b)  above. 

TI  =  Rz  sin  7  —  TZ  cos  I  —  (R2  —  RI)  sin  AI. 

To  end  a  compound  curve  in  a  new  tangent,  parallel  to  that  first  located. 

(a)  Move  the  curve  parallel  to  itself  along 

the  first  tangent,  a  distance  A  A'  =  ~. — j- 

(b)  Retaining  the  first  branch,  changing 
only  the  degree  of  the  second, 

K 
vers  A2 ' 

RI'  =  RI  ± — » 

vers  A! 

according  as  the  curve  ends  with  the  larger 
or  shorter  radius. 

(c)  Retaining  both  degrees,  changing  the  A's  and  the  station  of  CC. 
If  the  new  tangent  is  inside  and  the  longer  radius  ends  the  curve  the 
CC  is  advanced;   if  the  new  tangent  is  outside  the  CC  is  moved  back; 
if  the  shorter  radius  ends  the  curve  the  movement  of  the  CC  is  reversed. 
The  new  values  for  the  final  As  are  had  from 

vers  A2'  =  vers  A2  ±  -p ^~ ' 

vers  AI'  =  vers  AI  ±  -5 5-  • 


IO 


RAILROAD   FIELD   MANUAL 


To  change  the  direction  of  the  final  tangent  by  a  given  amount. 
Solve  the  triangle  VV'C  for  the  new  final  tangent  and  the  change  in  the 
initial  tangent.  The  new  /  being  known,  retain  the  first  radius  and 

solve  for  the  new  final  radius  and 
the  two  central  angles,  by  preced- 
ing equations. 

VERTICAL  CURVES 

The  rate  of  change  of  grade  in 
passing  sags  and  summits  in  the 
grade  line,  as  recommended  by 
the  American  Railway  Engineer- 
ing Association,  is:  For  first-class 
railways  change  not  more  than  o.i 
foot  per  station  on  summits  and 
not  more  than  0.05  foot  per  station 
in  sags;  for  second-class  roads  not 
more  than  double  these  rates. 

How  to  determine  the  elevation  of  the  several  stations  on  the  vertical 
curve  will  be  shown  by  two  examples.  The  first  step  is  to  determine  the 
length  of  the  curve;  it  will  be  convenient  to  adopt  a  rate  of  change 
that  will  give  an  even  number  of  stations  for  the  length. 

Example  I.  Two  grades,  —0.8  and  +0.6,  meet  at  station  462  where 
the  elevation  is  723.  Required  a  vertical  curve  to  connect  with  a 
change  of  o.i  per  station.  The  total  change  in  rate  is  0.8  +  0.6  =  1.4, 
giving  14  stations  =1.4  -5-  o.i,  of  curve,  or  7  stations  each  side  of  the 
vertex.  The  beginning  of  the  curve  is  therefore  at  sta.  462  —  7  =  455 
and  the  end  is  at  455  +  14  =  469.  The  elevation  of  455  is  723.0  + 
7  X  0.8  =728.6;  the  elevation  of  sta.  469  is  723.0  +  7  X  0.6  =  727.2. 
The  rate  of  change  for  the  first  station  is  taken  at  half  the  station 
rate  of  change  or  0.05.  Therefore  the  elevation  of 


FIG.  21. 


sta.  456  =  728.6 

457  ==  elev.  456  - 

458  =  elev.  457  - 

459  =  elev.  458  - 

460  =  elev.  459  — 

461  =  elev.  460  — 

462  =  elev.  461  — 

463  =  elev.  462  — 

464  =  elev.  463  — 


-  (0.8  -  0.05) 

(0.8  -  0.15)  = 

(0.8  -  0.25)  = 

(0.8  -  0.35)  = 

(0.8  -  0.45)  = 

(0.8  -  0.55)  = 

(0.8  -  0.65)  = 

(0.8  -  0.75)  = 

(0.8  -  0.85)  = 


=  728.6  - 

727.85  - 
727.20  - 
726.65  — 
726.20  — 

725.85  - 
725.60  - 

72545  - 
725.40  + 


•  0.75  =  727.85 
0.65  =  727.20 
0-55  =  726.65 
0.45  =  726.20 

0-35  =  725.85 
0.25  =  725.60 
0.15  =  725.45 
0.05  =  72540 
0.05  =  72545 


SIMPLE,   COMPOUND,  AND   VERTICAL   CURVES         II 

465  =  elev.  464  -  (0.8  -  0.95)  =  72545  +  0.15  =  725.60 

466  =  elev.  465  -  (0.8  -  1.05)  =  725.60  +  0.25  =  725.85 

467  =  elev.  466  -  (0.8  -  1.15)  =  725.85  +  0.35  =  726.20 

468  =  elev.  467  —  (0.8  —  1.25)  =  726.20  +  0.45  =  726.65 

469  =  elev.  468  —  (0.8  —  1.35)  =  726.65  +  0.55  =  727.20 

It  will  be  noticed  that  the  final  elevation  agrees  with  that  computed 
above;  this  proves  the  work.  It  will  also  be  noticed  that  after  the 
bottom  of  the  sag  is  passed  the  elevations  repeat  themselves  in  reverse 
order.  The  bottom  of  the  sag  is  not  always  the  same  station  as  the 
apex.  This  depends  on  the  relative  rates  of  the  grades. 

Example  2.  —  Two  grades,  —0.2  and  —  i.o,  meet  at  station  867.0, 
where  the  elevation  is  466.0.  To  connect  the  grades  with  a  vertical 
curve  changing  at  the  rate  of  o.i  per  station.  Total  change  in  rate 
0.8.  Length  of  curve  8  stations.  Beginning  of  curve  sta.  867  —  4  = 
863;  end  =  sta.  871. 

Elev.  sta.  863  =  466  +  4  X  0.2  =  466.8 
Elev.  sta.  871  =  466  —  4  X  i.o  =  462.0 

Elev.  sta.  864  =  elev.  863  —  (0.2  +  0.05)  =  466.8  —  0.25  =  466.55 
Elev.  sta.  865  =  elev.  864  —  (0.2  +0.15)  =  466.55  —  0.35  =  466.20 
Elev.  sta.  866  =  elev.  865  —  (0.2  +  0.25)  =  466.20  —  0.45  =  465.75 
Elev.  sta.  867  =  elev.  866  —  (0.2  +  0.35)  =  465.75  —  0.55  =  465.20 
Elev.  sta.  868  =  elev.  867  —  (0.2  +  0.45)  =  465.20  —  0.65  =  464.55 
Elev.  sta.  869  =  elev.  868  —  (0.2  +  0.55)  =  464.55  —  0.75  =  463.80 
Elev.  sta.  870  =  elev.  869  —  (0.2  +  0.65)  =  463.80  —  0.85  =  462.95 
Elev.  sta.  871  =  elev.  870  —  (0.2  +  0.75)  =  462.95  —  0.95  =  462.00 
The  work  is  proved  since  462.0  is  the  elevation  first  found  for  station 

871.     There  is  no  summit  or  bottom  in  this  case  as  both  grades  are  of 

the  same  sign. 


TABLE  I 

Radii  and  their  logarithms,  and  tangent  offsets,-  and  middle  ordinates,  for 
IOO  feet  chords  of  curves  of  degrees  given.  The  degrees  are  given  in  de- 
grees and  decimals  of  a  degree. 


Deg. 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

Deg. 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 

t 

Mid. 
Ord. 
m 

0 

0 

0.00 

00 

00 

.000 

.000 

1.  00 

5729-65 

3-75813 

.873 

.218 

.02 

286478.90 

5.45709 

.017 

.004 

.02 

5617-31 

-74953 

.890 

-223 

.04 

143239.45 

.15606 

.035 

.009 

.04 

5509-29 

.74110 

.908 

.227 

.06 

95492.97 

4-97997 

.052 

.013 

.06 

5405-34 

-73283 

•925 

•  231 

.08 

71619.73 

•85503 

.070 

.017 

.08 

5305.24 

.72471 

•942 

•  236 

.IO 

57295.79 

4-75812 

.087 

.022 

.IO 

5208.79 

3.71674 

.960 

.240 

.12 

47746.49 

.67894 

.105 

.026 

.12 

5115-78 

.70891 

•977 

•244 

.14 

40925.57 

.61199 

.122 

.031 

.14 

5026.03 

.70122 

•995 

.248 

.16 

35809.87 

•55400 

.140 

•035 

.16 

4939-38 

•69367 

I.OI2 

•253 

.18 

31831.00 

.50285 

•157 

.039 

.18 

4855.66 

.68625 

•030 

-257 

.20 

28647.90 

4-45709 

•175 

.044 

.20 

4774-74 

3-67895 

1.047 

.262 

.22 

26043.55 

.41570 

.192 

.048 

.22 

4696.46 

.67177 

-06S 

.266 

.24 

23873.26 

•37791 

.209 

.052 

.24 

4620.72 

.66471 

.082 

.271 

.26 

22036.86 

•34315 

.227 

•057 

.26 

4547.38 

.65776 

.100 

-275 

.28 

20462.80 

•31097 

•244 

.061 

.28 

4476.33 

•65092 

.117 

.279 

•30 

19098.61 

4.28100 

.262 

.065 

•30 

4407.46 

3.64419 

I-I34 

.284 

•32 

17904.95 

.25297 

.279 

.070 

•32 

4340.69 

.63756 

.152 

.288 

•34 

16851.73 

.22664 

•297 

•074 

•34 

4275-90 

•63103 

.169 

.292 

.36 

I59I5-52 

.20182 

•314 

.079 

.36 

4213.02 

•62459 

.187 

.297 

•38 

15077.86 

•17834 

•332 

•083 

•38 

4I5I-97 

.61825 

.204 

•301 

.40 

14323.97 

4.15606 

•349 

.087 

.40 

4092.66 

3.61201 

1.222 

•305 

.42 

13641.88 

•13487 

.367 

.092 

.42 

4035-02 

•60585 

•239 

•310 

•44 

13021.80 

.11467 

•384 

.096 

•44 

3978.98 

•59977 

•257 

•314 

.46 

12455-64 

•09537 

.401 

.100 

.46 

3924.47 

•59378 

.274 

•319 

.48 

11936.66 

.07688 

.419 

.105 

.48 

3871.44 

•58787 

.292 

•323 

•SO 

11459.19 

4.05915 

•436 

.109 

•50 

3819-83 

3.58204 

1.309 

•327 

•52 

11018.46 

.04212 

•454 

•113 

•52 

3769.57 

.57629 

.326 

•332 

•54 

10610.37 

•02573 

.471 

.118 

•54 

3720.62 

.57o6i 

•344 

.336 

•56 

10231.43 

.00994 

.489 

.122 

•56 

3672.92 

.56501 

•361 

•340 

.58 

9878.62 

3-99470 

.506 

.127 

•58 

3626.43 

•55948 

•379 

•345 

.60 

9549-34 

3-97997 

•524 

.131 

.60 

3581.10 

3-55402 

1.396 

•349 

.62 

9241-30 

•96573 

•541 

•135 

.62 

3536.89 

.54862 

.414 

•353 

.64 

8952.51 

•95194 

•559 

.140 

.64 

3493.76 

•54329 

•431 

•358 

.66 

8681.26 

•93858 

•576 

.144 

.66 

345I.67 

•53803 

•449 

•362 

.68 

8425.90 

.92562 

•593 

.I48 

.68 

3410.59 

•53283 

.466 

-367 

•70 

8185.16 

3-91303 

.611 

•153 

.70 

3370.46 

3-52769 

1.483 

•371 

•72 

7957.8o 

.90079 

.628 

•157 

•72 

333L28 

.52261 

•501 

•375 

•74 

7742.73 

.88889 

.646 

.l6l 

•74 

3292-99 

•51759 

.518 

-380 

•76 

7539-97 

-8773I 

•663 

.166 

•76 

3255-57 

.51263 

.536 

-384 

•78 

7345.67 

.86603 

.681 

.170 

•78 

3218.99 

.50772 

•553 

-388 

.80 

7162.03 

3-85504 

.698 

•175 

.80 

3183.23 

3.50287 

I-57I 

•393 

.82 

6987-35 

.84431 

.716 

.179 

.82 

3148.25 

.49807 

.588 

•397 

•84 

6820.99 

.83385 

•733 

•  I83 

-84 

3114-03 

•49332 

.606 

.401 

.86 

6662.36 

.82363 

•750 

.188 

.86 

3080.55 

.48863 

.623 

.406 

.88 

6510.95 

.81364 

.768 

.192 

.88 

3047-V8 

.48398 

.641 

.410 

.90 

6366.26 

3-80388 

.785 

.196 

.90 

3015-71 

3-47939 

1.658 

•415 

.92 

6227.87 

•79434 

.803 

.2OI 

.92 

2984.29 

.47484 

.675 

.419 

•94 

6095.36 

•78500 

.820 

.205 

•94 

2953-53 

-47034 

.693 

•423 

.96 

5968.38 

.77586 

.838 

.209 

.96 

2923.40 

.46589 

.710 

.428 

.98 

5846.58 

.76690 

.855 

.214 

.98 

2893-87 

.46148 

.728 

•432 

1.  00 

5729.65 

3-758i3 

.873 

.218 

2.OO 

2864.93 

3-457II 

1-745 

.436 

(12) 


TABLE   I.  — (Continued] 


Deg. 
0 

Radius 
R 

Logarithm 

LogR 

Tan. 
Off.' 

t 

Mid. 
Ord. 
m 

Deg. 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 

t 

Mid. 
Ord. 
m 

0 

o 

2.OO 

2864.93 

3-457" 

1-745 

•436 

3.00 

1910.08 

3.28105 

2.618 

.655 

.02 

2836.57 

•45279 

•763 

.441 

.02 

1897.43 

.27817 

•635 

•659 

.04 

2808.76 

•44852 

.780 

•445 

•04 

1884.95 

•27530 

•653 

•663 

.06 

2781.50 

.44428 

.798 

•449 

.06 

1872.63 

.27245 

.670 

.668 

.08 

2754.76 

.44008 

.815 

•454 

.08 

1860.48 

.26962 

.687 

.672 

.10 

2728.52 

3-43593 

1.832 

•458 

.10 

1848.48 

3.26681 

2.705 

.676 

.12 

2702.79 

•43181 

.850 

•463 

.12 

1836.63 

.26402 

.722 

.681 

.14 

2677-53 

•42773 

.867 

•467 

.14 

1824.93 

.26125 

•740 

.685 

.16 

2652.74 

•42369 

•885 

.471 

.16 

1813-39 

•25849 

•757 

.689 

.18 

2628.40 

.41969 

.902 

•476 

.18 

1801.99 

•25575 

•775 

•694 

.20 

2604.51 

3-4I573 

1.920 

.480 

.20 

1790.73 

3-25303 

2.792 

.698 

.22 

2581.05 

.41180 

•937 

•484 

.22 

1779-61 

•25032 

.810 

.702 

.24 

2558.01 

.40790 

•955 

.489 

.24 

1768.62 

.24764 

.827 

.707 

.26 

2535-38 

.40404 

.972 

•493 

.26 

1757-78 

.24496 

•845 

.711 

.28 

2513-14 

.40022 

•990 

•497 

.28 

1747-06 

•24231 

.862 

.716 

•30 

2491.29 

3-39642 

2.007 

•502 

•30 

1736.48 

3-23967 

2.879 

.720 

•32 

2469.81 

.39266 

.024 

•506 

•32 

1726.02 

•23705 

•897 

•724 

•34 

2448.71 

•38894 

.042 

•5ii 

•34 

1715-69 

•23444 

.914 

.729 

•36 

2427.96 

•38524 

•059 

•515 

•36 

1705.48 

•23185 

•932 

•733 

•38 

2407.56 

•38158 

•077 

•519 

•38 

1695-39 

.22927 

•949 

•737 

.40 

2387-50 

3-37794 

2.094 

•524 

.40 

1685.42 

3.22671 

2.967 

.742 

.42 

2367.77 

•37434 

.112 

•528 

.42 

1675.56 

.22416 

•984 

.746 

•44 

2348.36 

•37077 

.129 

•532 

•44 

1665.83 

.22163 

3.002 

•751 

.46 

2329.28 

.36722 

.147 

•537 

.46 

1656.19 

.21911 

.019 

•755 

.48 

2310.49 

•36370 

.164 

•541 

.48 

1646.68 

.21661 

•036 

•759 

•SO 

2292.01 

3-36022 

2.181 

•545 

•50 

1637.28 

3-21412 

3-054 

•764 

•52 

2273.83 

.35676 

.199 

•550 

•52 

1627.98 

.21165 

.071 

.768 

•54 

2255.92 

•35332 

.216 

•554 

•54 

1618.78 

.20919 

.089 

.772 

•56 

2238.30 

.34992 

•234 

•559 

•56 

1609.69 

.20674 

.106 

•777 

•58 

2220.95 

•34654 

.251 

•563 

.58 

1600.70 

.20431 

.124 

.781 

.60 

2203.87 

3.343I9 

2.269 

.567 

.60 

1591.81 

3.20189 

3-I4I 

.785 

.62 

2187.05 

.33986 

.286 

•572 

.62 

1583.02 

.19949 

•159 

.790 

.64 

2170.49 

.33656 

.304 

•576 

.64 

1574-32 

.19709 

.176 

•794 

.66 

2154.17 

.33328 

.321 

•580 

.66 

1565.72 

.19472 

•193 

•799 

.68 

2138.10 

•33003 

•339 

.585 

.68 

1557-22 

•19235 

.211 

.803 

.70 

2122.26 

3-32681 

2.356 

•589 

•70 

1548.80 

3.19000 

3-228 

.807 

•72 

2106.66 

•32359 

•373 

•593 

.72 

1540.48 

.18766 

.246 

.812 

•74 

2091.29 

•32041 

•391 

.598 

•74 

1532.24 

•18533 

•  263 

.816 

•76 

2076.13 

.31726 

.408 

.602 

•76 

1524.10 

.18301 

.281 

.820 

•78 

2061.20 

•31412 

.426 

.607 

•78 

1516.14 

.18071 

.298 

.825 

.80 

2046.48 

3-3IIOI 

2-443 

.611 

.80 

1508.06 

3-17842 

3.316 

.829 

.82 

2031.97 

.30792 

.460 

•615 

.82 

1500.17 

.17614 

•333 

•833 

.84 

2017.66 

•30485 

•478 

.620 

.84 

1492.36 

.17387 

•351 

•838 

.86 

2003.56 

.30180 

.496 

.624 

.86 

1484.63 

.17162 

•368 

.842 

.88 

1989-65 

.29878 

•513 

.628 

.88 

1476.98 

.16937 

•385 

.847 

.90 

1975-93 

3-29577 

2-530 

•633 

.90 

1469.41 

3.16714 

3-403 

•851 

.92 

1962.40 

.29279 

•548 

•637 

•92 

1461.91 

.16492 

.420 

•855 

•94 

1949.05 

.28982 

.565 

.641 

•94 

1454-49 

.16271 

•438 

.860 

.96 

1935-88 

.28688 

.583 

.646 

.96 

1447-15 

.16051 

•455 

.864 

.98 

1922.89 

.28396 

.600 

•650 

.98 

1439-88 

•15833 

•473 

.868 

3-oo 

1910.08 

3.28105 

2.618 

•655 

4-00 

1432.69 

3-15615 

3-490 

•873 

(13) 


TABLE   I.  — (Continued) 


Deg. 
0 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

Deg. 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

0 

o 

4-00 

1432.69 

3-15615 

3-490 

.873 

5.00 

1146.28 

3-05929 

4.362 

1.091 

.02 

1425-56 

•15399 

•507 

.877 

.02 

1141.72 

-05756 

•379 

•095 

.04 

1418.51 

.15183 

•525 

.881 

•04 

1137-19 

•05583 

•397 

.100 

.06 

1411-52 

.14969 

.542 

.886 

.06 

1132.70 

•05411 

.414 

.104 

.08 

1404.60 

•14755 

.560 

.890 

.08 

1128.24 

.05240 

.432 

.108 

.10 

1397.76 

3-14543 

3.577 

.895 

.10 

1123.82 

3-05070 

4-449 

1.113 

.12 

1390.98 

•14332 

•595 

.899 

.12 

1119.43 

.04900 

•467 

.117 

.14 

1384.26 

.14122 

.612 

.903 

•14 

1115.08 

•04731 

•484 

.122 

.16 

1377.61 

•13912 

.629 

.908 

.16 

IIII.OO 

•04571 

.501 

.126 

.18 

1371-02 

•13704 

•647 

.912 

.18 

1106.47 

•04394 

.519 

.130 

.20 

1364.49 

3-13497 

3-664 

.916 

.20 

IIO2.22 

3-04227 

4.536 

I-I35 

.22 

1358.03 

.13291 

.682 

.921 

.22 

1098.00 

.04060 

•554 

•139 

.24 

1351-31 

.13076 

•699 

•925 

.24 

1093.81 

.03894 

•571 

•143 

.26 

1345-28 

.12881 

.717 

.929 

.26 

1089.66 

.03729 

•589 

.I48 

.28 

1339-00 

.12678 

•734 

•934 

.28 

1085.53 

•03564 

.606 

.152 

•30 

1332.77 

3.12476 

3-752 

.938 

•30 

1081.44 

3.03400 

4-623 

I.I56 

•32 

1326.61 

.12274 

•769 

•943 

•32 

1077.38 

•03237 

.641 

.l6l 

•34 

1320.49 

.12074 

.786 

•947 

•34 

1073-34 

•03074 

.658 

.165 

.36 

1314.44 

.11874 

.804 

•951 

.36 

1069.34 

.02912 

.676 

.170 

•38 

1308.44 

.11675 

.821 

•956 

.38 

1065.37 

.02750 

•693 

.174 

.40 

1302.50 

3.11478 

3.839 

.960 

.40 

1061.43 

3-02589 

4-7II 

I.I78 

•42 

1296.61 

.11281 

.856 

.964 

.42 

1057.51 

.02429 

.728 

.183 

•44 

1290.77 

.11085 

•874 

.969 

•44 

1053.63 

.02269 

•746 

.I87 

•46 

1284.98 

.10890 

.891 

•973 

.46 

1049.77 

.02109 

•763 

.191 

.48 

1279.25 

.10696 

.909 

.978 

.48 

1045.94 

.01951 

.780 

.196 

•So 

1273-57 

3.10502 

3-926 

.982 

•50 

1042.14 

3-01793 

4.798 

I.2OO 

•52 

1267.93 

.10310 

•943 

.986 

•52 

1038.37 

.01635 

.815 

.205 

•54 

1262.35 

.10118 

.961 

.991 

•54 

1034.62 

.01478 

•833 

.209 

•56 

1256.82 

.09927 

.978 

•995 

•56 

1030.90 

.01322 

.850 

.213 

•58 

1251.33 

•09737 

•996 

•999 

•58 

1027.21 

.01166 

.868 

.218 

.60 

1245.89 

3-09548 

4.013 

1.004 

.60 

1023.55 

3.01011 

4-885 

1.222 

.62 

1240.50 

.09360 

.031 

.008 

.62 

1019.91 

.00856 

.902 

.226 

.64 

1235.16 

.09172 

.048 

.012 

.64 

IOl6.29 

.00702 

.920 

.231 

.66 

1229.86 

.08986 

.065 

.017 

.66 

IOI2.7O 

.00548 

-937 

•235 

.68 

1224.61 

.08800 

.083 

.021 

.68 

1009.14 

•00395 

•955 

-239 

•70 

1219.40 

3-08615 

4.100 

1.026 

•70 

1005.60 

3.00243 

4-972 

1.244 

•72 

1214.24 

.08430 

.118 

.030 

•72 

1002.09 

.00091 

.990 

.248 

•74 

1209.12 

.08247 

•135 

•034 

•74 

998.60 

2-99939 

5.007 

.253 

•76 

1204.04 

.08064 

.153 

•039 

•76 

995-14 

.99788 

.024 

•257 

•78 

1199.00 

.07882 

.170 

•043 

•78 

991.68 

.99638 

.042 

.261 

.80 

1194.01 

3-07701 

4.188 

1.047 

.80 

988.28 

2.99488 

5-059 

1.266 

.82 

1189.06 

.07520 

.205 

.052 

.82 

984.89 

•99339 

•077 

.270 

.84 

1184.15 

•07341 

.222 

.056 

.84 

981.52 

.99190 

.094 

•  274 

.86 

1179.28 

.07162 

.240 

.060 

.86 

978.17 

.99041 

.112 

.279 

.88 

1174-45 

.06983 

•257 

.065 

.88 

974.66 

.98885 

.129 

.283 

.90 

1169.66 

3.06806 

4-275 

1.069 

.90 

971-54 

2.98746 

5.146 

1.287 

.92 

1164.91 

.06629 

.292 

.074 

.92 

968.26 

.98599 

.164 

.292 

94 

1160.19 

•06453 

•310 

.078 

•94 

965.01 

.98453 

.I8l 

.296 

.96 

1155-52 

.06278 

•327 

.082 

.96 

961.77 

.98307 

.199 

.301 

•98 

1150.88 

.06103 

•345 

.087 

.98 

958.56 

.98162 

.216 

•305 

S.oo 

1146.28 

3-05929 

4-362 

I.09I 

6.00 

955-37 

2.98017 

5.234 

1.309 

(14) 


TABLE  I.  — (Continued} 


Deg. 
D 

Radius 
.R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

Deg. 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

o 

o 

6.00 

955-37 

2.98017 

5-234 

1.309 

7.00 

819.02 

2.91329 

6.105 

1.528 

.02 

952.20 

•97873 

•251 

•314 

.02 

816.69 

.91206 

.122 

•532 

.04 

949-05 

•97729 

.268 

•318 

.04 

814-37 

.91082 

.140 

•536 

.06 

945-92 

•97585 

.286 

•322 

.06 

812.07 

.90959 

•157 

•541 

.08 

942.81 

•97442 

•303 

•327 

.08 

809.78 

•90837 

•175 

•545 

.10 

939-72 

2.97300 

5-321 

1-331 

.10 

807.50 

2.90714 

6.192 

1-550 

.12 

936.65 

•97158 

.338 

•335 

.12 

805.23 

.90592 

.209 

•554 

.14 

933-60 

.97016 

-356 

-340 

•14 

802.98 

.90471 

.227 

•558 

.16 

930-57 

-96875 

•373 

-344 

.16 

800.74 

•90349 

•244 

-563 

.18 

927.58 

•96734 

•390 

-349 

.18 

798.51 

.90228 

.262 

.567 

.20 

924.58 

2.96594 

5-408 

1-353 

.20 

796.30 

2.90108 

6.279 

1-572 

.22 

921.61 

-96455 

.425 

•357 

.22 

794.10 

.89987 

.296 

•576 

.24 

918.66 

•96315 

•443 

•362 

•24 

791.90 

.89867 

•314 

•S8o 

.26 

915.72 

.96176 

.460 

•366 

.26 

789-73 

.89748 

•331 

•584 

.28 

912.81 

.96038 

.478 

•370 

.28 

787-56 

.89628 

•349 

•589 

•30 

909.92 

2.95900 

5-495 

1-375 

•30 

785.40 

2.89509 

6.366 

1-593 

•32 

906.48 

•95736 

•512 

•379 

•32 

783-26 

.89391 

.384 

-598 

•34 

904.18 

•95625 

•530 

.384 

•34 

781.13 

.89272 

.401 

.602 

.36 

901.34 

.95489 

•547 

-389 

.36 

779-01 

.89154 

.418 

.606 

.38 

898.52 

•95353 

.565 

•392 

•38 

776-90 

.436 

.611 

.40 

895.7I 

2.95217 

5-582 

1-397 

.40 

774-81 

2.88919 

6-453 

1.615 

.42 

892.92 

.95081 

.600 

.401 

.42 

772.72 

.88802 

.471 

.619 

•44 

890.15 

•94947 

.617 

•405 

•44 

770.65 

.88685 

.488 

.624 

•46 

887.40 

.94812 

•634 

.410 

.46 

768.58 

.88569 

•SOS 

.628 

•48 

884.67 

.94678 

•652 

.414 

.48 

766.53 

.88453 

.523 

-632 

•50 

881.95 

2-94544 

5-669 

1.418 

.50 

764.49 

2-88337 

6.540 

1-637 

•52 

879.24 

.94411 

.687 

.423 

•52 

762.46 

.88222 

.558 

.641 

•54 

876.56 

.94278 

.704 

.427 

.54 

760.44 

.88106 

•575 

.646 

•56 

873-89 

.94146 

.722 

•432 

.56 

758.45 

•87993 

•593 

.650 

•58 

871.24 

.94014 

•739 

•436 

.58 

756.43 

.87877 

.610 

-654 

.60 

868.60 

2.93882 

5.756 

1.440 

.60 

754-44 

2.87763 

6.627 

1.659 

.62 

865.98 

•93751 

•774 

•445 

.62 

752-47 

.87649 

•645 

.663 

.64 

863.37 

.93620 

.791 

•449 

.64 

750.50 

•87535 

.662 

.667 

.66 

860.78 

.93489 

.809 

•453 

.66 

748.54 

.87422 

.680 

.672 

.68 

858.21 

•93359 

.826 

-458 

.68 

746.60 

.87309 

.697 

.676 

•70 

855.65 

2.93230 

5.844 

1.462 

•70 

744.66 

2.87196 

6.714 

i.  680 

•72 

853-10 

•93100 

.861 

.466 

.72 

742-74 

.87083 

•732 

.685 

•74 

850.58 

.92971 

.878 

.471 

-74 

740.82 

.86971 

•749 

.689 

.76 

848.06 

•92843 

.896 

•475 

.76 

738.91 

.86859 

.767 

.694 

•78 

845-56 

•92715 

•913 

.480 

•78 

737.02 

.86748 

•784 

.698 

.80 

843.08 

2.92587 

5-931 

1.484 

.80 

735-13 

2.86636 

6.802 

1.702 

.82 

840.61 

.92459 

.948 

.488 

.82 

733-25 

.86525 

.819 

.707 

.84 

838.16 

.92332 

.965 

.493 

.84 

731.38 

.86415 

.836 

.711 

.86 

835.71 

.92206 

-983 

•497 

.86 

729.53 

.86304 

•854 

.715 

.88 

833-29 

.92080 

6.000 

1.501 

.88 

727.68 

.86194 

.871 

.720 

.90 

830.88 

2.91954 

6.018 

1-505 

.90 

725-85 

2.86084 

6.889 

1.724 

.92 

828.48 

.91828 

•035 

.510 

.92 

724.01 

.85974 

.906 

•729 

.94 

826.09 

-91703 

•053 

.515 

.94 

722.19 

.85865 

•923 

-733 

.96 

823.72 

.91578 

.070 

•519 

.96 

720.38 

.85756 

.941 

•737 

.98 

821.36 

-91454 

.087 

•523 

.98 

7i8.57 

.85647 

•958 

•742 

7.00 

819.02 

2.91329 

6.105 

1.528 

8.00 

716.78 

2.85539 

6.976 

1.746 

(15) 


TABLE  I.  — (Continued} 


Deg. 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

Deg. 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

0 

o 

8.00 

716.78 

2.85539 

6.976 

1.746 

9.00 

637-27 

2.80433 

7.846 

1.965 

.02 

714.99 

•85430 

•993 

•750 

.02 

635-86 

.80336 

•863 

•969 

.04 

713-22 

-85322 

7.010 

•755 

.04 

634-46 

.80240 

.881 

•973 

.06 

7H-45 

.85215 

.028 

•759 

.06 

633-06 

.80145 

.898 

•978 

.08 

709.69 

.85107 

•045 

-764 

.08 

631-67 

.80049 

.916 

.982 

.10 

707.94 

2.85000 

7-063 

1.768 

.10 

630.29 

2-79954 

7-933 

1.987 

.12 

706.20 

.84893 

.080 

•772 

.12 

628.91 

.79859 

•950 

.991 

.14 

704.47 

.84786 

.098 

•777 

.14 

627.53 

•79764 

.968 

•995 

.16 

702.75 

.84680 

•"5 

.781 

.16 

626.17 

.79669 

-985 

•999 

.18 

701-03 

.84574 

•  132 

.785 

.18 

624.81 

•79574 

8.002 

2.004 

.20 

699-33 

2.84468 

7.I50 

1.790 

.20 

623.45 

2.79480 

8.020 

2.008 

.22 

697-63 

.84362 

.167 

•794 

.22 

622.10 

.79386 

•037 

.013 

.24 

695.94 

.84257 

•  185 

•798 

-24 

620.76 

.79292 

.055 

.017 

.26 

694-25 

.84152 

.202 

•803 

.26 

619.42 

.79198 

.072 

.021 

.28 

692.58 

.84047 

.219 

.807 

.28 

618.09 

•79105 

.090 

.026 

•30 

690.91 

2.83942 

7-237 

1.811 

•30 

616.76 

2.79012 

8.107 

2.030 

•32 

689.26 

.83838 

•254 

.816 

.32 

615.44 

.78919 

.124 

•034 

•34 

687.61 

•83734 

.272 

.820 

•34 

614.12 

.78826 

.142 

•039 

•36 

685.96 

.83630 

.289 

•825 

•36 

612.82 

.78733 

.159 

•043 

.38 

684.33 

•83527 

-306 

.829 

•38 

611.51 

.78640 

.176 

.048 

.40 

682.70 

2.83423 

7-324 

1-833 

•40 

610.21 

2.78548 

8.194 

2.052 

.42 

681.09 

.83320 

•341 

•838 

•42 

608.92 

.78456 

.211 

.056 

•44 

679.47 

•83217 

•359 

.842 

•44 

607.63 

•78364 

.229 

.O6l 

.46 

677-87 

•83115 

•376 

-847 

•46 

606.35 

.78272 

.246 

•065 

.48 

676.27 

.83012 

•393 

•851 

.48 

605.08 

.78181 

.263 

.069 

•50 

674-69 

2.82910 

7.411 

1-855 

•So 

603.80 

2.78090 

8.281 

2.074 

•52 

673-11 

.82808 

.428 

.860 

.52 

602.54 

•77999 

.298 

.078 

•54 

671-53 

.82707 

•446 

.864 

.54 

601.28 

.77908 

.316 

.083 

•56 

669.97 

.82605 

•463 

.868 

•56 

600.02 

.77817 

•333 

.087 

•58 

668.41 

.82504 

.480 

-873 

.58 

598.77 

.77726 

•350 

.091 

.60 

666.86 

2.82403 

7.498 

1.877 

.60 

597-53 

2.77636 

8.368 

2.096 

.62 

665.33 

.82303 

•515 

.881 

.62 

596.29 

•77546 

•385 

.IOO 

.64 

663.77 

.82202 

•533 

.886 

.64 

595-o6 

•77456 

•403 

.104 

.66 

662.24 

.82102 

•550 

.890 

.66 

593-83 

.77366 

.420 

.109 

.68 

660.72 

.82002 

-567 

-895 

.68 

592.60 

.77276 

•437 

•113 

.70 

659-21 

2.81902 

7.585 

1.899 

.70 

591-38 

2.77187 

8-455 

2.II7 

.72 

657.70 

.81803 

.602 

-903 

.72 

590.17 

.77098 

•472 

.121 

•74 

656.19 

-81703 

.620 

.908 

.74 

588.96 

.77009 

•490 

.126 

.76 

654.70 

.81604 

•637 

.912 

.76 

587-76 

.76920 

•507 

.131 

.78 

653-21 

.81505 

•655 

.916 

.78 

586.56 

.76831 

•524 

.135 

.80 

65I-73 

2.81407 

7.672 

1.921 

.80 

585-36 

2.76743 

8.542 

2.139 

.82 

650.25 

.81308 

.689 

•925 

.82 

584-17 

•76654 

•559 

.144 

.84 

648.79 

.81210 

.707 

•930 

.84 

582.99 

•76566 

•576 

.I48 

.86 

647.32 

.81112 

.724 

•934 

.86 

581.81 

-76478 

•594 

.152 

.88 

645.87 

.81014 

•742 

.938 

.88 

580.64 

•76390 

.611 

•157 

.90 

644.42 

2.80917 

7-759 

1-943 

.90 

579.46 

2.76303 

8.629 

2.161 

.92 

642.98 

.80820 

-776 

•947 

.92 

578.30 

.76215 

.646 

.166 

•94 

641.54 

.80723 

-794 

•951 

•94 

577-14 

.76128 

-663 

.170 

.96 

640.11 

.80626 

.811 

.956 

•96 

575-99 

.76041 

.681 

.174 

.98 

638.69 

.80529 

.829 

.960 

.98 

574-83 

•75954 

.698 

•179 

9,00 

637.27 

2.80433 

7.846 

1.965 

10.00 

573.69 

2.75867 

8.716 

2.183 

(16) 


TABLE  I.— (Continued) 


Deg. 
D 

Radius 
R 

Logarithm 

LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

Deg. 
D 

Radius 
R 

Logarithm) 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

o 

o 

IO.Q 

S73-69 

2.75867 

8.716 

2.183 

15.0 

383-06 

2-58327 

13-053 

3-277 

.1 

568.02 

.75436 

.803 

.205 

.1 

380.54 

.58040 

•139 

•299 

.2 

562.47 

.75010 

.889 

.227 

.2 

378.05 

•57755 

.226 

.321 

•3 

557-02 

.74587 

.976 

•234 

•3 

375.6o 

•57472 

.312 

•343 

.4 

551-68 

.74169 

9-063 

.270 

•4 

373.17 

.57191 

•399 

•365 

.5 

546.44 

2-73754 

9-150 

2.293 

.5 

370-78 

2.56912 

13-485 

3.387 

.6 

54L30 

•73344 

•  237 

•314 

.6 

368.42 

•56634 

•572 

•409 

.7 

536.25 

.72937 

.324 

.336 

.7 

366.09 

•56358 

.658 

•431 

.8 

53I-30 

•72534 

.411 

.358 

.8 

363-78 

.56084 

•744 

•452 

•9 

526.44 

•72135 

.498 

.380 

•9 

361.51 

•55812 

•831 

•474 

II.  0 

521.67 

2.71740 

9-585 

2.402 

16.0 

359-26 

2-55541 

I3.9I7 

3.496 

.1 

516.99 

.71348 

.671 

•423 

.1 

357-05 

•55273 

14.004 

•5i8 

.2 

512.38 

.70960 

•758 

•445 

.2 

354-86 

.55006 

.090 

•540 

•3 

507-86 

.70575 

.845 

.467 

-3 

352.70 

•54740 

.177 

.562 

.4 

503-42 

.70193 

•932 

.489 

•4 

350.56 

•54476 

•263 

•584 

•5 

499.06 

2.69815 

10.019 

2.511 

•S 

348.45 

2.54214 

14-349 

3.606 

.6 

494-77 

.69441 

.106 

•533 

.6 

346.37 

•53953 

.436 

.628 

•7 

490.56 

.69069 

.192 

•555 

•7 

344-31 

•53694 

•522 

•650 

.8 

486.42 

.68701 

•279 

•577 

.8 

342.27 

•53437 

.608 

.672 

•9 

482.34 

.68336 

.366 

.598 

•9 

340.26 

•53i8i 

.695 

•694 

12.0 

478.34 

2.67974 

10.453 

2.620 

17.0 

338-27 

2.52927 

14.781 

3.7i6 

.1 

474-40 

.67614 

•540 

.642 

.1 

336.31 

.52674 

.867 

•738 

.2 

470-53 

•67258 

.626 

.664 

.2 

334-37 

•52423 

•954 

.760 

•3 

466.72 

.66905 

•713 

.686 

•3 

332-45 

•52173 

15.040 

.781 

•4 

462.96 

•66555 

.800 

.708 

•4 

330.56 

•51924 

.126 

.803 

•5 

459-28 

2.66207 

10.887 

2.730 

•5 

328.69 

2.51677 

15.212 

3-825 

.6 

455-65 

.65863 

•973 

•752 

.6 

326.83 

•51432 

•299 

.847 

.7 

452.07 

.65521 

1  1  .060 

•774 

•7 

325.00 

.51188 

.385 

.869 

.8 

448.56 

.65182 

•147 

-795 

.8 

323.i8 

.50945 

.471 

.891 

•9 

445.09 

•64845 

.234 

.817 

•9 

321.39 

.50704 

•557 

•913 

13-0 

441.68 

2.64511 

11.320 

2.839 

18.0 

319-62 

2.50464 

15-643 

3-935 

.1 

438.33 

.64180 

.407 

.861 

.1 

317.87 

.50225 

•730 

•957 

.2 

435-02 

-63851 

•494 

.883 

.2 

316.14 

.49988 

.816 

•979 

•3 

43I-76 

•63525 

.580 

•90S 

•3 

3I4.43 

•49752 

.902 

4.001 

•4 

428.56 

.63201 

.667 

•927 

•4 

312.73 

•49517 

.988 

.023 

•5 

425-40 

2.62879 

H-754 

2-949 

•5 

311.06 

2.49284 

16.074 

4-045 

.6 

422.28 

.62560 

.840 

•971 

.6 

309-40 

.49052 

.160 

.067 

.7 

419.22 

.62244 

.927 

•992 

•7 

307.76 

.48821 

.246 

.089 

.8 

416.19 

.61929 

12.014 

3.014 

.8 

306.14 

.48591 

•333 

.in 

•9 

413-21 

.61617 

.100 

.036 

•9 

304.53 

•48363 

.419 

-133 

14.0 

410.28 

2.61308 

12.187 

3-058 

19.0 

302.94 

2.48136 

16.505 

4-155 

.1 

407.38 

.61000 

•274 

.080 

.1 

301.37 

.47910 

•591 

.177 

.2 

404.53 

.60695 

.360 

.102 

.2 

299.82 

.47686 

•677 

.199 

•3 

401.71 

•60391 

•447 

.124 

•3 

298.28 

.47462 

•763 

.221 

•4 

398.94 

.60090 

-533 

.146- 

•4 

296.75 

.47240 

.849 

•243 

•5 

396.20 

2.59791 

12.620 

3-i68 

•S 

295.25 

2.47019 

16.935 

4-265 

.6 

393-50 

•59495 

.706 

.190 

.6 

293.76 

•46799 

17.021 

.287 

•7 

390.84 

.59200 

•793 

.211 

•7 

292.28 

.46580 

.107 

.308 

.8 

388.21 

.58907 

.880 

•233 

.8 

290.82 

.46362 

•193 

•330 

•9 

385-62 

.58616 

.966 

•255 

•9 

289-37 

.46145 

•  279 

•352 

15.0 

383-06 

2.58327 

13-053 

3-277 

20.  o 

287.94 

2-45930 

17-365 

4-374 

(17) 


TABLE  I.  — (Continued) 


D3g. 

D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

Deg. 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 

t 

Mid. 
Ord. 
m 

o 

0 

20.0 

287.94 

2-45930 

17-365 

4-374 

25.0 

231.01 

2.36363 

21.644 

5-476 

.1 

286.52 

.457i6 

•451 

.396 

.1 

230.11 

.36193 

.729 

•498 

.2 

285.12 

•45502 

•537 

.418 

.2 

229.21 

.36023 

.814 

.520 

•3 

283.73 

.45290 

•623 

•440 

•3 

228.32 

•35854 

•899 

.542 

•4 

282.35 

•45079 

.708 

.462 

•4 

227.43 

-35685 

•985 

•564 

•5 

280.99 

2.44869 

17-794 

4.484 

•5 

226.55 

2.35517 

22.070 

5-586 

.6 

279.64 

.44660 

.880 

.506 

.6 

225.68 

•35350 

^SS 

.608 

•7 

278.30 

.44452 

.966 

.528 

•7 

224.82 

-35184 

.240 

.630 

.8 

276.98 

•44245 

18.052 

.550 

.8 

223.96 

.35018 

•325 

.653 

•9 

275.67 

.44039 

.138 

•572 

•9 

223.11 

-34853 

.410 

.675 

21.0 

274-37 

2.43834 

18.224 

4-594 

26.0 

222.27 

2.34688 

22.495 

5-697 

.1 

273-08 

•43630 

•309 

.616 

.1 

221.43 

•34524 

.580 

.719 

.2 

271.81 

•43427 

•395 

.638 

.2 

220.60 

.34361 

.665 

.741 

•3 

270.55 

.43225 

.481 

.660 

•3 

219.78 

•34199 

.750 

.763 

•4 

269.30 

.43024 

.567 

.682 

•4 

218.96 

•34037 

.835 

.785 

•5 

268.06 

2.42824 

18.652 

4.704 

•5 

218.15 

2.33875 

22.920 

5-807 

.6 

266.84 

.42624 

.738 

.726 

.6 

217-34 

•33715 

23-005 

.829 

•7 

265.62 

.42426 

.824 

-748 

•7 

216.54 

•33555 

.090 

.852 

.8 

264.42 

.42229 

.910 

•770 

.8 

215-75 

•33395 

•175 

.874 

•9 

263.22 

•42033 

•995 

.792 

•9 

214.96 

.33237 

.260 

.896 

22.0 

262.04 

2.41837 

19.081 

4.814 

27.0 

214.18 

2.33078 

23-345 

5.918 

.1 

260.87 

.41643 

.167 

.836 

.1 

213.41 

.32921 

.429 

.940 

.2 

259-71 

.41449 

.252 

.858 

.2 

212.64 

.32764 

•514 

.962 

.3 

258.56 

.41256 

.338 

.881 

•3 

211.87 

.32608 

•599 

•984 

•4 

257-42 

.41064 

•423 

•903 

•4 

211.  II 

•32452 

.684 

6.006 

.5 

256.29 

2.40873 

19.509 

4-925 

•5 

210.36 

2.32297 

23.769 

6.029 

.6 

255-17 

.40683 

•595 

•947 

.6 

209.6l 

.32142 

.853 

.051 

.7 

254-06 

.40494 

.680 

-969 

•7 

208.87 

.31988 

.938 

•073 

.8 

252.96 

.40306 

.766 

.991 

.8 

208.14 

•3i835 

24.023 

•095 

•9 

251.87 

.40118 

.851 

5-013 

•9 

207.40 

.31682 

.108 

.117 

23.0 

250.79 

2.39931 

19-937 

5-035 

28.0 

206.68 

2.31529 

24.192 

6.139 

.1 

249.72 

•39746 

20.022 

•057 

.1 

205.96 

•31378 

•277 

.161 

.2 

248.66 

•3956i 

.108 

.079 

.2 

205.24 

•31227 

.362 

.184 

•3 

247.61 

.39376 

•193 

.101 

•3 

204.53 

•31076 

•446 

.206 

•4 

246.56 

•39193 

•279 

•123 

•4 

203.83 

.30926 

•531 

.228 

.5 

245-53 

2.39010 

20.364 

5-145 

•5 

203.13 

2.30776 

24-615 

6.250 

.6 

244.50 

•38829 

.450 

.167 

.6 

202.43 

.30627 

.700 

.272 

.7 

243.49 

.38647 

•535 

.189 

•7 

201.74 

•30479 

.784 

•294. 

.8 

242.48 

•38467 

.620 

.211 

.8 

201.05 

•30331 

.869 

.316 

•9 

241.48 

.38288 

.706 

•233 

•9 

200.37 

.30184 

•954 

•339 

24.0 

240.49 

2.38109 

20.791 

5.255 

29.0 

199.70 

2.30037 

25-038 

6.361 

.1 

239-50 

.37931 

•877 

.278 

.1 

199.02 

.29891 

.122 

.383 

.2 

238.53 

•37754 

.962 

•299 

.2 

198.36 

-29745 

.207 

/•405 

•3 

237-56 

•37578 

21.047 

•  321 

•3 

197.70 

.29600 

.291 

•427 

•4 

236.60 

-37402 

.132 

•343 

•4 

197.04 

•29455 

.376 

•450 

•5 

235-65 

2.37227 

21.218 

5-366 

•5 

196.38 

2.29311 

25.460 

6.472 

.6 

234-71 

-37053 

•303 

.388 

.6 

195-74 

.29167 

•545 

•494 

.7 

233-77 

.36879 

.388 

.410 

.7 

195-09 

.29024 

.629 

.516 

.8 

232.84 

.36707 

•474 

.432 

.8 

194-45 

.28881 

•713 

-538 

•9 

231-92 

•36535 

•559 

-454 

•9 

193-82 

•28739 

.798 

-560 

25.0 

231.01 

2.36363 

21.644 

5.476 

30.0 

193.19 

2.28597 

25.882 

6.583 

(18) 


TABLE   I.  — (Concluded) 


Deg. 
D 

Radius 
R 

.ogarithm 
LogR 

Tan. 
Off. 

t 

Mid. 
Ord. 
m 

Deg, 
D 

Radius 
R 

Logarithm 
LogR 

Tan. 
Off. 
t 

Mid. 
Ord. 
m 

0 

0 

30.0 

193-19 

2.28597 

25.882 

6.583 

35.0 

166.28 

2.22083 

30.071 

7.696 

.1 

192.56 

.28456 

.966 

.605 

.1 

165.82 

.21963 

•154 

.718 

.2 

191.94 

.28315 

26.050 

.627 

.2 

165.36 

.21843 

•237 

.740 

•3 

191-32 

.28175 

•135 

•649 

•3 

164.91 

.21724 

.320 

.763 

•4 

190.70 

.28036 

.219 

.671 

•4 

164.46 

.21605 

•403 

•785 

•5 

190.09 

2.27896 

26.303 

6.694 

•5 

164.01 

2.21486 

30.486 

7.807 

.6 

189.49 

•27757 

•387 

.716 

.6 

163.56 

.21368 

•570 

.830 

•7 

188.88 

.27619 

.471 

.738 

•7 

163.12 

.21250 

.653 

.852 

.8 

188.28 

.27481 

•556 

.760 

.8 

162.68 

.21133 

•736 

-874 

•9 

187.69 

•27344 

.640 

.782 

•9 

162.24 

.21016 

.819 

•897 

31-0 

187.10 

2.27207 

26.724 

6.805 

36.0 

161.80 

2.20899 

30.902 

7.919 

.1 

186.51 

.27071 

.808 

.827 

.1 

161.37 

.20782 

•985 

•942 

.2 

185-93 

•26935 

.892 

.849 

.2 

160.94 

.20666 

3i'.o68 

•964 

•3 

185.35 

.26799 

•976 

.871 

•3 

160.51 

•20550 

•151 

.986 

•4 

184.77 

.26664 

27.060 

.894 

•4 

160.08 

.20435 

•233 

8.009 

•5 

184.20 

2.26530 

27.144 

6.916 

•5 

159.66 

2.20320 

31-316 

8.031 

.6 

183.63 

•26395 

.228 

.938 

.6 

159.24 

.20205 

•399 

•053 

•7 

183.07 

.26262 

.312 

.960 

•7 

158.82 

.20091 

.482 

.076 

.8 

182.51 

.26128 

•396 

•983 

.8 

158.40 

.19977 

.565 

.098 

•9 

181.95 

.25996 

.480 

7.005 

•9 

157-99 

.19863 

.648 

.121 

32.0 

181.40 

2.25863 

27.564 

7.027 

37-0 

157.58 

2.19749 

3I-730 

8.143 

.1 

180.85 

•25731 

.648 

•049 

.1 

I57.I7 

.19636 

.8x3 

.165 

.2 

180.30 

.25600 

•731 

.072 

.2 

156.76 

•19523 

.896 

.188 

•3 

179.76 

-25469 

.815 

•094 

•3 

156.35 

.19411 

•979 

.210 

•4 

179.22 

•25338 

•899 

.116 

•4 

155-95 

.19299 

32.061 

•233 

•5 

178.68 

2.25208 

27.983 

7-138 

•5 

155-55 

2.19187 

32.144 

8.255 

.6 

178.15 

.25078 

28.067 

.161 

.6 

155.15 

.19076 

.227 

•277 

•7 

177.62 

.24949 

.150 

.183 

•7 

154-75 

.18964 

•309 

.300 

.8 

177.09 

.24820 

•234 

.205 

.8 

154-36 

.18854 

•392 

.322 

•9 

176.57 

.24691 

.318 

.227 

•9 

153-97 

•18743 

•474 

•345 

33-0 

176.05 

2.24563 

28.402 

7.250 

38.0 

153.58 

2.18633 

32.557 

8.367 

.1 

175-53 

•24435 

•485 

.272 

.1 

I53-I9 

.18523 

•639 

•390 

.2 

175.02 

.24308 

•569' 

•294 

.2 

152.80 

.18413 

.722 

.412 

•3 

I74-5I 

.24181 

.652 

•316 

•3 

152.42 

.18304 

.804 

•434 

•4 

174.00 

.24054 

.736 

•339 

•4 

152.04 

•18195 

.887 

•457 

•5 

173-49 

2.23928 

28.820 

7.361 

•5 

151.66 

2.18086 

32.969 

8.479 

.6 

172.99 

.23802 

•903 

•383 

.6 

151.28 

.17978 

33.051 

.502 

•7 

172.49 

.23677 

•987 

.406 

•7 

150.90 

.17870 

•134 

•524 

.8 

172.00 

•23552 

29.070 

.428 

.8 

150.53 

.17762 

.216 

•547 

•9 

171.50 

.23428 

i54 

•450 

•9 

150.16 

-17655 

.298 

•569 

34-0 

171.02 

2.23303 

29.237 

7-473 

39-o 

149.79 

2.17547 

33.38i 

8.592 

.1 

170-53 

.23180 

.321 

•495 

.1 

149-42 

.17441 

•463 

.614 

.2 

170.04 

.23056 

.404 

.517 

.2 

149.05 

•17334 

•545 

•636 

•3 

169.56 

.22933 

.487 

•539 

•3 

148.69 

.17228 

.627 

•659 

•4 

169.09 

.22811 

•571 

.562 

•4 

148.33 

.17122 

.710 

.681 

•5 

168.61 

2.22688 

29.654 

7.584 

•5 

147-97 

2.17016 

33.792 

8.704 

.6 

168.14 

.22567 

•737 

.606 

.6 

147.61 

.16911 

.874 

.726 

•7 

167.67 

.22445 

.821 

.629 

•7 

147.25 

.16805 

.956 

•749 

.8 

167.20 

.22324 

.904 

.651 

.8 

146.89 

.16701 

34-038 

.771 

•9 

166.74 

.22203 

•987 

.673 

•9 

146.54 

.16596 

.120 

•794 

35-0 

166.28 

2.22083 

30.071 

7.696 

40.0 

146.19 

2.16492 

34.202 

8.816 

(19) 


TABLE  II.  —  TANGENT  DISTANCES  FOR  A  i°  CURVE  FOR  VARYING  /'s 
TD  =  Tv/D  +  C  of  Table  III 


/ 

0° 

i° 

2° 

3° 

4° 

5° 

6° 

7* 

/ 

.00 

o.oo 

50.00 

IOO.OI 

150.04 

200.08 

250.16 

300.28 

350.44 

.00 

.02 

I.OO 

51.00 

101.01 

151-04 

201.08 

251.16 

301  .  28 

351-44 

.02 

.04 

2.OO 

52.00 

102.01 

152.04 

202.09 

252.17 

302.28 

352.45 

.04 

.06 

3-00 

53-00 

103  .  01 

153-04 

203.09 

253  17 

303.29 

353-45 

.06 

.08 

4.00 

54-00 

IO4.OI 

154.04 

204.09 

254.17 

304.29 

354.46 

.08 

.10 

S.oo 

55-00 

105.01 

155-04 

205.09 

255.17 

305.29 

355.46 

.10 

.12 

6.00 

56.00 

106.01 

156.04 

206.09 

256.17 

306.30 

356.46 

.12 

.14 

7.00 

57-00 

107.01 

157.04 

207.09 

257-18 

307-30 

357-47 

.14 

.16 

8.00 

58.00 

108.01 

158.04 

208.09 

258.18 

308.30 

358.47 

.16 

.18 

•9.00 

59-00 

109.01 

159.04 

209.10 

259-18 

309.30 

359-48 

.18 

20 

10.  OO 

60.00 

I  10.  01 

160.04 

210.10 

260.18 

310.31 

360.48 

.20 

.22 

11.00 

61.00 

III.  02 

161.04 

211.  IO 

261.18 

311.31 

361.48 

.22 

.24 

12.  OO 

62.00 

112.02 

162.05 

212.10 

262.19 

312.31 

362.49 

.24 

.26 

13.00 

63.00 

113.02 

163.05 

213.10 

263.19 

313-32 

363.49 

.26 

.28 

14.00 

64.00 

114.02 

164.05 

214.10 

264.19 

314.32 

364.50 

.28 

30 

15.00 

65.00 

115.02 

165.05 

215.10 

265.19 

315-32 

365.50 

30 

32 

16.00 

66.00 

116.02 

166.05 

2l6.II 

266.19 

316.32 

366.50 

32 

34 

17.00 

67.00 

117.02 

167.05 

217.11 

267.20 

317-33 

367.51 

34 

.36 

18.00 

68.00 

118.02 

168.05 

2l8.II 

268.20 

318.33 

368.51 

.36 

.38 

19.00 

69.00 

119.02 

169.05 

219.11 

269.20 

319.33 

369.52 

.38 

.40 

20.00 

70.00 

120.  O2 

170.05 

220.11 

270.20 

320.34 

370.52 

.40 

.42 

21.00 

71.00 

121.  O2 

171.05 

221.  II 

271.21 

321.34 

371.52 

•42 

•44 

22.OO 

72.00 

122.  O2 

172.05 

222.11 

272.21 

322.34 

372.53 

•44 

.46 

23.0O 

73-00 

123.02 

173-05 

223.12 

273.21 

323.35 

373-53 

-46 

.48 

24.00 

74-01 

124.02 

174.06 

224.12 

274.21 

324.35 

374-54 

•48 

•  SO 

25.OO 

75-01 

125.02 

I75.o6 

225.12 

275.21 

325.35 

375-54 

SO 

.52 

26.OO 

76.01 

126.02 

176.06 

226.12 

276.22 

326.36 

376.55 

•52 

•  54 

27.00 

77-01 

127.02 

177-06 

227.12 

277.22 

327.36 

377-55 

•  54 

-56 

28.00 

78.01 

128  .  O2 

178.06 

228.12 

278.22 

328.36 

378.55 

.56 

.58 

29.OO 

79-01 

129.02 

179.06 

229.12 

279.22 

329.37 

379.56 

.58 

.60 

30.00 

80.01 

I3O.02 

180.06 

230.13 

280.23 

330.37 

380.56 

.60 

.62 

3I.OO 

81.01 

131  .  O2 

181.06 

231.13 

281.23 

331-37 

381.57 

.62 

.64 

32.00 

82.01 

132.03 

182.06 

232.13 

282.23 

332.38 

382.57 

-64 

.66 

33-00 

83.01 

133.03 

183.06 

233.13 

283.23 

333.38 

383.58 

.66 

.68 

34.00 

84.01 

134.03 

184.07 

234.13 

284.24 

334-38 

384.58 

.68 

.70 

35-00 

85.01 

135.03 

185.07 

235.13 

285.24 

335.39 

38S.S9 

.70 

•72 

36.00 

86.01 

136.03 

186.07 

236.14 

286.24 

336.39 

386.59 

•72 

•74 

37-00 

87.01 

137-03 

187.07 

237.14 

287.24 

337-39 

387.59 

74 

.76 

38.00 

88.01 

138.03 

188.07 

238.14 

288.25 

338.40 

388.60 

.76 

.78 

39-00 

89.01 

139-03 

189.07 

239.14 

289.25 

339-40 

389.60 

•78 

.80 

40.00 

90.01 

140.03 

190.07 

240.14 

290.25 

340.40 

390.61 

.80 

.82 

41.00 

91.01 

141.03 

191.07 

24LI5 

291.25 

341-41 

39i.6i 

.82 

.84 

42.00 

92.01 

142.03 

192.07 

242.15 

292.26 

342.41 

392.62 

84 

.86 

43.00 

93-01 

143.03 

193.07 

243.15 

293.26 

343-42 

393.62 

.86 

.88 

44.00 

94.01 

144-03 

194.08 

244-IS 

294.26 

344.42 

394.63 

.88 

.90 

45-00 

95.01 

145.03 

195-08 

245-15 

295.26 

345.42 

395.63 

.90 

.92 

46.00 

96.01 

146.03 

196.08 

246.15 

296.27 

346.43 

396.64 

•92 

•94 

47.00 

97-01 

147.03 

197.08 

247.16 

297.27 

347-43 

397.64 

•94 

.96 

48.00 

98.01 

148.03 

198.08 

248.16 

298.27 

348.43 

398.65 

•96 

•98 

49.00 

99.01 

149.04 

199-08 

249.16 

299.28 

349-44 

399.65 

.98 

1.00 

50.00 

100.01 

150.04 

200.08 

250.16 

300.28 

350-44 

400.66 

1.00 

(20) 


TABLE   II.  —  (Continued) 


I 

8° 

9° 

10° 

11° 

12° 

13° 

14° 

15° 

I 

.00 

400.00 

450.93 

501.28 

551-70 

602.21 

652.81 

703.51 

754-32 

.00 

.02 

401.66 

451-94 

502.29 

552.71 

603.22 

653.82 

704.53 

755-34 

.02 

.04 

402.67 

452.95 

503.29 

553-72 

604.23 

654.84 

705-54 

756.36 

.04 

.06 

403.67 

453-95 

504.30 

554-73 

605.24 

655.85 

706.56 

757.38 

.06 

.08 

404.68 

454-96 

505.31 

555-74 

606.26 

656.86 

707-57 

758.39 

.08 

.10 

405-68 

455.96 

506.32 

556.75 

607.27 

657-88 

708.59 

759-41 

.10 

.12 

406.69 

456.97 

507.33 

557.76 

608.28 

658.89 

709.60 

760.43 

.12 

.14 

407.69 

457-98 

508.33 

558.77 

609.29 

659.90 

710.62 

76i.45 

-14 

.16 

408.70 

458.98 

509.34 

559.78 

6lO.3O 

660.92 

711.63 

762.46 

.16 

.18 

409.70 

459-99 

510.35 

560.79 

6II.3I 

661.93 

712.65 

763.48 

.18 

.20 

410.71 

461.00 

5H.36 

561.80 

612.32 

662.94 

713.67 

764.50 

.20 

.22 

411.71 

462.00 

512.37 

562.81 

613.33 

663.96 

714.68 

765-52 

.22 

.24 

412.72 

463.01 

513.37 

563-82 

614.35 

664.97 

715.70 

766.53 

.24 

.26 

413-72 

464.02 

514.38 

564-83 

615.36 

665.98 

716.71 

767.55 

.26 

.28 

414.73 

465.02 

515-39 

565.84 

6l6.37 

667.00 

717-73 

768.57 

.28 

•30 

415.73 

466.03 

516.40 

566.85 

617.38 

668.01 

718.74 

769.59 

.30 

32 

416.74 

467.04 

5I7.4I 

567.86 

618.39 

669.02 

719-76 

770-61 

3* 

34 

417.74 

468.04 

518.41 

568.87 

619.40 

670.04 

720.78 

771-62 

34 

.36 

418.75 

469.05 

519.42 

569-88 

62O.42 

671.05 

721-79 

772.64 

-36 

•38 

419-75 

470.06 

520.43 

570.89 

621.43 

672.07 

722.81 

773-66 

•38 

.40 

420.76 

471-06 

521.44 

571-90 

622.44 

673-08 

723-82 

774-68 

.40 

42 

421.76 

472.07 

522.45 

572.91 

623.45 

674-09 

724.84 

775-70 

.42 

•44 

422.77 

473.08 

523-46 

573-92 

624.46 

675-11 

725.86 

776.72 

•44 

•46 

423.78 

474-08 

524.46 

574-93 

625.47 

676.12 

726.87 

777-73 

.46 

.48 

424.78 

475-09 

525.47 

575-94 

626  .  49 

677.13 

727.89 

778-75 

48 

.50 

425.79 

476.10 

526.48 

576.95 

627.50 

678.15 

728.90 

779-77 

•SO 

•52 

426.79 

477-10 

527.49 

577.96 

628.51 

679.16 

729.92 

780.79 

52 

•54 

427.80 

478.ii 

528.50 

578.97 

629.52 

680.18 

730.94 

781.81 

•54 

.56 

428.80 

479-12 

529.51 

579-98 

630.54 

681  .  19 

731-95 

782.83 

•56 

.58 

429.81 

480.13 

530.51 

580.99 

631.55 

682.21 

732.97 

783-85 

•58 

.60 

430.81 

481  .  13 

531.52 

582.00 

632.56 

683.22 

733-99 

784-86 

.60 

.62 

431-82 

482.14 

532.53 

583.01 

633.57 

684.23 

735-00 

785-88 

.62 

.64 

432.83 

483.15 

533-54 

584-02 

634-58 

685.25 

736.02 

786.90 

•64 

.66 

433.83 

484.15 

534-55 

585.03 

635-60 

686.26 

737-03 

787.92 

.66 

.68 

434.84 

485.16 

535.56 

586.04 

636.61 

687.28 

738.05 

788.94 

.68 

.70 

435.84 

486.17 

536.57 

587-05 

637.62 

688.29 

739-0? 

789.96 

.70 

.72 

436.85 

487.18 

537-57 

588.06 

638.63 

689.31 

740-08 

790.98 

•72 

•74 

437-85 

488.18 

538.58 

589.07 

639.65 

690.32 

741  -  io 

792-00 

•74 

.76 

438.86 

489.19 

539-59 

590.08 

640.66 

691.33 

742.12 

793-02 

.76 

.78 

439.87 

490.20 

540.6o 

591.09 

641.67 

692.35 

743-13 

794-04 

•78 

80 

440.87 

491.20 

54i.6i 

592.10 

642.68 

693.36 

744-15 

795-05 

.80 

.82 

441-88 

492.21 

542.62 

593.ii 

643.70 

694.38 

745-17 

796.07 

.82 

•84 

442.88 

493-22 

543.63 

594-12 

644.71 

695.39 

746.19 

797.09 

•84 

.86 

443.89 

494-23 

544.64 

595-13 

645.72 

696.41 

747-20 

798.ii 

.86 

.88 

444-90 

495.23 

545.65 

596.14 

646.73 

697.42 

748.22 

799-13 

.88 

•90 

445-90 

496.24 

546.66 

597.16 

647.75 

698.44 

749-24 

800.15 

.90 

•92 

446.91 

497-25 

547-67 

598.17 

648.76 

699.45 

750.25 

801  .  17 

.92 

•94 

447-91 

498.26 

548.67 

599-18 

649.77 

700.47 

751-27 

802.19 

•94 

.96 

448.92 

499-26 

549-68 

600.19 

650.79 

701.48 

752.29 

803.21 

.96 

•98 

449-93 

500.27 

550.69 

601  .  20 

651.80 

702.50 

753-31 

804.23 

.98 

1.00 

450.93 

501.28 

551.70 

602.21 

652.81 

703-51 

754-32 

805.25 

1.00 

(21) 


TABLE   II.  —  (Continued) 


I 

16° 

17° 

18° 

19° 

20° 

21° 

22° 

23° 

7 

.00 

805.25 

856.30 

907.49 

958.81 

1010.29 

1061  .  93 

1113-73 

1165.71 

.00 

.02 

806.27 

857.32 

908.51 

959-84 

1011.32 

1062.96 

HI4-77 

1166.75 

.02 

.o/ 

807.29 

858.35 

909.54 

960.87 

1012.35 

1064.00 

III5.8I 

1167.79 

.04 

.06 

808.31 

859.37 

910.56 

961.90 

1013-39 

1065.03 

III6.85 

1168.83 

.06 

.08 

809.33 

860.39 

911-59 

962.93 

1014.42 

1066  .  07 

1117.88 

1169.88 

.08 

.10 

810.35 

861.41 

912.61 

963.96 

ioiS-45 

1067.10 

III8.92 

1170.92 

.10 

.12 

8ii.37 

862.44 

913-64 

964.98 

1016.48 

1068.14 

1119.96 

1171.96 

.12 

.It 

812.39 

863.46 

914.66 

966.01 

1017.51 

1069.17 

1121.00 

1173.00 

14 

.16 

813.41 

864.48 

915.69 

967.04 

1018.54 

1070.21 

1122.04 

1174.04 

.16 

.18 

814.43 

865.51 

916.72 

968.07 

1019.58 

1071.24 

1123.07 

1175.09 

.18 

.20 

815.45 

866.53 

917.74 

969-10 

1020.61 

1072.27 

1124.  II 

1176.13 

.20 

.22 

816.47 

867.55 

9i8.77 

970.13 

1021.64 

1073.31 

H25.I5 

1177.17 

.22 

,2i 

817.49 

868.57 

919.79 

971.16 

IO22  .  67 

1074-35 

1126.19 

1178.21 

.24 

.26 

818.51 

869.60 

920.82 

972.19 

IO23  .  7O 

1075.38 

1127.23 

1179.25 

.26 

.28 

819.53 

870.62 

921.84 

973-21 

1024.73 

1076.42 

1128.27 

1180.30 

.28 

30 

820.55 

871.64 

922.87 

974-24 

1025.77 

1077-45 

1129.31 

1181.34 

30 

32 

821.57 

872.67 

923.90 

975-27 

1026.80 

1078.49 

1130.35 

1182.38 

32 

•34 

822.59 

873.69 

924.92 

976.30 

1027.83 

1079.52 

1131.38 

1183.43 

34 

.36 

823.61 

874.71 

925.95 

977-33 

1028.86 

1080.56 

1132.42 

1184.47 

36 

.38 

824.63 

875.74 

926.97 

978.36 

1029.89 

1081.59 

1133.46 

1185.51 

.38 

.40 

825.66 

876.76 

928.00 

979-39 

1030.93 

1082.63 

1134.50 

1186.55 

.40 

.42 

t  826.  68 

877.78 

929-03 

980.42 

1031.96 

1083.66 

1135-54 

1187.60 

•42 

•44 

827.70 

878.81 

930.05 

981.45 

1032.99 

1084.70 

1136.58 

1188.64 

•44 

.46 

828.72 

879.83 

93i.o8 

982.48 

1034.02 

1085.74 

1137.62 

1189.68 

.46 

•48 

829.74 

880.85 

932.ii 

983.50 

1035.06 

1086.77 

1138.66 

1190.73 

.48 

•SO 

830.76 

881.88 

933-13 

984.53 

1036  .  09 

1087.81 

1139.70 

1191.77 

•SO 

•52 

831.78 

882.90 

934.i6 

985.56 

1037-12 

1088.84 

1140.74 

1192.81 

52 

•  54 

832.80 

883.92 

935-19 

986.59 

I038.I6 

1089.88 

1141.78 

1193.86 

•54 

•56 

833.82 

88-4.95 

936.21 

987-62 

I039.I9 

1090.92 

1142.82 

1194.90 

.56 

.58 

834.84 

885.97 

937-24 

988.65 

IO4O.22 

1091.95 

1143-86 

1195.94 

.58 

.60 

835.87 

887.00 

938.27 

989.68 

1041.25 

1092.99 

1144.90 

1196.99 

.60 

.62 

836.89 

888.02 

939-29 

990.71 

1042.29 

1094.03 

1145-94 

1198.03 

.62 

.64 

837.91 

889.04 

940.32 

991-74 

1043.32 

1095.06 

1146.98 

1199.07 

.64 

.66 

838.93 

890.07 

941-35 

992-77 

1044-35 

1096.10 

1148.02 

1200.12 

.66 

.68 

839-95 

891.09 

942.37 

993.80 

1045-39 

1097.14 

II49.O6 

I2OI.I6 

.68 

.70 

840.97 

892.12 

943-40 

994.83 

1046.42 

1098.17 

II50.IO 

I2O2.2I 

.70 

.72 

841.99 

893.14 

944-43 

995-86 

1047-45 

1099.21 

II5I.I4 

I2O3  .  25 

•72 

•74 

843.02 

894.17 

945.46 

996.89 

1048.49 

1100.25 

II52.I8 

1204.29 

•  74 

.76 

844-04 

895.19 

946.48 

997-92 

1049.52 

1101.28 

1153-22 

1205.34 

•  76 

.78 

845.06 

896.21 

947-51 

998.95 

1050.55 

1102.32 

1154.26 

1206.38 

.78 

.80 

846.08 

897-24 

948.54 

999.98 

1051.59 

1103.36 

1155.30 

1207-43 

.80 

.82 

847.10 

898.26 

949-57 

1001.01 

IO52.62 

1104-39 

1156.34 

1208.47 

.82 

.84 

848.12 

899.29 

950.59 

1002.04 

1053.66 

1105-43 

H57.38 

1209.52 

.84 

.86 

849.15 

900.31 

951-62 

1003.08 

1054.69 

1106.47 

1158.42 

I2IO.56 

.86 

.88 

850.17 

901.34 

952.65 

1004.11 

1055.72 

1107.51 

H59.46 

I2II.6O 

.88 

90 

85LI9 

902.36 

953-68 

1005.14 

1056.76 

1108.54 

1160.50 

1212.65 

.90 

92 

852.21 

903.39 

954-70 

1006.17 

1057-79 

1109.58 

II6I.55 

1213.69 

.92 

•94 

853-24 

904.41 

955-73 

1007.20 

1058.83 

1110.62 

II62.59 

1214.74 

•94 

.96 

854.26 

905.44 

956.76 

1008.23 

1059.86 

mi.  66 

1163.63 

1215.78 

.96 

•98 

855.28 

906.46 

957-79 

1009.26 

1060.89 

1112.69 

1164.67 

I2I6.83 

•98 

1.00 

856.30 

907.49 

958.81 

1010.29 

1061.93 

1113-73 

II65.7I 

1217.87 

.00 

(22) 


TABLE    II.  —  (Continued} 


I 

24° 

25° 

26° 

27° 

28° 

29° 

30° 

3ie 

I 

.00 

1217.87 

1270.23 

1322.79 

1375-57 

1428.56 

1481.79 

1535.25 

1588.97 

.00 

.02 

1218.92 

1271.28 

1323-85 

1376.62 

1429.62 

1482.86 

1536.33 

1590.05 

.02 

•04 

1219.97 

1272.33 

1324.90 

1377-68 

1430.69 

1483.92 

1537.40 

1591-13 

.04 

.06 

I22I.OI 

1273.38 

1325.95 

1378.74 

I43I-7S 

1484.99 

1538.47 

1592.20 

.06 

.08 

1222  .  06 

1274.43 

1327.01 

1379.80 

1432.81 

1486.06 

1539-54 

1593-28 

.08 

.10 

1223.10 

1275.48 

1328.06 

1380.86 

1433.87 

1487.12 

1540.62 

1594.36 

.10 

.12 

1224.14 

1276.53 

1329.12 

1381.91 

1434.94 

1488.19 

1541.69 

1595-44 

.12 

.14 

1225.19 

1277.58 

1330.17 

1382.97 

1436.00 

1489.26 

1542.76 

1596.51 

•14 

.16 

1226.24 

1278.63 

1331.22 

1384-03 

1437-06 

1490.33 

1543.83 

1597-59 

.16 

.18 

1227.28 

1279.68 

1332.28 

1385-09 

1438.13 

1491.39 

1544-91 

1598.67 

.18 

.20 

1228.33 

1280.73 

1333.33 

1386.15 

1439-19 

1492.46 

1545-98 

1599-75 

.20 

.22 

1229.38 

1281.78 

1334.39 

1387-21 

1440.25 

1493-53 

1547.05 

1600.82 

.22 

.24 

1230.42 

1282.83 

1335-44 

1388.27 

1441.32 

i494.6o 

1548.12 

1601.90 

.24 

.26 

1231-47 

1283.88 

1336.50 

1389.32 

1442.38 

1495-67 

1549-20 

1602.98 

.26 

.28 

1232.52 

1284.93 

1337-55 

1390.38 

1443-44 

1496.73 

1550.27 

1604.06 

.28 

30 

1233-56 

1285.98 

1338.60 

1391-44 

1444.51 

i497.8o 

I55L34 

1605.14 

30 

32 

I234.6I 

1287.03 

1339-66 

1392.50 

1445-57 

1498.87 

1552.42 

1606.22 

32 

•34 

1235.65 

1288.08 

1340.71 

1393.56 

1446.63 

1499-94 

1553-49 

1607.30 

•34 

.36 

1236.70 

1289.13 

1341-77 

1394-62 

1447.70 

1501.01 

I554-56 

1608.37 

.36 

.38 

1237-75 

1290.18 

1342.82 

1395-68 

1448.76 

1502  .  08 

1555.64 

1609.45 

•38 

.40 

1238.79 

1291.23 

1343-88 

1396.74 

1449.82 

1503.15 

1556.71 

1610.53 

.40 

.42 

1239.84 

1292.28 

1344-93 

1397.80 

1450.89 

1504.21 

1557-79 

1611.61 

.42 

-44 

1240.89 

1293.33 

1345-99 

1398.86 

1451.95 

1505.28 

1558.86 

1612.69 

•44 

-46 

1241.93 

1294.39 

1347-04 

1399-92 

1453-02 

1506.35 

1559-93 

i6i3.77 

.46 

.48 

1242.98 

1295.44 

1348.10 

1400.98 

1454.08 

1507-42 

1561.01 

1614.85 

.48 

•50 

1244.03 

1296.49 

1349.15 

1402.04 

1455.15 

1508.49 

1562.08 

i6i5.93 

•50 

-52 

1245.08 

1297.54 

1350.21 

1403.10 

1456.21 

1509-56 

1563.16 

1617.01 

•52 

-54 

1246.12 

1298.59 

1351.26 

1404.16 

1457.27 

1510.63 

1564.23 

1618.09 

•54 

-56 

1247.17 

1299.64 

1352.32 

1405.22 

1458.34 

1511.70 

1565.31 

1619.17 

.56 

-58 

1248.22 

1300.69 

1353-38 

1406.28 

1459-40 

1512.77 

1566.38 

1620.25 

.58 

.60 

1249.27 

1301.74 

1354-43 

1407.34 

1460.47 

1513-84 

1567.46 

1621.33 

.60 

.62 

1250.31 

1302.80 

1355-49 

1408.40 

1461.53 

1514-91 

1568.53 

1622.41 

.62 

-64 

1251.36 

1303-85 

1356.54 

1409.46 

1462.60 

1515.98 

1569.60 

1623.49 

.64 

.66 

1252.41 

1304.90 

1357.60 

1410.52 

1463.66 

1517-05 

1570.68 

1624.57 

.66 

.68 

1253.46 

1305.95 

1358.66 

1411-58 

1464.73 

1518.12 

1571.76 

1625  .  65 

.68 

.70 

1254-50 

1307.00 

1359.71 

1412.64 

1465.80 

1519.19 

1572.83 

1626.73 

.70 

-72 

1255.55 

1308.06 

1360.77 

1413.70 

1466.86 

1520.26 

I573.9I 

1627.81 

.72 

-74 

I256.6O 

1309.11 

1361.83 

1414-76 

1467.93 

1521.33 

1574.98 

1628.89 

74 

-76 

1257.65 

1310.16 

1362.88 

1415.82 

1468.99 

1522.40 

1576.06 

1629.97 

-76 

-78 

1258.70 

1311.21 

1363-94 

1416.88 

1470.06 

1523.47 

1577-13 

1631.05 

.78 

.80 

1259-75 

1312.27 

1365.00 

1417.94 

1471-12 

1524-54 

1578.21 

1632  .  14 

.80 

.82 

1260.79 

1313.32 

1366.05 

1418.01 

1472.19 

1525.61 

1579-28 

1633-21 

.82 

-84 

I26I.84 

1314.37 

1367-11 

1420.07 

1473.26 

1526.68 

1580.36 

1634.30 

.84 

.86 

1262.89 

1315.42 

1368.17 

1421.13 

1474-32 

1527.76 

1581.44 

1635.38 

.86 

.88 

1263.94 

1316.48 

1369.22 

1422.19 

1475-39 

1528.83 

1582.51 

1636  .  46 

.88 

.90 

1264.99 

1317.53 

1370.28 

1423-25 

1476.45 

1529.90 

1583.59 

1637.54 

•90 

•  92 

1266.04 

1318.58 

1371.34 

1424.31 

1477-52 

1530.97 

1584-67 

1638.62 

•92 

-94 

1267  .  O9 

1319.63 

1372.39 

1425.38 

1478.59 

1532.04 

1585.74 

1639.70 

•94 

.96 

1268.14 

1320.69 

1373-45 

1426.44 

1479-66 

i533.li 

1586.82 

1640.79 

•96 

98 

1269.18 

1321.74 

I374-5I 

1427.50 

1480.72 

1534.18 

1587.90 

1641.87 

98 

1.00 

1270.23 

1322.79 

1375-57 

1428.56 

1481.79 

1535.25 

1588.97 

1642.95 

1.00 

(23) 


TABLE   II.  —  (Continued^ 


I 

32° 

33° 

34° 

35° 

36° 

37° 

38° 

39° 

7 

.00 

1642.95 

1097  .  20 

1751.73 

1806.55 

1861.68 

I9I7-II 

1972.88 

2028.98 

.00 

.02 

1644.04 

1698.29 

1752.82 

1807.65 

1862.78 

1918.23 

1974-00 

2030  .  10 

.02 

.04 

1645-12 

1699.37 

I753.92 

1808.75 

1863.89 

1919.34 

I975.il 

2031.23 

.04 

.06 

1646  .  20 

I7O0.46 

1755-01 

1809.85 

1864.99 

1920.45 

1976.23 

2032.35 

.06 

.08 

1647  .  28 

1701.55 

1756.10 

1810.95 

1866.10 

1921.56 

1977-35 

2033.48 

.08 

.10 

1648.36 

1702.64 

1757-20 

1812.05 

1867.21 

1922.68 

1978.47 

2034.60 

.IO 

.12 

1649.45 

I703.73 

1758.29 

1813.15 

1868.31 

1923.79 

1979-59 

2035-73 

.12 

.14 

1650.53 

1704.82 

1759-39 

1814.25 

1869.42 

1924.90 

1980.71 

2036.86 

•14 

.16 

1651.61 

1705.91 

1760.48 

I8I5.35 

1870.53 

1926.01 

1981.83 

2037.98 

.16 

.18 

1652  .  70 

1706.99 

1761.58 

1816.45 

1871.63 

1927.13 

1982.95 

2039.11 

.18 

.20 

1653.78 

1708.08 

1762.67 

1817-55 

1872.74 

1928.24 

1984-07 

2040.24 

.20 

.22 

1654.86 

1709.17 

1763.77 

1818.65 

1873.85 

1929.35 

1985.19 

2041.36 

.22 

.24 

1655.95 

I7IO.26 

1764.86 

I8I9.75 

1874.95 

1930.47 

1986.31 

2042.49 

24 

.26 

1657.03 

1711-35 

1765.95 

1820.85 

1876.06 

1931.58 

1987.43 

2043.62 

.26 

.28 

1658.11 

1712.44 

1767.05 

1821.96 

1877.17 

1932.69 

1988.55 

2044.74 

.28 

30 

1659.20 

1713.53 

1768.14 

1823.06 

1878.27 

I933.8I 

1989.67 

2045.87 

•30 

32 

1660.28 

1714.62 

1769.24 

1824.16 

1879.38 

1934.92 

1990.79 

2047  .  oo 

3* 

34 

1661.36 

1715.71 

1770.34 

1825  .  26 

1880.49 

1936.04 

I99L9I 

2048.13 

34 

.36 

1662.45 

I7I6.80 

1771-43 

1826.36 

1881.60 

1937.15 

1993.03 

2049.26 

.36 

.38 

1663.53 

1717.89 

1772.53 

1827.46 

1882.71 

1938.26 

I994-I5 

2050.38 

.38 

.40 

1664.62 

1718.98 

1773.62 

1828.56 

1883.81 

1939.38 

1995.28 

2051.51 

.40 

.42 

1665.70 

I72O.O7 

I774.72 

1829.67 

1884.92 

1940.49 

1996.40 

2052.64 

•42 

•44 

1666.79 

I72I.I6 

I775.8I 

1830.77 

1886.03 

1941.61 

1997.52 

2053.77 

•44 

.46 

1667.87 

1722.25 

1776.91 

1831.87 

1887.14 

1942.72 

1998.64 

2054.90 

.46 

.48 

1668.96 

1723.34 

1778.00 

1832.97 

1888.25 

1943.84 

1999.76 

2056.03 

•48 

•So 

1670.04 

1724.43 

1779-10 

1834-08 

1889.36 

1944-95 

2000.88 

2057.15 

50 

•52 

1671.13 

1725.52 

1780.20 

1835-18 

1890.46 

1946.07 

20O2  .  OI 

2058.38 

52 

•54 

1672.21 

I726.6I 

1781.30 

1836.28 

1891.57 

1947-18 

2003.13 

2059.41 

•54 

.56 

1673.30 

1727.70 

1782.39 

1837.38 

1892.68 

1948.30 

2004.25 

2060.54 

.56 

•  58 

1674-38 

1728.79 

1783.49 

1838.49 

1893.79 

1949.42 

2005.37 

2061.67 

-58 

.60 

1675.47 

1729.88 

1784.59 

1839.59 

1894.90 

1950.53 

2006.49 

2062.80 

.60 

.62 

1676.55 

1730.97 

1785.68 

1840.69 

1896.01 

1951.65 

2OO7  .  62 

2063.93 

.62 

.64 

1677-64 

1732.07 

1786.78 

1841.80 

1897.12 

1952.76 

2008.74 

2065.06 

.64 

.66 

1678.72 

I733.I6 

1787.88 

1842.90 

1898.23 

1953.88 

2OO9.86 

2066.19 

.66 

.68 

1679.81 

1734.25 

1788.98 

1844-00 

1899.34 

1955.00 

2010.99 

2067.32 

.68 

.70 

1680.90 

1735-34 

1790.07 

1845.11 

1900.45 

1956.12 

2OI2.II 

2068.45 

.70 

.72 

1681.98 

1736.43 

I79LI7 

1846.21 

1901.56 

1957.23 

2013.23 

2069.58 

•72 

•74 

1683.07 

1737.52 

1792.27 

I847.3I 

1902.67 

1958.35 

2014.36 

2070.71 

•74 

.76 

1684.15 

1738.62 

1793-37 

1848.42 

1903.78 

1959-47 

2015.48 

2071.84 

.76 

.78 

1685.24 

1739-71 

1794.46 

1849.52 

1904.89 

1960.58 

2OI6.60 

2072.97 

.78 

.80 

1686.33 

1740.80 

1795.56 

1850.63 

1906.00 

1961  .  70 

2017.73 

2074.10 

.80 

.82 

1687.41 

1741.89 

1796.66 

I85I.73 

1907.11 

1962.82 

2018.85 

2075.24 

.82 

.84 

1688.50 

1742.99 

1797.76 

1852.84 

1908.22 

1963.93 

2019.98 

2076.37 

.84 

.86 

1689.59 

1744-08 

1798.86 

1853.94 

1909.33 

1965-05 

2O2I  .  10 

2077.50 

.86 

.88 

1690.67 

I745-I7 

1799.96 

1855.04 

1910.44 

1966.17 

2022.22 

2078  .  63 

.88 

.90 

1691.76 

1746.26 

1801.06 

1856.15 

1911.56 

1967.28 

2023.35 

2079.76 

•90 

•92 

1692.85 

1747.36 

1802.15 

1857.25 

1912.67 

1968.40 

2024-47 

2080.89 

-92 

•94 

1693.94 

1748.45 

1803.25 

1858.36 

I9I3.78 

1969.52 

2O25  .  60 

2082.03 

94 

.96 

1695.02 

1749-54 

1804.35 

1859.46 

1914-89 

1970.64 

2026.72 

2083.16 

.96 

•98 

1696.11 

1750.64 

1805.45 

1860.57 

1916.00 

1971.76 

2027.85 

2084.29 

•98 

1.00 

1697.20 

1751-73 

1806.55 

1861.68 

1917-11 

1972.88 

2028.98 

2085.42 

1.00 

(24) 


TABLE   II.  —  (Continued) 


I 

40° 

41° 

42° 

43° 

44° 

45° 

46° 

47° 

/ 

.00 

2085.42 

2142.23 

2199.41 

2256.97 

2314.93 

2373  30 

2432.09 

249L32 

.00 

.02 

2086.55 

2143.37 

2200.55 

2258.12 

2316.09 

2374-47 

2433.27 

2492.51 

.02 

.04 

2087.69 

2144.51 

2201  .  70 

2259.28 

2317.26 

2375.64 

2434-45 

2493.70 

.04 

.06 

2088.82 

2145.65 

2202.85 

2260.44 

2318.42 

2376.81 

2435.63 

2494.89 

.06 

.08 

2089.95 

2146.79 

2204  .  oo 

2261.59 

23I9-58 

2377-99 

2436.71 

2496.08 

.08 

.10 

2091.09 

2147.93 

2205.15 

2262.75 

2320.75 

2379-16 

2438  .  oo 

2497.27 

.10 

.12 

2092.22 

2149.07 

2206.29 

2263.90 

2321.91 

2380.33 

2439.18 

2498.46 

.12 

•14 

2093.35 

2150.21 

2207.44 

2265.06 

2323.08 

2381.50 

2440.36 

2499.65 

•14 

.16 

2094.49 

2151.35 

2208.59 

2266  .  22 

2324.24 

2382.68 

2441.54 

2500.84 

.16 

.18 

2095  .  62 

2152.49 

2209.74 

2267.37 

2325.40 

2383.85 

2442.72 

2502.03 

.18 

.20 

2096.75 

2153.63 

2210.89 

2268.53 

2326.57 

2385.02 

2443.90 

2503-22 

.20 

.22 

2097.89 

2154-78 

22I2.O4 

2269.69 

2327.73 

2386.20 

2445.08 

2504.41 

.22 

.24 

2099.02 

2155.92 

2213.19 

2270.84 

2328.90 

2387.37 

2446.27 

2505.60 

.24 

.26 

2100.16 

2157.06 

2214.33 

2272.OO 

2330.06 

2388.54 

2447.45 

2506.80 

.26 

.28 

2101.29 

2158.20 

2215.48 

2273.16 

2331.23 

2389.72 

2448.63 

2507.99 

.28 

•30 

2102.43 

2159.34 

2216.63 

2274.31 

2332.40 

2390.89 

2449.82 

2509.18 

•30 

32 

2103.56 

2160.48 

2217.78 

2275-47 

2333.56 

2392.07 

2451.00 

2510.37 

•32 

34 

2104.70 

2161.63 

2218.93 

2276.63 

2334-73 

2393.24 

2452.18 

2511.56 

•34 

.36 

2105.83 

2162.77 

2220.08 

2277-79 

2335.89 

2394-41 

2453.36 

2512.75 

.36 

.38 

2106.97 

2163.91 

2221  .  23 

2278.95 

2337.06 

2395-59 

2454.55 

2513.95 

.38 

.40 

2108.10 

2165.05 

2222.38 

228O.IO 

2338.23 

2396.76 

2455.73 

2515.14 

.40 

.42 

2109.24 

2166.20 

2223.53 

2281.26 

2339-39 

2397.94 

2456.91 

2516.33 

.42 

-44 

2110.37 

2167.34 

2224.68 

2282.42 

2340.56 

2399-H 

2458.10 

2517.53 

•44 

.46 

2111.51 

2168.48 

2225.84 

2283.58 

2341.73 

2400.29 

2459.28 

2518.72 

.46 

-48 

2112.64 

2169.63 

2226.99 

2284.74 

2342.89 

2401.47 

2460.47 

2519.91 

.48 

50 

2113.78 

2170.77 

2228.14 

2285.90 

2344.06 

2402  .  64 

2461.65 

2521.11 

•50 

•52 

2114.92 

2171.91 

2229.29 

2287.06 

2345.23 

2403.82 

2462.84 

2522.30 

•52 

•  54 

2116.05 

2173.06 

2230.44 

2288.22 

2346  .  40 

2404.99 

2464  .  02 

2523.49 

•54 

.56 

2117.19 

2174.20 

2231.59 

2289.38 

2347.56 

2406.17 

2465.21 

2524.69 

•56 

.58 

2118.32 

2175.34 

2232.74 

2290.54 

2348.73 

2407.35 

2466.39 

2525.88 

•58 

GO 

2119.46 

2176.  49 

2233.90 

2291  .  70 

2349.90 

2408  .  52 

2467.58 

2527.08 

.60 

.62 

2120.60 

2177-63 

2235.05 

2292.86 

2351.07 

2409.70 

2468.76 

2528.27 

.62 

.64 

2121.74 

2178.78 

2236.20 

2294  .  O2 

2352.24 

2410.88 

2469.95 

2529.47 

.64 

.66 

2122.87 

2179.92 

2237-35 

2295.18 

2353.41 

2412.05 

2471.13 

2530.66 

.66 

.68 

2124.01 

2181.07 

2238.51 

2296.34 

2354.58 

2413-23 

2472.32 

2531-86 

.68 

.70 

2125.15 

2182.21 

2239.66 

2297.50 

2355-74 

2414.41 

2473.51 

2533-05 

.70 

•72 

2126.29 

2183.36 

2240.81 

2298.66 

2356.91 

2415.59 

2474.69 

2534.25 

•72 

•74 

2127.42 

2184.50 

2241.97 

2299.82 

2358.08 

2416.76 

2475.88 

2535-44 

•74 

-76 

2128.56 

2185.65 

2243.12 

2300.98 

2359.25 

2417.94 

2477.07 

2536.64 

.76 

.78 

2129.70 

2186.79 

2244.27 

2302.14 

2360.42 

2419.12 

2478.25 

2537.83 

•  78 

.80 

2130.84 

2187.94 

2245-43 

2303.30 

2361.59 

2420.30 

2479-44 

2539-03 

.80 

.82 

2131.98 

2189.09 

2246.58 

2304.47 

2362.76 

2421.48 

2480.63 

2540.23 

.82 

.84 

2133.11 

2190.23 

2247.73 

2305.63 

2363.93 

2422.66 

2481.82 

2541.43 

.84 

.86 

2134.25 

2191.38 

2248.89 

2306.79 

2365.10 

2423.84 

2483.00 

2542.62 

.86 

.88 

2135.39 

2192.52 

2250.O4 

2307.95 

2366.27 

2425.01 

2484.19 

2543.82 

.88 

90 

2136.53 

2193-67 

2251.20 

2309.12 

2367.44 

2426  .  19 

2485.38 

2545.02 

90 

92 

2137.67 

2194.82 

2252.35 

2310.28 

2368.61 

2427.37 

2486.57 

2546.21 

•92 

•94 

2138.81 

2195.97 

2253-50 

2311.44 

2369.78 

2428.55 

2487.76 

2547-41 

-94 

•  96 

2139.95 

2197.11 

2254-66 

2312.60 

2370.96 

2429.73 

2488.95 

2548.61 

-96 

.98 

2141.09 

2198.26 

2255.81 

23*3.77 

2372.13 

2430.91 

2490.13 

2549.81 

-98 

1.00 

2142.23 

2I99-4I 

2256.97 

2314.93 

2373.30 

2432.09 

2491.32 

2551-00 

1.00 

(25) 


TABLE   II.  —  (Continued) 


I 

48° 

49° 

50° 

5i° 

52° 

53° 

54° 

55° 

/ 

00 

2551-00 

2611.15 

2671.78 

2732.90 

2794.54 

2856.70 

2919.40 

2982.67 

.00 

.02 

2552.20 

2612.36 

2672.99 

2734.13 

2795.77 

2857  '95 

2920.66 

2983.94 

.02 

.04 

2553.40 

2613.57 

2674.21 

2735.36 

2797.01 

2859.20 

2921.92 

2985.21 

.04 

.06 

25S4.6o 

2614.78 

2675-43 

2736.59 

2798.25 

2860.44 

2923.18 

2986.48 

.06 

.08 

2555.8o 

2615.98 

2676.65 

2737.81 

2799.49 

2861.69 

2924.44 

2987.75 

.08 

.10 

2557.00 

2617.19 

2677.86 

2739.04 

2800.73 

2862.94 

2925.70 

2989.02 

.10 

.12 

2558.20 

2618.40 

2679.09 

2740.27 

2801.97 

2864.19 

2926.96 

2990-30 

.12 

.14 

2559.40 

2619.61 

2680.31 

2741.50 

2803.21 

2865.44 

2928.23 

2991.57 

•14 

.16 

2560.60 

2620.82 

2681.53 

2742-73 

2804.45 

2866.69 

2929.49 

2992.84 

.16 

.18 

2561  .  80 

2622  .  03 

2682.74 

2743.96 

2805.69 

2867.94 

2930.75 

2994.12 

.18 

.20 

2563  .  oo 

2623.24 

2683.96 

2745  •  19 

2806.93 

2869.20 

2932.01 

2995-39 

.20 

.22 

2564  .  20 

2624.45 

2685.18 

2746.42 

2808.17 

2870.45 

2933.27 

2996.66 

.22 

.24 

2565.40 

2625.66 

2686.40 

2747.65 

2809.41 

2871.70 

2934-53 

2997-94 

24 

.26 

2566.60 

2626.87 

2687.62 

2748.88 

2810.65 

2872.95 

2935.8o 

2999.21 

.26 

.28 

2567.80 

2628.08 

2688.84 

2750.11 

2811.89 

2874.20 

2937.06 

3000.48 

.28 

30 

2569  .  oo 

2629.29 

2690.06 

2751.34 

2813.13 

2875-45 

2938.32 

3001.76 

30 

32 

2570.20 

2630.50 

2691.28 

2752.57 

2814.37 

2876.70 

2939-59 

3003.03 

32 

•34 

2571.40 

2631.71 

2692.50 

2753.80 

2815.61 

2877.96 

2940.85 

3004.31 

34 

36 

2572.60 

2632.92 

2693.73 

2755.03 

2816.85 

2879.21 

2942.11 

3005.58 

.36 

.38 

2573.80 

2634.13 

2694.95 

2756.26 

2818.10 

2880.46 

2943.38 

3006.86 

•38 

.40 

2575.01 

2635-34 

2696.17 

2757-49 

2819.34 

2881.71 

2944.64 

3008.13 

.40 

.42 

2576.21 

2636.56 

2697.39 

2758.73 

2820.58 

2882.97 

2945.90 

3009.41 

•42 

•44 

2577.41 

2637.77 

2698.61 

2759.96 

2821.82 

2884.22 

2947.17 

3010.68 

•44 

.46 

2578.61 

2638.99 

2699.83 

2761.19 

2823.06 

2885.47 

2948.43 

3011.96 

.46 

.48 

2579.82 

2640.19 

2701.06 

2762.42 

2824.31 

2886.73 

2949.70 

3013-24 

.48 

So 

258l  .  02 

2641.40 

2702.28 

2763.65 

2825.55 

2887.98 

2950.96 

3014-51 

•  50 

•  52 

2582.22 

2642.62 

2703.50 

2764.89 

2826.79 

2889.24 

2952.23 

3015-79 

52 

•54 

2583.43 

2643-83 

2704.72 

2766.12 

2828.04 

2890.49 

2953-49 

3017-07 

•  54 

.56 

2584.63 

2645.04 

2705.95 

2767.35 

2829.29 

2891.74 

2954.76 

3018.35 

•56 

.58 

2585.83 

2646.26 

2707.17 

2768.59 

2830.52 

2893.00 

2956.03 

3019.62 

.58 

.60 

2587.04 

2647.47 

2708.39 

2769.82 

2831.77 

2894.26 

2957.29 

3020.90 

.60 

.62 

2588.24 

2648.68 

2709.62 

2771.05 

2833.01 

2895.51 

2958.56 

3022.18 

.62 

.64 

2589.44 

2649.90 

2710.84 

2772.29 

2834.26 

2896.77 

2959.83 

3023.46 

.64 

.66 

2590.65 

2651.11 

2712.06 

2773.52 

2835.50 

2898.02 

2961.09 

3024.74 

.66 

.68 

2591.85 

2652.33 

2713.29 

2774.76 

2836.75 

2899.28 

2962.36 

3026.02 

.68 

.70 

2593.06 

2653.54 

2714-51 

2775-99 

2837.99 

2900.53 

2963-63 

3027.29 

.70 

•72 

2594.26 

2654.76 

2715.74 

2777-23 

2839.24 

2901.79 

2964.90 

3028.57 

•72 

•74 

2595-47 

2655.97 

2716.96 

2778.46 

2840.48 

2903.05 

2966.16 

3029.85 

-74 

.76 

2596.67 

2657-18 

2718.19 

2779-70 

2841.73 

2904.30 

2967.43 

3031  •  13 

.76 

-78 

2597.88 

2658.40 

2719.41 

2780.93 

2842.98 

2905.56 

2968.70 

3032.41 

-78 

.80 

2599.08 

2659.62 

2720.64 

2782.17 

2844.22 

2906.82 

2969.97 

3033.69 

.80 

.82 

26OO.29 

2660.83 

2721.86 

2783.41 

2845.47 

2908.07 

2971.24 

3034-97 

.82 

.84 

26OI  .  5O 

2662.05 

2723.09 

2784.64 

2846.72 

2909.33 

2972.51 

3036.25 

.84 

.86 

26O2.7O 

2663.26 

2724.32 

2785.88 

2847.96 

2910.59 

2973.78 

3037.54 

.86 

.88 

2603.91 

2664.48 

2725.54 

2787.11 

2849.21 

2911.85 

2975.05 

3038.82 

.88 

90 

2605.12 

2665.69 

2726.77 

2788.35 

2850.46 

2913-11 

2976.31 

3040.10 

.90 

.92 

2606.32 

2666.91 

2727.99 

2789-59 

2851.71 

2914.37 

2977.58 

3041-38 

-92 

-94 

2607.53 

2668.13 

2729.22 

2790.82 

2852.95 

2915.63 

2978.86 

3042.66 

•94 

.96 

2608.74 

2669.34 

2730.45 

2792  .  06 

2854.20 

2916.88 

2980.13 

3043.94 

•96 

.98 

2609.94 

2670.56 

2731.68 

2793.30 

2855.45 

2918.14 

2981.48 

3045-23 

•  98 

1.00 

26II.I5 

2671.78 

2732.90 

2794-54 

2856.70 

2919-40 

2982.67 

3046.51 

1.00 

(26) 


TABLE   II.  —  (Continued) 


I 

56° 

57° 

58° 

59° 

60° 

61° 

62° 

63° 

/ 

.00 

3046.51 

3110.95 

3176.00 

3241.68 

3308.01 

3375-02 

3442.72 

3511-14 

.00 

.02 

3047.79 

3112.24 

3177.30 

3243-00 

3309.35 

3376.37 

3444-08 

3512.51 

.02 

.04 

3049.07 

3H3-54 

3178.61 

3244-32 

3310.38 

3377-72 

3445-44 

3513-88 

.04 

.06 

3050.36 

3H4.83 

3179.92 

3245.64 

3312.02 

3379.06 

3446.81 

3415.26 

.06 

.08 

3051-64 

3116.13 

3181.23 

3246.96 

3313.35 

338o.4i 

3448.17 

3516.64 

.08 

.10 

3052.92 

3H7.42 

3182.54 

3248.28 

3314.69 

3381.76 

3449-53 

3518.02 

.IO 

.12 

3054.21 

3118.72 

3183.85 

3249-61 

3316.02 

3383-11 

3450.89 

3519-39 

.12 

•14 

3055.49 

3120.02 

3I85.I5 

3250.93 

3317.36 

3384.46 

3452.26 

3520.77 

•14 

.16 

3056.78 

3121.31 

3186.46 

3252.25 

3318.69 

3385.81 

3453-62 

3522.15 

.16 

.18 

3058.06 

3122.61 

3187.77 

3253.57 

3320.03 

3387.16 

3454-98 

3523.53 

.18 

.20 

3059.35 

3I23-9I 

3189.08 

3254-89 

3321.36 

3388.51 

3456.35 

3524.90 

.20 

.22 

3060.63 

3125-20 

3190.39 

3256.22 

3322.70 

3389.85 

3457-71 

3526.28 

.22 

.24 

3061.92 

3126.50 

3191.70 

3257.54 

3324.03 

3391-21 

3459.07 

3527.66 

•24 

.26 

3063.20 

3127-80 

3I93.0I 

3258.86 

3325.37 

3392.56 

3460.44 

3529.04 

.26 

.28 

3064.49 

3129.10 

3194.32 

3260-  .19 

3326.71 

3393-91 

3461.80 

3530.42 

.28 

30 

3065-78 

3130.40 

3195.63 

3261.51 

3328.05 

3395.26 

3463.17 

3531.80 

30 

32 

3067.06 

3131.69 

3196.95 

3262.83 

3329.38 

3396.61 

3464.53 

3533.18 

32 

34 

3068.35 

3132.99 

3198.26 

3264.16 

3330.72 

3397-97 

3465.90 

3534.56 

•34 

.36 

3069.64 

3U4.29 

3199-57 

3265.48 

3332.06 

3399-31 

3467.27 

3535-94 

-36 

.38 

3070.92 

3135.59 

3200.88 

3266.81 

3333-40 

3400.66 

3468.63 

3537-32 

.38 

.40 

3072.21 

3136.89 

3202.19 

3268.14 

3334-74 

3402.02 

3470.00 

3538.70 

.40 

.42 

3073.50 

3138.19 

3203.51 

3269.46 

3336.08 

3403-37 

3471-37 

3540.09 

•42 

•44 

3074.79 

3139-49 

3204.82 

3270.79 

3337-41 

3404.72 

3472.73 

3541-47 

•44 

.46 

3076.08 

3140.79 

3206.13 

3272.11 

3338.75 

3406.08 

3474-10 

3542.85 

.46 

.48 

3077.36 

3142.09 

3207.44 

3273.44 

3340.09 

3407.43 

3475-47 

3544-23 

-48 

•  50 

3078.65 

3143.39 

3208.76 

3274.76 

3341-43 

3408.78 

3476.84 

3545.62 

•So 

•52 

3079-94 

3144.69 

3210.07 

3276.09 

3342.77 

3410.14 

3478.20 

3547.00 

•  52 

-54 

3081.23 

3146.00 

3211.39 

3277-42 

3344-11 

34H.49 

3479-57 

3548.38 

•54 

.56 

3082.52 

3147.30 

3212.70 

3278.75 

3345.46 

3412.85 

3480.94 

3549.76 

•56 

.58 

3083.81 

3148.60 

3214.01 

3280.07 

3346.80 

3414.20 

3482.31 

3551.15 

•  58 

.60 

3085.10 

3149.90 

3215.33 

3281.40 

3348.14 

3415.56 

3483.68 

3552.53 

.60 

.62 

3086.39 

3151.20 

3216.64 

3282.73 

3349-48 

34I6.9I 

3485.05 

3553-92 

.62 

.64 

3087.68 

3152.51 

3217-96 

3284.06 

3350.82 

3418.27 

3486.42 

3555-30 

.64 

.66 

3088.97 

3I53.8I 

3219.27 

3285.39 

3352.16 

3419.62 

3487.79 

3556.69 

.66 

.68 

3090.26 

3i55.li 

3220.59 

3286.72 

3353-51 

3420.98 

3489.16 

3558.07 

.68 

•70 

3091.55 

3156.42 

3221.91 

3288.04 

3354-85 

3422.34 

3490.53 

3559.46 

.70 

•72 

3092.84 

3157.72 

3223.22 

3289.37 

3356.19 

3423-69 

349L90 

3560.84 

•72 

•74 

3094.13 

3159-02 

3224.54 

3290.70 

3357-53 

3425.05 

3493-27 

3562.23 

•74 

.76 

3095.43 

3160.33 

3225.86 

3292.03 

3358.88 

3426.41 

3494.65 

3563.62 

•76 

.78 

3096.72 

3161.64 

3227.17 

3293.36 

3360.22 

3427.77 

3496.02 

3565.01 

.78 

.80 

3098.01 

3162.94 

3228.49 

3294.69 

3361.57 

3429.12 

3497-39 

3566.39 

.80 

.82 

3099-30 

3164.24 

3229.81 

3296.03 

3362.91 

3430.48 

3498.77 

3567.78 

.82 

.84 

3100.60 

3165.55 

3231-13 

3297.36 

3364.26 

3431.84 

3500.14 

3569.17 

.84 

.86 

3101.89 

3166.85 

3232.45 

3298.69 

3365.60 

3433-20 

3501.51 

3570.56 

.86 

.88 

3103.18 

3168.16 

3233.76 

3300.02 

3366.94 

3434-57 

3502.89 

3571-95 

.88 

.90 

3104.48 

3169.46 

3235.08 

3301.35 

3368.29 

3435.92 

3504.26 

3573-33 

90 

.92 

3105-77 

3170.77 

3236.40 

3302.68 

3369.64 

3437-28 

3505.63 

3574-72 

92 

•94 

3107  .  06 

3172.08 

3237.72 

3304.02 

3370.98 

3438.64 

3507.01 

3576.li 

•94 

.96 

3108.36 

3173.38 

3239-04 

3305.35 

3372.33 

3440.00 

3508.38 

3577-50 

•96 

-98 

3109-65 

3174.69 

3240.36 

3306.68 

3373.67 

3441.36 

3509.76 

3578.89 

•98 

1.00 

3110.95 

3176.00 

3241.68 

3308.01 

3375-02 

3442.72 

35II-I4 

3580.28 

1.00 

(27) 


TABLE  II.  —  (Continued) 


I 

64° 

65° 

66° 

67° 

68° 

69° 

?o° 

71° 

/ 

.00 

3580.28 

3650.19 

3720.88 

3792.37 

3864.70 

3937-88 

4011.94 

4086.92 

.00 

.02 

3581.67 

3651-60 

3722.30 

3793-81 

3866.15 

3939-35 

4013.43 

4088.43 

.02 

.04 

3583-06 

3653.00 

3723.72 

3795-25 

3867.61 

3940.82 

4014.93 

4089.94 

.04 

.06 

3584-46 

3654.41 

3725.15 

3796.69 

3869.06 

3942.30 

4016.42 

4091.45 

.06 

.08 

3585.85 

3655.82 

3726.57 

3798.13 

3870.52 

3943-77 

4017-91 

4092.96 

.08 

.10 

3587.24 

3657.22 

3727.99 

3799-57 

3871-98 

3945.25 

4019.40 

4094-47 

.10 

.12 

3588.63 

3658.63 

3729.41 

3801.01 

3873.43 

3946.72 

4020.89 

4095.98 

.12 

.14 

3590.02 

3660.04 

3730.84 

3802.45 

3874.89 

3948.19 

4022.39 

4097.49 

•14 

.16 

3591-42 

3661.45 

3732.26 

3803.89 

3876-35 

3949-67 

4023.88 

4099.00 

.16 

.18 

3592.81 

3662  86 

3733-69 

3805.33 

3877-81 

3951.15 

4025.37 

4100.51 

.18 

.20 

3594-20 

3664.26 

3735.11 

3806.77 

3879.27 

3952.62 

4026.86 

4102.03 

.20 

.22 

3595.6o 

3665.67 

3736.54 

3808.21 

3880.72 

3954-10 

4028.36 

4103.54 

.22 

.24 

3596.99 

3667.08 

3737.96 

3809.65 

3882.18 

3955-57 

4029.85 

4105.05 

.24 

.26 

3598.39 

3668.49 

3739-39 

3811.10 

3883.67 

3957-05 

4031.35 

4106.57 

.26 

.28 

3599.78 

3669.88 

3740.81 

3812.54 

3885-10 

3958.53 

4032.84 

4108.08 

.28 

30 

3601  .  17 

3671.31 

3742.24 

3813.98 

3886.56 

3960.00 

4034-34 

4109.59 

•30 

32 

3602.57 

3672.72 

3743.67 

3815.42 

3888.02 

3961.48 

4035-84 

4111.  ii 

•32 

•  34 

3603.96 

3674.13 

3745-09 

3816.87 

3889-48 

3962.96 

4037-33 

4112.62 

•  34 

•  36 

3605.36 

3675.55 

3746.52 

3818.31 

3890.94 

3964.44 

4038.83 

4114.14 

.36 

.38 

3606.76 

3676.96 

3747-95 

3819.76 

3892.40 

3965.92 

4040.33 

4115.65 

.38 

.40 

3608.15 

3678.37 

3749.38 

3821.20 

3893.87 

3967.40 

4041.82 

4"7.I7 

.40 

.42 

3609.55 

3679.78 

3750.81 

3822.65 

3895.33 

3968.88 

4043-32 

4118.69 

•  42 

•  44 

3610.95 

368l  .  20 

3752.24 

3824.09 

3896.79 

3970.36 

4044.82 

4120.20 

-44 

.46 

3612.34 

3682.61 

3753-66 

3825.54 

3898.25 

3971.84 

4046.32 

4121.72 

.46 

-48 

3613.74 

3684.02 

3755.09 

3826.98 

3899.73 

3973-32 

4047.82 

4123.24 

-48 

•  50 

3615-14 

3685.43 

3756.52 

3828.43 

3901  .  18 

3974-So 

4049.32 

4124.76 

•  So 

52 

3616.54 

3686.85 

3757-95 

3829.88 

3902.64 

3976.28 

4050.82 

4126.28 

•  52 

•  54 

3617.94 

3688.26 

3759.38 

3831.32 

3904.li 

3977.76 

4052.32 

4127.80 

•  54 

.56 

3619.34 

3689.68 

3760.81 

3832.77 

3905.57 

3979-24 

4053-82 

4129.31 

.56 

.58 

3620.74 

3691.09 

3762.24 

3834-22 

3907-04 

3980.73 

4055.32 

4130.83 

.58 

.60 

3622.14 

3692.51 

3763.68 

3835.67 

3908.50 

3982.21 

4056.82 

4132.35 

.60 

.62 

3623.54 

3693.92 

3765." 

3837.12 

3909.97 

3983.69 

4058.32 

4133.87 

.62 

.64 

3624.93 

3695.34 

3766.54 

3838.56 

3911-43 

3985.18 

4059-82 

4135.40 

.64 

.66 

3626.34 

3696.76 

3767.97 

3840.01 

3912.90 

3986.66 

4061.32 

4136.92 

.66 

.68 

3627.74 

3698.17 

3769.41 

3841.46 

3914.37 

3988.15 

4062.83 

4138.44 

.68 

.70 

3629.14 

3699.59 

3770.84 

3842.91 

3915.83 

3989.63 

4064.33 

4139-96 

•70 

.72 

3630.54 

3701  .  oi 

3772.27 

3844.36 

3917.30 

3991-12 

4065.83 

4141.48 

.72 

.74 

3631.94 

3702.42 

3773-71 

3845.81 

3918.77 

3992.60 

4067.34 

4143.00 

.74 

.76 

3633.34 

3703.84 

377S-  14 

3847-26 

3920.24 

3994.09 

4068.84 

4144-53 

.76 

-78 

3634.74 

3705.26 

3776.57 

3848.71 

3921.70 

3995-57 

4070.34 

4146.05 

.78 

.80 

3636.15 

3706.68 

3778.01 

3850.17 

3923.17 

3997-06 

4071.85 

4148.57 

.80 

.82 

3637.55 

3708.10 

3779-44 

3851-62 

3924.64 

3998.55 

4073.36 

4149.10 

.82 

.84 

3638.95 

3709.52 

3780.88 

3853.07 

3926.li 

4000.03 

4074-86 

4150.62 

.84 

.86 

3640.36 

3710.93 

3782.31 

3854.52 

3927.58 

4001.52 

4076.37 

4152.15 

.86 

.88 

3641-76 

3712.35 

3783.75 

3855.97 

3929.05 

4003  .  oi 

4077-87 

4153.67 

.88 

.90 

3643-16 

3713.77 

3785.19 

3857.43 

3930.68 

4004.50 

4079.38 

4155.20 

.90 

.92 

3644.57 

3315.19 

3786.62 

3858.88 

3931-99 

4005.99 

4080.89 

4156.73 

.92 

•  94 

3645.97 

3716.61 

3788.06 

3860.33 

3933.46 

4007.48 

4082.39 

4158.25 

-94 

.96 

3647.38 

3718.04 

3789.50 

3861.79 

3934-94 

4008.96 

4083.90 

4159.78 

.96 

•  98 

3648.78 

3719.46 

3790.93 

3863.24 

3936.41 

4010.45 

4085.41 

4161.31 

.98 

1.00 

3650.19 

3720.88 

3792.37 

3864.70 

3937-88 

4011.94 

4086.92 

4162.83 

1.00 

(28) 


TABLE   II.  —  (Continued) 


I 

72° 

73° 

74° 

75° 

76° 

77° 

78° 

/ 

.00 

4162.83 

4239.72 

43i7.6o 

4396.52 

4476.50 

4557.56 

4639.78 

.00 

.02 

4164.36 

4241.27 

43I9.I7 

4398.11 

4478.10 

4559-20 

4641.44 

.02 

•  04 

4165-89 

4242.81 

4320.74 

4399-69 

4479-72 

4560.84 

4643.09 

.04 

.06 

4167.42 

4244  .,36 

4322.31 

4401.28 

4481.33 

4562.47 

4644.75 

.06 

.08 

4168.95 

4245.9I 

4323.88 

4402.87 

4482.94 

4564.10 

4646.41 

.08 

.10 

4170.48 

4247.46 

4325.45 

4404.46 

4484.55 

4565.74 

4648.06 

.10 

.12 

4172.01 

4249.01 

4327.02 

4406.06 

4486.16 

4567.37 

4649.72 

.12 

.14 

4173-54 

4250.56 

4328.59 

4407.65 

4487.78 

4569-01 

4651.38 

•14 

.16 

4175.07 

4252.11 

4330.16 

4409.24 

4489.39 

4570.65 

4653-04 

.16 

.18 

4176.60 

4253.66 

4331-73 

4410.83 

4491-01 

4572.28 

4654.70 

.18 

.20 

4178.13 

4255.21 

4333-30 

4412.42 

4492.62 

4573-92 

4656.36 

.20 

.22 

4179-66 

4256.77 

4334.87 

4414.02 

4494-23 

4575.56 

4658.02 

.22 

.24 

4181.20 

4258.32 

4336.45 

4415.63 

4495-85 

4577-19 

4659-68 

•34 

.26 

4182.73 

4259.87 

4338.02 

4417.21 

4497-47 

4578.83 

4661.34 

.26 

.28 

4184  .  26 

4261.42 

4339-59 

4418.80 

4499-09 

4580.47 

4663.01 

.28 

•30 

4185.80 

4262.98 

4340.97 

4420.39 

4500.70 

4582.11 

4664.67 

•30 

33 

4187.33 

4264.53 

4342.74 

4421-99 

4502.32 

4583.75 

4666.33 

•33 

•  34 

4188.87 

4266.09 

4344-32 

4423.59 

4503.94 

4585.39 

4668.00 

•  34 

-36 

4190.40 

4267.64 

4345.89 

4425-18 

4505.55 

4587.03 

4669.66 

-36 

•  38 

4I9L93 

4269.19 

4347-47 

4426.78 

4507.17 

4588.67 

4671.32 

.38 

.40 

4193.47 

4270.85 

4349-04 

4428.38 

4508.79 

4590.31 

4672.99 

.40 

•  43 

4195.01 

4272.31 

4350.62 

4429.97 

4510.41 

4591.96 

4674.65 

•43 

•  44 

4196.54 

4273-86 

4352.19 

4431-57 

4512.03 

4593.6o 

4676.32 

•  44 

.46 

4198.08 

4275.42 

4353-77 

4433-17 

4513.65 

4595.24 

4677.99 

.46 

.48 

4199.62 

4276.98 

4355-35 

4434-77 

4515.27 

4596.89 

4679.65 

.48 

•  50 

4201.15 

4278.53 

4356.93 

4436.37 

4516.89 

4598.53 

4681.32 

•  So 

•  53 

4202  .  69 

4280.09 

4358.51 

4437-97 

45I8.5I 

4600.18 

4682.99 

•  53 

•  54 

4204.23 

4281.65 

4360.08 

4439-57 

4520.14 

4601.82 

4684.66 

•  54 

.56 

4205.77 

4283.21 

4361.66 

444LI7 

4521.76 

4603.47 

4686.32 

-56 

•  58 

4207.31 

4284.77 

4363.24 

4442.77 

4523.38 

4605.19 

4687.99 

.58 

.60 

4208.85 

4286.33 

4364.81 

4444-37 

4525.01 

4606.76 

4689.67 

.60 

.62 

4210.39 

4287.89 

4366.40 

4445-97 

4526.63 

4608  .  40 

4691.33 

.62 

-64 

42H.93 

4289.45 

4367.98 

4447.58 

4528.25 

4610.05 

4693-00 

.64 

.66 

4213.47 

4291.01 

4369.56 

4449-18 

4529.88 

4611.70 

4694-68 

.66 

.68 

4215.01 

4292.57 

4371.15 

4450.78 

4531.50 

4613.35 

4696.35 

.68 

.70 

4216.55 

4294.13 

4372.73 

4452-39 

4533-13 

4614.99 

4698.02 

.70 

.73 

4218.09 

4295.69 

4374-31 

4453-99 

4534.76 

4616.64 

4699.69 

.73 

•  74 

4219.63 

4297.25 

4375-90 

4455-59 

4536.38 

4618.29 

4701.37 

•  74 

.76 

4221.18 

4298.82 

4377.48 

4457-20 

4538.01 

4619.94 

4703.04 

-76 

•  78 

4222.72 

4300.38 

4379-06 

4458.81 

4539.64 

4621.59 

4704.71 

.78 

.80 

4224.26 

4301.94 

4380.65 

4460.41 

4541.27 

4623.24 

4706.39 

.80 

.82 

4225.81 

4303.51 

4382.23 

4462  .  02 

4542.89 

4624.90 

4708.06 

.82 

.84 

4227.35 

4305.07 

4383-82 

4463.62 

4544-52 

4626.55 

4709.74 

.84 

.86 

4228.90 

4306.64 

4385.40 

4465.23 

4546.15 

4628.20 

47II-4I 

.86 

.88 

4230.44 

4308.20 

4386.99 

4466.84 

4547.78 

4629.85 

4713.09 

.88 

.90 

4231.98 

4309-77 

4388.58 

4468.45 

4549.41 

4631.51 

4714-77 

.90 

93 

4233.53 

43H.33 

4390.16 

4470.05 

4551.04 

4633-16 

4716.45 

•93 

•  94 

4235.08 

4312.90 

4391-75 

4471-66 

4552.67 

4634-81 

4718.12 

94 

.96 

4236.62 

4314.46 

4393-34 

4473-27 

4554-31 

4636.47 

4719.80 

•  96 

.98 

4238.17 

4316.03 

4394-93 

4474.88 

4555-94 

4638.12 

4721.48 

-98 

1.00 

4239.72 

4317.60 

4396.52 

4476.50 

4557.56 

4639.78 

4723-16 

1.00 

(29) 


TABLE  II.  —  (Continued) 


I 

79° 

80° 

81° 

82° 

83° 

84° 

85° 

I 

.00 

4723.16 

4807.85 

4893.58 

4980.71 

5069.17 

5I59.00 

5250.26 

.00 

.02 

4724.84 

4809.45- 

4895-31 

4982.47 

5070.95 

5160.80 

5252-10 

.02 

.04 

4726.52 

4811.16 

4897.04 

4984-22 

5072.73 

5162.62 

5253.94 

.04 

.06 

4728.20 

4812.86 

4898.78 

4985.98 

5074.52 

5164.43 

5255.78 

.06 

.08 

4729-88 

4814.57 

4900.51 

4987.74 

5076.30 

5166.25 

5257.62 

.08 

.10 

4731.56 

4816.27 

4902.24 

4989-49 

5078.09 

5168-06 

5259.46 

.10 

.12 

4733-25 

4817.98 

4903.97 

4991-25 

5079.87 

5169.88 

5261.30 

.12 

.14 

4734-93 

4819.69 

4905.70 

4993-01 

5081.66 

5171-69 

5263.15 

•14 

.16 

4736.6i 

4821.40 

4907.44 

4994-77 

5083.45 

5173.50 

5264.99 

.16 

.18 

4738.29 

4823.10 

4909.17 

4996-53 

5085.23 

5175-32 

5266.84 

.18 

.20 

4739-98 

4824.81 

4910.90 

4998-29 

5087.02 

5I77-I4 

5268.68 

.20 

.22 

4741.66 

4826  .  52 

4912.64 

5000.05 

5088.81 

5178-95 

5270.53 

.22 

.24 

4743-35 

4828.23 

4914.37 

5001.82 

5090.60 

5180.77 

5272.38 

•24 

.26 

4745-03 

4829.94 

4916.11 

5003.58 

5092.39 

5182.59 

5274.22 

.26 

.28 

4746.72 

4831-65 

4917.83 

5005.34 

5094.18 

5184-41 

5276.07 

.28 

-30 

4748.41 

4833.36 

4919.58 

5007.10 

5095.97 

5186.23 

5277.92 

•30 

•32 

4750.09 

4835.08 

4921.32 

5008.87 

5097.76 

5188.05 

5279.77 

•32 

•  34 

4751.78 

4836.79 

4923-06 

5010.63 

5099.55 

5189.87 

5281.62 

34 

.36 

4753-47 

4838.50 

4924-80 

5012.40 

5101.34 

5191-69 

5283.47 

.36 

.38 

4755-16 

4840  .  22 

4926.54 

5014.16 

5103.14 

5193.51 

5285.32 

•  38 

.40 

4756.85 

4841.93 

4928.28 

5015.93 

5104.93 

5195.33 

5287.17 

.40 

.42 

4758.54 

4843.64 

4930.02 

5017.70 

5106.73 

5197.15 

5289  .  02 

.42 

44 

4760.23 

4845.36 

493I-76 

5019.46 

5108.52 

5198.98 

5290.87 

•  44 

•  46 

4761.92 

4847.08 

4933-50 

5021.23 

5110.32 

5200.80 

5292.73 

.46 

.48 

4763-61 

4848.79 

4935.24 

5023.00 

5112.11 

5202.62 

5294.58 

•  48 

•50 

4765.30 

4850.51 

4936.98 

5024.77 

5H3.9I 

5204.45 

5296.42 

50 

•  52 

4766.99 

4852.22 

4938.73 

5026.54 

5H5.70 

5206.27 

5298.29 

-52 

•  54 

4768.69 

4853.94 

4940.47 

5028.31 

5H7.50 

5208.10 

5300.13 

-54 

•  56 

4770.38 

4855.66 

4942.21 

5030.08 

5II9.30 

5209.93 

5302  .  oo 

-56 

-58 

4772.07 

4857.38 

4943.96 

5031.85 

5121.10 

5211.75 

5303.86 

-58 

.60 

4773-76 

4859.10 

4945-70 

5033.62 

5122.90 

5213.58 

5305.71 

.60 

.62 

4775-46 

4860.82 

4947-45 

5035.39 

5124.70 

52I5.4I 

5307.57 

.62 

.64 

4777-15 

4862.54 

4949-19 

5037.17 

5126.50 

5217.24 

5309.43 

-64 

.66 

4778.85 

4864.26 

4950.94 

5038.94 

5128.30 

5219-07 

5311.29 

.66 

.68 

4780.55 

4865.98 

4952.68 

5040.71 

5130.10 

5220.90 

5313.15 

.68 

.70 

4782.24 

4867.70 

4954-43 

5042.49 

5131.90 

5222.73 

5315.01 

-70 

•  72 

4783.94 

4869.42 

4956.18 

5044-26 

5133.70 

5224.56 

5316.87 

-72 

•  74 

4785.64 

4871.14 

4957-93 

5046.04 

5135.51 

5226.39 

5318.73 

-74 

.76 

4787.33 

4872.87 

4959-68 

5047.81 

5I37.3I 

5228.22 

5320.59 

-76 

.78 

4789.03 

4874.59 

4961.63 

5049.59 

5139-12 

5230.06 

5322.46 

-78 

.80 

4790.73 

4876.31 

4963-18 

5051.37 

5140.92 

5231.89 

5324.32 

.80 

.82 

4792.43 

4878.04 

4964.93 

5053.14 

5142-73 

5233.72 

5326.18 

.82 

.84 

4794-13 

4879.76 

4966.68 

5054.92 

5144.53 

5235.56 

5328.05 

-84 

.86 

4795.83 

4881.49 

4968.43 

5056.70 

5146.34 

5237-39 

5329.91 

.86 

.88 

4797-53 

4883.22 

4970.18 

5058.48 

5148.15 

5239-23 

5331.78 

.88 

•90 

4799-23 

4884.94 

4971.94 

5060.26 

5149-95 

5241.07 

5333.65 

-90 

.92 

4800.93 

4886.67 

4973.69 

5062.04 

5151.76 

5242.90 

5335.51 

-92 

•  94 

4802  .  64 

4888.40 

4975-44 

5063.82 

5153-57 

5244.74 

5337.38 

-94 

•  96 

4804.34 

4890.13 

4977.20 

5065.60 

5155.38 

5246.58 

5339.25 

-96 

.98 

4806  .  04 

4891.85 

4978.95 

5067-38 

5157.19 

5248.42 

5341-12 

-98 

1.00 

4807.85 

4893.58 

4980.71 

5069.17 

5159-00 

5250.26 

5342.99 

1  00 

(30) 


TABLE   II.  —'(Continued) 


I 

86° 

87° 

88° 

89° 

90° 

9i° 

92° 

/ 

.00 
.02 

.04 
.06 

.08 

.10 

.12 

.14 
.16 
.18 

.20 

.22 

.24 
.26 

.28 
•30 
32 

•34 
.36 
.38 
.40 

.42 
•44 
.46 

-48 
•So 

•  52 

•54 
.56 
•58 
.60 
.62 
.64 
.66 

.68 

-70 

.72 

•74 
-76 
.78 
.80 
.82 
.84 
.86 

.88 
.90 
.92 

•94 
.96 
.98 
1.00 

5342.99 

5437-24 

5533-06 

5630.51 

5729.65 

5830.53 

5933-23 

.00 

.02 

.04 

.06 
.08 

.10 
.12 

.14 
.16 
.18 

.20 

.22 

•24 
.26 

.28 
•30 
•32 

•34 
.36 
.38 
.40 
•42 
•44 
.46 

.48 
•SO 
-52 

•54 
•56 
•58 
.60 
.62 
.64 
.66 

.68 
•70 
.72 

•74 
.76 
.78 
.80 
.82 
.84 
.86 

.88 
.90 
.92 

•94 
•96 
•98 
1.00 

5344.8s 
5346.73 
5348.6o 

5350.46 
5352.34 
5354-21 

5356.09 
5357.96 
5359.84 

5439-14 
544L04 
5442.94 

5444.84 
5446.75 
5448.65 

5450.55 
5452.46 
5454-37 

5534-99 
5536.92 
5538.86 

5540.79 
5542-73 
5544.67 
5546.6o 
5548.54 
5550.48 

5632.48 
5634.44 
5636.41 
5638.38 
5640.35 
5642.32 

5644.29 
5646.26 
5648.23 

5731.65 
5733-65 
5735.65 

5737-65 
5739-66 
5741-66 

5743.67 
5745.67 
5747-68 

5832.57 
5834-61 
5836.64 

5838.68 
5840.72 
5842.76 
5844.80 
5846.84 
5848.88 

5935-30 
5937-37 
5939-45 

5941.52 
5943-60 
5945.67 

5947-75 
5949-83 
5951-91 

536I.7I 

5456.27 

5552.42 

5650.20 

5749.69 

5850.93 

5953-99 

5363.59 
5365.46 
5367.34 
5369.22 
5371-10 
5372.98 
5374-86 
5376.74 
5378.62 

5458.18 
5460.09 
5462  .  oo 

5463.91 
5465.81 
5467.72 

5469-64 
5471-55 
5473.46 

5554.36 
5556.30 
5558.24 

5560.18 
5562.12 
5564.06 

5566.01 
5567.95 
5569.90 

5652.18 
5654.15 
5656.12 

5658.10 
5660.07 
5662.05 

5664.03 
5666.00 
5667.98 

5751.69 
5753-70 
5755-71 
5757-72 
5759-73 
5761.74 

5763.75 
5765.76 
5767.78 

5852.97 
5855-01 
5857-05 

5859.10 
5861.15 
5863.20 

5865.24 
5867.29 
5869.34 

5956.07 
5958.15 
5960.23 

5962.31 
5964.40 
5966.48 

5968.56 
5970.6s 
5972.74 

5380.50 

5475.37 

5571.84 

5669.96 

5769.79 

5871.38 

5974-82 

5382.38 
5384-26 
5386.15 
5388.03 
5389.92 
539i.8o 

5393.69 
5395-57 
5397.46 

5474.29 
5479-20 
5481.12 

5483.03 
5484.95 
5486.86 

5488.78 
5490.70 
5492.62 

5573-79 
5575-73 
5577-68 

5579.63 
5581.58 
5583.53 
5585.48 
5587.43 
5589.38 

5671.94 
5673.92 
5675.90 
5677-88 
5679.87 
5681.85 

5683.83 
5685.82 
5687.80 

5771.80 
5773-82 
5775-84 

5777.85 
5779-87 
5781.89 

5783.91 
5785-93 
5787.95 

5873.44 
5875.49 
5877.54 
5879-60 
5881.65 
5883.71 

5885.76 
5887.82 
5889.87 

5976.91 
5979-00 
5981-09 
5983.18 
5985.27 
5987.36 

5989.46 
5991-55 
5993.64 

5399-35 

5494-54 

5591-33 

5689.79 

5789.97 

5891.93 

5995-74 

5401.24 
5403.13 

5405.02 

5406.91 
5408.80 
5410.69 

5412.58 
5414.47 
5416.37 

5496.46 
5498.38 
5500.30 

55O2  .  22 
5504.14 
5506.07 

5507.99 
5509.92 
55H.84 

5593.29 
5595.24 
5597-19 

5599-15 
5601.10 
5603.06 

5605.01 
5606.97 
5608.93 

5691-78 
5693.76 
5695.75 

5697.74 
5699.73 
5701-72 

5703.71 
5705.70 
5707.69 

5791-99 
5794-01 
5796.03 
5798.06 
5800.08 
5802.11 

5804.13 
5806.16 
5808.19 

5893.98 
5896.05 
5898.10 

5900.16 
5902.23 
5904-29 

5906.35 
5908.41 
5910.48 

5997.83 
5999-93 
6002.02 

6004.12 
6006.22 
6008.32 

6010.42 
6012.52 
6014.62 

5418.26 

5513.77 

5610.89 

5709.68 

5810.21 

5912-54 

6016.72 

5420.16 
5422.05 
5423.95 

5425.84 
5427.74 
5429.64 

5431-54 
5433-44 
5435-34 

5515.69 
5517.62 
5519.55 

5521.48 
5523.40 
5525.33 
5527.26 
5529.19 
5531.13 

5612.85 
5614.81 
5616.77 

56i8.73 
5620.69 
5622.65 

5624.62 
5626.58 
5628.55 

5711-68 
5713.67 
5715.67 
5717.66 
5719-66 
5721.65 

5723.65 
5725.65 
5727.65 

5812.24 
5814-27 
5816.30 

5818.33 
5820.37 
5822.40 

5824.43 
5826.47 
5828.50 

59i4.6i 
5916.67 
5918.74 
5920.81 
5922.87 
5924.94 

5927.01 
5929-08 
5931.15 

6018.83 
6020.93 
6023  .  04 

6025.14 
6027.25 
6029.35 
6031.46 
6033-57 
6035.68 

5437-24 

5533.06 

5630.51 

5729.65 

5830.53 

5933-23 

6037.79 

(31) 


TABLE   It.  —  (Continued) 


I 

93° 

94° 

95° 

96° 

97° 

98° 

99° 

7 

.00 
.02 

.04 
.06 

6037.79 

6144.30 

6252.82 

6363.42 

6476.19 

6591.21 

6708  .  56 

.00 

.02 
.04 
.06 

6039.90 
6042  .  01 
6044.12 

6146.45 
6148.60 
6150.75 

6255  .  01 
6257.20 
6259.39 

6365.66 
6367.89 
6370.13 

6478.47 
6480.75 
6483.03 

6593.53 
6595-86 
6598.18 

6710.93 
6713.30 
6715.67 

.08 

.10 
.12 

6046.25 
6048.35 
6050.47 

6152.90 
6155.06 
6157-21 

6261.59 
6263.78 
6265.98 

6372.36 
6374.60 
6376.84 

6485.31 
6487.59 
6489.87 

6600.51 
6602.84 
6605.16 

6718.05 
6720.42 
6722.80 

.08 
.10 
.12 

.14 
.16 
.18 

.20 

.22 

.24 
.26 

6052.58 
6054.70 
6056.82 

6i59.37 
6161.52 
6163.68 

6268.16 
6270.37 
6272.57 

6379-08 
6381.32 
6383.56 

6492.16 
6494.44 
6496.73 

6607.49 
6609.83 
6612.16 

6725.18 
6727.56 
6729.93 

•14 
.16 
.18 

.20 

.22 

.24 
.26 

6058.96 

6165.84 

6274.77 

6385.80 

6499-01 

6614.49 

6732.32 

6061.05 
6063.17 
6065.29 

6168.00 
6170.15 
6172.32 

6276.97 
6279.17 
6281.37 

6388.04 
6390-29 
6392.53 

6501.30 
6503.59 
6505.88 

6616.82 
6619.17 
6621.49 

6734.70 
6737.08 
6739.46 

.28 
30 
32 

6067.42 
6069.55 
6071.66 

6174-48 
6176.64 
6178.80 

6283.57 
6285.78 
6287.98 

6394.77 
6397-02 
6399.27 

6508.17 
6510.46 
6512.75 

6623.83 
6626.16 
6628.50 

6741-85 
6744.23 
6746.62 

.28 
30 
•32 

•34 
36 
•38 
.40 
.42 
•44 
•46 

6073.78 
6075.91 
6078.03 

6180.96 
6183.13 
6185.29 

6290.18 
6292.39 
6294.60 

6401  .  52 
6403.76 
6406.01 

6515.04 
6517.33 
6519.63 

6630.84 
6633.18 
6635  .  52 

6749.00 
6751.39 
6753.78 

•34 
.36 
-38 
.40 

•42 
•44 
.46 

6080.16 

'  6187.46 

6296.80 

6408.26 

6521.92 

6637.86 

6756.17 

6082.28 
6084.41 
6086.54 

6189.63 
6191.79 
6193.96 

6299.01 
6301.22 
6303.43 

6410.52 
6412.77 
6415.02 

6524.22 
6526.62 
6528.81 

6640.21 
6642.55 
6644.90 

6758.56 
6760.96 
6763.35 

•48 
•  50 
•52 

6088.67 
6090.80 
6092.93 

6196.13 
6198.30 
6200.47 

6305.64 
6307.85 
6310.07 

6417.28 
64I9.53 
6421.79 

6531-11 
6533.41 
6535.71 

6647.24 
6649.59 
6651.93 

6765.74 
6768.14 
6770.53 

.48 
•50 
•52 

•54 
-56 
•58 
.60 
.62 
•64 
.66 

6095.06 
6097.19 
6099.32 

6202.64 
6204.81 
6206.99 

6312.28 
6314.49 
6316.71 

6424  .  04 
6426.30 
6428.56 

6538.02 
6540.32 
6542.62 

6654.28 
6656.63 
6658.98 

6772.93 
6775.33 
6777.73 

•54 
•56 
.58 
.60 
.62 
.64 
.66 

6101.46 

6209.16 

6318.92 

6430.82 

6544.93 

6661.33 

6780.12 

6103.59 
6105.73 
6107.86 

6211.34 
6213.51 
6215.69 

6321.14 
6323.36 
6325.58 

6433-08 
6435.34 
6437.60 

6547.23 
6549.54 
6551.85 

6663.69 
6666.04 
6668.39 

6782.53 
6784.93 
6787.33 

.68 
70 
.72 

6110.00 
6112.14 
6114.28 

6217.87 
6220.04 
6222.22 

6327.80 
6330.02 
6332.24 

6439.86 
6442.13 
6444.39 

6554.15 
6556.46 
6558.77 

6670.75 
6673.10 
6675.46 

6789.73 
6792.14 
6794.55 

.68 
.70 

•72 

•74 
•76 
-78 
.80 
.82 
.84 
.86 

6116.42 
6118.55 
6120.70 

6224.40 
6226.58 
6228.77 

6334.46 
6336.68 
6338.90 

6446.66 
6448.93 
6451-19 

6561.08 
6563-39 
6565.71 

6677.82 
6680.18 
6682.54 

6796.95 
6799.36 
6801.77 

•74 
.76 
.78 
.80 
.82 
.84 
.86 

6122.84 

6230.95 

634LI3 

6453.46 

6568.02 

6684.90 

6804.18 

6124.98 
6127.12 
6129.27 

6233.13 
6235-31 
6237.50 

6343.35 
6345.58 
6347-81 

6455.73 
6458  .  oo 
6460.27 

6570.34 
6572.65 
6574.97 

6687.26 
6689.62 
6691.99 

6806.59 
6809.00 
6811.41 

.88 
.90 
•92 

6131.42 
6133.56 
6I35-70 

6239-69 
6241.87 
6244.06 

6350.04 
6352.26 
6354.49 

6462.54 
6464.81 
6467.09 

6577.29 
6579-6o 
6581.92 

6694.35 
6696.72 
6699.08 

6813.83 
6816.24 
6818.66 

.88 
.90 

.92 

•94 
•96 
•98 
1.00 

6137.85 
6140.00 
6142.15 

6246.25 
6248.44 
6250.63 

6356.72 
6358.96 
6361  .  19 

6469.36 

6471.64 
6473.91 

6584.24 
6586.56 
6588.89 

6701.45 
6703.82 
6706.19 

6821.07 
6823.49 
6825.91 

•94 
•96 
•98 
1.00 

6144.30 

6252.82 

6363.42 

6476.19 

6591-21 

6708.56 

6828.33 

(32) 


TABLE  III.  —  TANGENT  DISTANCE  CORRECTIONS 
TD  =  Tio/D  +  tabular  correction 


X; 

2° 

4° 

6° 

8° 

10° 

12° 

14° 

16° 

18° 

20° 

D    / 
/  I 

i 

o.oo 

0.00 

o.oo 

O.OI 

O.OI 

O.OI 

O.OI 

O.OI 

O.OI 

O.OI 

i 

2 

.00 

.00 

.01 

.01 

.01 

.02 

.02 

.02 

.02 

•03 

2 

4 

.00 

.01 

.01 

.02 

.03 

•03 

.04 

.04 

•  05 

.05 

4 

6 

.01 

.01 

.02 

•03 

.04 

•  OS 

•  05 

.06 

.07 

.08 

6 

8 

.01 

.02 

.03 

.04 

.05 

.06 

•  07 

.08 

.09 

.10 

8 

10 

O.OI 

O.02 

0.04 

0.05 

0.06 

O.O8 

0.09 

O.IO 

O.II 

0.13 

IO 

12 

.01 

.03 

.04 

.06 

.08 

.09 

.11 

.12 

.14 

•  15 

12 

14 

.01 

.03 

.05 

.07 

.09 

.11 

.13 

14 

.16 

.18 

14 

16 

.02 

.04 

.06 

.08 

.10 

.12 

.14 

.16 

.18 

.20 

16 

18 

.02 

.04 

.07 

.09 

.11 

•  14 

.16 

.18 

.21 

.23 

18 

20 

0.02 

0.05 

0.07 

O.IO 

0.13 

0.15 

0.18 

0.21 

0.23 

0.26 

20 

22 

.02 

.05 

.08 

.11 

.14 

.17 

.20 

•23 

.25 

.29 

22 

24 

.02 

.06 

.09 

.12 

.15 

.18 

.22 

•  25 

.28 

.31 

24 

26 

•  03 

.06 

.10 

.13 

.17 

.20 

.24 

.27 

•30 

•  34 

26 

28 

.03 

.07 

.11 

.14 

.18 

.22 

•25 

•29 

•  33 

•  36 

28 

30 

0.03 

0.07 

O.II 

0.15 

0.19 

0.23 

0.27 

0.31 

0.35 

0.39 

30 

32 

.03 

.08 

.12 

.16 

.21 

•  25 

.29 

•  33 

•  38 

•  42 

32 

34 

.03 

.08 

.13 

.18 

.22 

.27 

•  31 

.36 

.40 

.45 

34 

36 

.04 

.09 

•  14 

.19 

.23 

.28 

.33 

•  38 

•  43 

•  47 

36 

38 

.04 

.09 

.15 

.20 

.25 

•  30 

-35 

•  40 

.45 

•  50 

38 

40 

0.04 

O.IO 

0.15 

O.2I 

O.26 

0.32 

o.37 

0.42 

0-47 

0.53 

40 

42 

.04 

.10 

.16 

.22 

.28 

•  33 

•  39 

•  45 

•50 

.56 

42 

44 

.04 

.11 

.17 

.23 

•29 

•  35 

•  41 

•  47 

•  53 

•  59 

44 

46 

.05 

.12 

.18 

.24 

-31 

.37 

•  43 

•  49 

•56 

.62 

46 

48 

.05 

.12 

.19 

.26 

•  32 

•  39 

.45 

.52 

•  59 

•  65 

48 

So 

0.05 

0.13 

0.20 

0.27 

0-34 

0.40 

0.47 

0.54 

0.61 

0.68 

50 

52 

.05 

.13 

.21 

.28 

•  35 

.42 

•  50 

•  57 

•  64 

•  71 

52 

54 

.06 

.14 

.22 

.29 

.37 

•  44 

•  52 

•  59 

•  67 

•  74 

54 

56 

.06 

.15 

.23 

.30 

.38 

.46 

•  54 

.62 

.70 

•  77 

56 

58 

.06 

.15 

.24 

.32 

.40 

•  48 

•56 

.64 

•  73 

.80 

58 

60 

0.06 

0.16 

0.24 

0.33 

0.42 

0.50 

0.58 

0.67 

0.75 

0.84 

60 

62 

.07 

.16 

.25 

•  34 

•  43 

•  52 

.61 

.70 

•  79 

.87 

62 

64 

.07 

.17 

.27 

.36 

•  45 

•  54 

.64 

•  73 

.82 

•  91 

64 

66 

.07 

.18 

.28 

•  37 

•  47 

.56 

.66 

•  75 

.85 

•  95 

66 

68 

.07 

.18 

.29 

•  39 

.49 

•  59 

•  69 

•  78 

.88 

•  98 

68 

70 

0.08 

0.19 

0.30 

0.40 

0.50 

0.61 

0.71 

0.81 

0.91 

.02 

70 

72 

.08 

.20 

.31 

•  42 

•  52 

.63 

•  74 

.84 

•95 

.06 

72 

74 

.08 

.21 

.32 

•  43 

•  54 

.65 

•  77 

.87 

•  99 

.10 

74 

76 

.09 

.21 

•  33 

•  45 

.56 

.68 

•  79 

•  91 

.02 

•  14 

76 

78 

.09 

.22 

•  34 

.46 

•  58 

•  70 

.82 

-.94 

.06 

.18 

78 

80 

0.09 

0.23 

0.36 

0.48 

0.60 

0-73 

0.84 

0-97 

.IO 

.22 

80 

82 

.09 

.24 

•  37 

.50 

.63 

•  75 

.88 

I.OI 

•  14 

.27 

82 

84 

.10 

•25 

.38 

•  52 

.65 

.78 

•  91 

1.05 

.18 

•  31 

84 

86 

.10 

•25 

.40 

•  53 

.67 

.81 

•  95 

1.  08 

.22 

•36 

86 

88 

.11 

.26 

•  41 

•  55 

•  70 

.84 

•  98 

1.  12 

.26 

•  41 

88 

90 

O.II 

0.27 

0.42 

0.57 

0.72 

0.87 

1.02 

1.16 

-31 

•  45 

90 

92 

.11 

.28 

•  44 

•  59 

•  75 

.90 

1.05 

1.20 

•36 

•  50 

92 

94 

.12 

.29 

.46 

.61 

•  77 

•  93 

1.09 

1.24 

•  40 

•  56 

94 

96 

.12 

.30 

•  47 

.64 

.80 

•  96 

1.  13 

1.29 

•  45 

.62 

96 

98 

.13 

.31 

•  49 

.66 

.83 

I.OO 

1.  17 

1-34 

•  51 

.68 

98 

100 

0.13 

o.33 

3.51 

0.68 

0.86 

1.03 

1.  21 

1.38 

1.56 

1-74 

100 

(33) 


TABLE  IV.  —  EXTERNAL  DISTANCES  FOR  A  i°  CURVE 

ED  =  Ei°/D  (approx.)    > 


I 

o° 

10° 

20° 

30" 

40° 

50° 

60°          70° 

80° 

90° 

.0 

.0 

21.9 

88.4 

202.1 

367.7 

592.3 

886.4 

1265  .  o 

1749.9 

2373.3 

.a 

.0 

22.8 

90.2 

04.9 

71.6 

97-5 

93-1 

73-5 

60.9 

87.5 

•  4 

.0 

23-7 

92.0 

07-7 

75-5 

602.7 

99-8 

82.1 

71-9 

2401.8 

.6 

.1 

24.6 

93-8 

10.5 

79-4 

07-9 

906.5 

90.8 

83.0 

16.1 

.8 

.1 

25-5 

95-7 

13-4 

83.4 

13-1 

13-3 

99-5 

94-1 

30.5 

I.O 

.2 

26.5 

97-6 

216.2 

387-4 

618.4 

920.1 

1308.2 

1805.3 

2444-9 

.2 

•  3 

27-5 

99-5 

I9-I 

91-4 

23-7 

27.0 

17.0 

16.6 

59-5 

•4 

.4 

28.5 

101.4 

22.0 

95-4 

29.0 

33-9 

25.8 

27-9 

74.2 

.6 

.6 

29-5 

103-3 

25.0 

99-5 

34-4 

40.8 

34-7 

39-3 

88.8 

.8 

.7 

30.5 

105-3 

27-9 

403.5 

39-8 

47-8 

43-6 

50-7 

2503.6 

2.0 

•9 

31.6 

107.2 

230.9 

407-6 

645.2 

954-8 

1352.6 

1862.2 

2518.5 

.a 

i.i 

32.6 

9-2 

33-9 

n.  8 

50.6 

61.8 

61.6 

73-8 

33-4 

•  4 

1-3 

33-7 

II.  2 

36.9 

15-9 

56.1 

68.8 

70.6 

85-4 

48.5 

.6 

1-5 

34-8 

13-3 

39-9 

20.1 

61.6 

75  9 

79-7 

97-0 

63.6 

.8 

1-7 

35-9 

15-3 

43-0 

24-3 

67.1 

83.1 

88.9 

1908.7 

78.7 

30 

2.0 

37-1 

II7.4 

246.1 

428.5 

672.7 

990.2 

1398.0 

1920.5 

2594-0 

.a 

2.2 

38.2 

19-5 

49-2 

32-7 

78.2 

97-4 

1407.3 

32.4 

2609.4 

•  4 

2-5 

39-4 

21.6 

52-3 

37-0 

83.9 

1004.7 

16.5 

44-3 

24.8 

.6 

2.8 

40.6 

23-7 

55-4 

41-3 

89-5 

12.0 

25-9 

56.3 

40-3 

.8 

3.2 

41.8 

25.8 

58.6 

45-6 

95-2 

19-3 

35.3 

68.3 

55-9 

4.0 

3.5 

43-0 

128.0 

261.8 

450.0 

700.9 

1026.6 

1444.6 

1980.4 

2671.6 

.2 

3.9 

44-3 

30.2 

65.0 

54-3 

06.6 

34-0 

54-1 

92.5 

87.4 

.4 

4.2 

45-5 

32.4 

68.2 

58.7 

12.4 

41-4 

63.6 

2004.7 

2703.3 

.6 

4.6 

46.8 

34-6 

71-5 

63.2 

18.2 

48.9 

73-2 

17.0 

19-2 

.8 

S.o 

48.1 

36.9 

74.8 

67.6 

24.0 

56.4 

82.8 

29  3 

35-2 

50 

5-5 

49-4 

I39-I 

278.1 

472.1 

.  729.9 

1063.9 

1492.4 

2041.7 

2751.3 

.2 

5-9 

50.8 

41-4 

81.4 

76.6 

35.7 

71-5 

1502.1 

54.2 

67-5 

.4 

6.4 

52.1 

43-7 

84.7 

81.1 

41.6 

79-1 

II.  8 

66.7 

83.8 

.6 

6.8 

53-5 

46.0 

88.1 

85.6 

47.6 

86.8 

21.7 

79-3 

2800.1 

.8 

7-3 

54-9 

48.4 

91-5 

90.2 

53-6 

94-5 

31.5 

91-9 

16.6 

6.0 

7-9 

56.3 

150.7 

294-9 

494-8 

759-6 

II02.2 

I54L4 

2104.6 

2833.2 

.2 

8.4 

57-7 

53-1 

98-3 

99-4 

65.6 

09-9 

51-3 

17-4 

49-8 

•  4 

8.9 

59  2 

55-5 

301-7 

504.1 

71-7 

17-7 

61.3 

30.3 

66.5 

.6 

9-5 

60.6 

57-9 

05.2 

08.8 

77-8 

25.6 

71-3 

43-2 

83-4 

.8 

10.  1 

62.1 

60.4 

08.7 

13-5 

83.9 

33-5 

8L  4 

56.2 

2900.3 

7-0 

10.7 

63.6 

162.8 

312.2 

518.2 

790.1 

1141.4 

I59I-6 

2169.2 

2917.3 

.2 

II.  3 

65.2 

65-3 

15.8 

22.9 

96-3 

49-3 

1601.8 

82.4 

34-4 

•  4 

12.0 

66.7 

67-8 

19-3 

27.7 

802.5 

57-3 

12.0 

95-5 

51.6 

.6 

12.6 

68.3 

70.3 

22.9 

32.5 

08.8 

65-4 

22.3 

2208.8 

68.9 

.8 

13  3 

69.8 

72.8 

26.5 

37-4 

15-2 

73-4 

32.6 

22.1 

86.3 

8.0 

14.0 

71-4 

175-4 

330.1 

542.2 

821.4 

1181.6 

1643.0 

2235.5 

3003.8 

.2 

14-7 

73-0 

78.0 

33.8 

47-1 

27-7 

89-7 

63-5 

48-9 

21.4 

.4 

15-4 

74-7 

80.6 

37-5 

52.0 

34.1 

97-9 

64.0 

62.5 

39-1 

.6 

16.2 

76.3 

83.2 

41.2 

57-0 

40.5 

1206.  I 

74-5 

?6.I 

56.8 

.8 

16.9 

78.0 

85.8 

44-9 

61.9 

47-0 

14-4 

85.1 

89.8 

74-7 

9.0 

17.7 

79-7 

188.5 

348.6 

566.9 

853.5 

1222.7 

1695.8 

2303.5 

3092.7 

.2 

18.5 

81.4 

91.2 

52-4 

72.0 

60.0 

31.  1 

1706.5 

17-3 

3110.8 

•  4 

19.3 

83.1 

93-9 

56.2 

77-0 

66.5 

39-5 

17-3 

3L2 

28.9 

.6 

20.2 

84-8 

96.6 

60.0 

82.1 

73-1 

48.0 

28.1 

45-  1 

47-2 

.8 

21.  0 

86.6 

99-4 

63.9 

87.2 

79-7 

56.4 

39-0 

59-2 

65.6 

10.0 

21.9 

88.4 

202.  1 

367.7 

592-3 

886.4 

1265.0 

1749-9 

2373-3 

3184.1 

/ 

0° 

10° 

20° 

30° 

40° 

50° 

60° 

70° 

80° 

90° 

(34) 


TABLE  V.  —  LONG  CHORDS  AND  ACTUAL  ARCS 


Degree 
of 
curve 

Actual 
arc,  one 
station 

2Sta. 

3Sta. 

4Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 
of 
curve 

0.2 

•  4 
.6 
.8 

I.O 
.2 

•  4 
.6 
.8 
2.0 

.2 

.4 
.6 

.8 
30 

.2 

•  4 
.6 
.8 
4.0 

.2 

•  4 

.6 
.8 
5-0 

.2 

•  4 
.6 
.8 
6.0 

.2 

.4 
.6 

.8 

7.o 

.2 

'.6 
.8 
8.0 

.2 
•  4 
.6 

.8 
90 

.2 

•  4 

.6 
.8 
10.0 

IOO.OOO 

200.  o 

300.0 

400.0 

500.0 

600.0 

700.0 

800.0 

0.2 

•4 
.6 
.8 

I.O 
.2 

•  4 
.6 
.8 
2.0 

.2 

•  4 
.6 

.8 
30 

.2 

•  4 
.6 
.8 
4.0 

.2 

•  4 
.6 

.8 
S.o 

.2 

•  4 
.6 
.8 
6.0 

.2 

•  4 

.6 
.8 
7.o 

.2 

•  4 
.6 
.8 
8.0 

.2 

.6 

.8 
9.o 

.2 

•  4 
.6 
.8 
10.0 

.000 

.000 
.001 

IOO.OOI 

.002 

.002 

.003 
.004 

oo.o 
oo.o 
oo.o 

2OO.O 

oo.o 
oo.o 
oo.o 
oo.o 

oo.o 
oo.o 
oo.o 
300.0 
oo.o 

299.9 

99-9 
99-9 

oo.o 
oo.o 
oo.o 

399.9 

99-9 
99-9 
99-8 
99-8 

00.0 

499.9 
99.9 

499-8 
99-8 
99-7 
99-6 
99-5 

oo.o 

599.9 

99-8 

599-7 
99-6 
99-5 
99-3 
99-1 

699.9 
699-8 
99-7 
699-6 
99-4 
99-2 

98.9 
98.6 

799-9 
799-8 
99-6 
799-4 
99-1 
98.8 

98.4 
97-9 

100.005 

2OO.O 

299.9 

399-7 

499-4 

598.9 

698.3 

797-4 

.006 

.007 
.009 

.010 

IOO.OII 

.013 

.015 
.016 
.018 

oo.o 
oo.o 
oo.o 

199.9 
199.9 
99.9 
99.9 

99  9 

99.9 

99-9 
99-8 
99-8 
99-8 
299-7 
99-7 
99-6 
99-6 
99-6 

99-6 
99-6 
99-5 
99-4 
399-3 
99-2 

99-1 
99-0 
98.9 

99-3 
99-i 
99-0 
98.8 
498.6 
98.4 
98.2 
98.0 
97-8 

98-7 
98-5 
98.2 

97-9 
597-6 
97-3 

96.9 
96.6 
96.2 

97-9 
97-5 
97.1 

96.7 
696.2 
95.6 
95-1 
94.5 
93-9 

96.9 
96.3 
95-7 
95-0 
794-3 
93-5 
92.6 
91.7 
90.8 

IOO  .  O20 

199.9 

299-5 

398.8 

497-6 

595-7 

693.2 

789.8 

.022 
.025 
.027 
.029 
100.032 

•  034 

.037 
.040 
•  043 

99-9 
99-9 
99-8 

99-8 
199.8 
99-8 
99-8 
99-8 
99-7 

99-5 
99-4 
99-4 

99-3 
299.2 
99-2 

99-1 
99-0 
99-0 

98.7 
98.5 
98-4 
98.2 
398.1 
97-9 
97.8 
97-6 
97.4 

97-3 
97-1 
96.8 

96.5 
496.2 
95-9 
95.6 
95.2 
94-9 

95-3 
94-9 
94-4 
93-9 
593-4 
92.8 

92.3 
91.7 
91.  i 

92-5 
91.8 
91.0 
90.2 
689.4 
88.5 
87.6 
86.7 
85".  7 

88.8 
87-7 
86.5 

85-3 

784.1 
82.8 

8i.5 
80.  i 
78.7 

100.046 

199-7 

298.9 

397-3 

494-5 

590.4 

684.7 

777-2 

.049 
.052 
•  055 

•  059 
100.062 
.066 
.070 
•  073 
.077 

99-7 
99-7 
99-7 
99-6 
199-6 
99-6 
99-6 
99-6 
99-5 

98.8 
98.8 
98-7 
98.6 
298.5 
98.4 

98-3 
98.2 
98.1 

97-1 
96.9 
96.7 
96-5 
396-3 
96.1 

95.8 
95.6 
95-4 

94.2 
93.8 
93-4 
93-0 
492.6 
92.1 

91-7 
91.2 
90.8 

89.8 
89.1 
88.5 

87-7 
587.0 
86.3 
85.5 
84.7 
83.9 

83-7 
82.7 
81.6 

80.4 
679.3 
78.1 

76.9 
75.6 
74-3 

75-6 
74-0 
72.4 

70.7 
769.0 
67.2 

65.4 
63.5 
61.6 

100.081 

-085 
.090 
•  094 
.098 
100.103 
.108 
.112 
.117 

.122 

199-5 

298.1 

395-1 

490.3 

583-1 

673.0 

759-7 

99-5 
99-5 
99-4 
99-4 
199-4 
99-4 
99-3 
99-3 
99-3 

98.0 
97-9 
97-8 
97-6 
297-5 
97-4 
97-3 
97-2 
97.1 

94-9 
94-6 
94-4 
94-1 
393-9 
93-6 

93-3 
93.o 
92.7 

89.8 
89-3 
88.8 

88.3 
487.7 
87.2 

86.6 
86.1 
85-5 

82.2 
81.4 
80.5 
79-6 
578.6 
77-7 
76.7 
75-7 
74-7 

71.7 
70.3 
68.9 

67.4 
666.0 
64.4 
62.9 
61.3 
59-7 

57-7 
55.6 
53-5 

51-4 
749-2 
46.9 
44-6 
42.3 
39-9 

IOO.I27 

199.2 

297.0 

392.4 

484-9 

573-7 

658.1 

737-5 

Degree 

Actual  arc 

2Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 

(35) 


TABLE  V.  —  (Continued) 


Degree 
of  curve 

Actual  arc 
one  station 

2  Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 
of  curve 

10.0 

100.127 

199.2 

297.0 

392.4 

484.9 

573-7 

658.1 

737-5 

10.0 

.2 

.132 

99-2 

96.8 

92.1 

84-3 

72.6 

56.5 

35-1 

.2 

•  4 

.137 

99-2 

96-7 

91.8 

83.7 

71.6 

54-8 

32.5 

.4 

.6 

.143 

99-1 

96.6 

91-5 

83.1 

70.5 

53-0 

30.0 

.6 

.8 

.148 

99-1 

96.5 

91.2 

82.4 

69.4 

51-3 

27-4 

.8 

II.  0 

100.154 

I99-I 

296.3 

390.8 

481.8 

568.2 

649.5 

724.8 

II.  O 

.2 

•  159 

99-0 

96.2 

90.5 

81.1 

67.1 

47-7 

22.1 

.2 

•  4 

.165 

99-0 

96.1 

90.2 

80.4 

65-9 

45-8 

19-4 

•4 

.6 

.171 

99-0 

95-9 

89.8 

79-7 

64.8 

44-0 

16.6 

.6 

.8 

.177 

98.9 

95.8 

89-5 

79-0 

63-5 

42.1 

13-8 

.8 

12.0 

100.183 

198.9 

295-6 

389.1 

478-3 

562.3 

640.1 

710.9 

12.0 

.2 

.189 

98-9 

95-5 

88.7 

77-6 

61.1 

38.2 

08. 

.2 

•  4 

-195 

98.8 

95-3 

88.4 

76.9 

59-8 

36.2 

05- 

•  4 

.6 

.202 

98.8 

95-2 

88.0 

76.2 

58.5 

34-2 

702. 

.6 

.8 

.208 

98.8 

95-0 

87.6 

75-4 

57-2 

32.1 

699. 

.8 

13  o 

100.215 

198.7 

294-9 

387.2 

474-6 

555-9 

630.1 

696. 

13  o 

.2 

.222 

98.7 

94-7 

86.8 

73-9 

54-6 

28.0 

93- 

.2 

•  4 

.228 

98.6 

94-6 

86.5 

73-1 

53-2 

25.8 

89-9 

.4 

.6 

•235 

98.6 

94-4 

86.0 

72.3 

Si-9 

23-7 

86.7 

.6 

.8 

.242 

98.5 

94.2 

85.6 

71-5 

50.5 

21.5 

83.5 

.8 

14.0 

IOO.249 

198.5 

294.1 

385.2 

470.6 

549-1 

619.3 

680.3 

14.0 

.2 

.256 

98-5 

93-9 

84.8 

69.8 

47-6 

17.0 

77.0 

.2 

•  4 

.264 

98-4 

93-7 

84.4 

69.0 

46.2 

14.8 

73-7 

.4 

.6 

.271 

98.4 

93-5 

83.9 

68.1 

44-7 

12.5 

70-3 

.6 

.8 

.279 

98.3 

93-4 

83.5 

67-3 

43-2 

10.2 

66.9 

.8 

15.0 

100.286 

198.3 

293-2 

383.1 

466.4 

541-7 

607.8 

663.5 

15.0 

.2 

•  294 

98.2 

93-0 

82.6 

65-5 

40.2 

05-4 

60.0 

.2 

•  4 

.302 

98.2 

92.8 

82.2 

64.6 

38.7 

O3.0 

56-5 

.4 

.6 

.310 

98.2 

92.6 

81.7 

63.7 

37-1 

600.6 

53-0 

.6 

.8 

.318  - 

98.1 

92.4 

81.2 

62.8 

35-6 

598.2 

49-4 

.8 

16.0 

100.326 

198.1 

292.3 

380.8 

461.9 

534-0 

595-7 

645-8 

16.0 

.2 

•  334 

98.0 

92.1 

80.3 

60.9 

32-4 

93-2 

42.2 

.2 

•  4 

.342 

98.0 

91.9 

79-8 

60.0 

30.7 

90.7 

38.5 

•  4 

.6 

•  351 

97-9 

91-7 

79-3 

59  o 

29.1 

88.1 

34-8 

.6 

.8 

•359 

97-9 

91-5 

78.8 

58. 

27-5 

85-5 

31-1 

.8 

17.0 

100.368 

197.8 

291-3 

378.3 

457- 

525-8 

582.9 

627.3 

17.0 

.2 

.376 

97-8 

9I-I 

77-8 

56- 

24.1 

80.3 

23-5 

.2 

•  4 

.385 

97-7 

90.8 

77-3 

55- 

22.4 

77-7 

19.6 

•  4 

.6 

•  394 

97-6 

90.6 

76.8 

54- 

20.7 

75-0 

15-8 

.6 

.8 

.403 

97-6 

90.4 

76.3 

53-0 

18.9 

72.3 

11.9 

.8 

18.0 

100.412 

197-5 

290.2 

375-7 

452.0 

517.2 

569-6 

608.0 

18.0 

.2 

.422 

97-5 

90.0 

75-2 

51-0 

15-4 

66.8 

04.0 

.2 

•  4 

•  431 

97-4 

89.8 

74-7 

49-9 

13-6 

64.1 

600.0 

•  4 

.6 

.440 

97-4 

89.6 

74-1 

48.9 

II.  8 

61.3 

596.0 

.6 

.8 

•  450 

97-3 

89-3 

73-6 

47-8 

10.  0 

58.5 

92.0 

.8 

19.0 

100.460 

197-3 

289.1 

373-0 

446.7 

508.1 

555-6 

587.9 

19.0 

.2 

.469 

97-2 

88.9 

72-5 

45-6 

06.3 

52.8 

83.8 

.2 

•  4 

•  479 

97-1 

88.6 

71-9 

44-5 

04-4 

49-9 

79-7 

•  4 

.6 

.489 

97-1 

88.4 

71-3 

43-4 

02.5 

47-0 

75-5 

.6 

.8 

•  499 

97-0 

88.2 

70.7 

42-3 

500.6 

44.1 

71-3 

.8 

20.0 

100.510 

197.0 

287.9 

370.2 

441.1 

498-7 

541.  1 

567.1 

20.0 

Degree 

Actual  arc 

2  Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 

(36) 


TABLE  VI.  —  MIDDLE  ORDINATES 


Degree 
of  curve 

iSta. 

2Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 
of  curve 

0.2 

.04 

•  17 

•  39 

•  70 

1.09 

1-57 

2.14 

2-79 

0.2 

•  4 

.09 

•  35 

.78 

1.40 

2.18 

3-14 

4.28 

5.58 

•  4 

.6 

•  13 

•  52 

1.18 

2.09 

3-27 

4-71 

6.41 

8.38 

.6 

.8 

•  I? 

•  70 

1.57 

2.79 

4.36 

6.28 

8.55 

11.17 

.8 

I.O 

.22 

.87 

1.96 

3-49 

5-45 

7-85 

10.69 

13-96 

I.O 

.2 

.26 

1.05 

2.36 

4-19 

6.54 

9-42 

12.82 

16.75 

.2 

•  4 

•30 

1.22 

2.75 

4.89 

7-63 

10.99 

14-96 

19-53 

.4 

.6 

•  35 

1.40 

3-14 

5.58 

8.72 

12.56 

17.09 

22.32 

.6 

.8 

•  39 

1-57 

3-53 

6.28 

9.81 

I4-I3 

19.22 

25.10 

.8 

2.0 

•  44 

1.75 

3  93 

6.98 

10.90 

15-69 

21.36 

27.88 

2.0 

.2 

.48 

1.92 

4-32 

7.68 

11.99 

17.26 

23-48 

30.66 

.2 

•  4 

•  52 

2.09 

4-71 

8.37 

13.08 

18  83 

25.61 

33-43 

•  4 

.6 

•  57 

2.27 

5-10 

9-07 

14.17 

20.39 

27.74 

36.21 

.6 

.8 

.61 

2.44 

5-50 

9-77 

15.25 

21.95 

29.86 

38.98 

.8 

30 

.65 

2.62 

5-89 

10.46 

i6.34 

23  52 

31.98 

41-74 

30 

.2 

.70 

2.79 

6.28 

ii.  16 

17-43 

25.08 

34-10 

44-50 

.2 

-4 

•  74 

2.97 

6.67 

11.86 

18.51 

26.64 

36.22 

47.26 

.4 

.6 

.78 

3-14 

7.06 

12.55 

19.60 

28.20 

38.34 

50.01 

.6 

.8 

.83 

3-32 

7.46 

13-25 

20.68 

29-75 

40.45 

52.76 

.8 

4.0 

.87 

3-49 

7.85 

13-94 

21-77 

31  31 

42.56 

55-50 

4.0 

.2 

.92 

3-66 

8.24 

14.64 

22.85 

32.86 

44-66 

58.24 

.2 

•  4 

.96 

3-84 

8.63 

15-33 

23.93 

34-41 

46.77 

60.97 

•  4 

.6 

1.  00 

4.01 

9.02 

16.03 

25.01 

35.96 

48.87 

63.69 

.6 

.8 

.05 

4-19 

9.42 

16.72 

26.09 

37-51 

50.96 

66.42 

.8 

S.o 

.09 

4.36 

9.81 

17.42 

27.17 

39  06 

53-05 

69.13 

50 

.2 

.14 

4-54 

10.20 

18.11 

28.25 

40.60 

55-14 

71.84 

.2 

•  4 

.18 

4-71 

10.59 

18.80 

29-33 

42.15 

57-23 

74-54 

.4 

.6 

.22 

4-89 

10.98 

19.49 

30.40 

43.69 

59-31 

77-23 

.6 

.8 

.27 

5.o6 

11-37 

20.19 

31.48 

45-22 

61.38 

79-92 

.8 

60 

31 

5  23 

11.76 

20.88 

32.55 

46.76 

63-46 

82.60 

6.0 

.2 

•  35 

5-41 

12.15 

21.57 

33.63 

48.29 

65-52 

85-27 

.2 

•  4 

.40 

5.58 

12.54 

22.26 

34-70 

49.82 

67.58 

87.93 

•  4 

.6 

.44 

5.76 

12-93 

22.95 

35-77 

51.35 

69.64 

90-59 

.6 

.8 

•  48 

5-93 

13-32 

23.64 

36.84 

52.88 

71.70 

93-23 

.8 

7-0 

•  S3 

6.  ii 

13  71 

24  33 

37.91 

54-40 

73-74 

95.87 

7-0 

.2 

•  57 

6.28 

14.10 

25.02 

38.97 

55.92 

75-79 

98.50 

.2 

•  4 

.62 

6-45 

14-49 

25-71 

40.04 

57-44 

77-82 

101.12 

.4 

.6 

.66 

6.63 

14.88 

26.39 

41.10 

58-95 

79-85 

103-73 

.6 

.8 

•  70 

6.80 

15.27 

27.08 

42.17 

60.46 

81.88 

106.33 

.8 

8.0 

•  75 

6.98 

15-66 

27-77 

43  23 

6i.97 

83  90 

108.92 

8.0 

.2 

•79 

7-iS 

16.05 

28.45 

44-29 

63.47 

85.92 

111.50 

.2 

.4 

.83- 

7-32 

16.44 

29.14 

45-35 

64.97 

87.92 

II4.o6 

•  4 

.6 

.88 

7-50 

16.83 

29.82 

46.40 

66.47 

89-92 

II6.62 

.6 

.8 

.92 

7-67 

17.22 

30.51 

47.46 

67.97 

91.92 

119.17 

.8 

9.0 

•  97 

7-85 

17.61 

3i  19 

48.51 

69.46 

93-91 

121.71 

9.0 

.2 

2.00 

8.02 

18.00 

31.87 

49-56 

70-95 

95-89 

124.23 

.2 

.4 

2.05 

8.19 

18.38 

32.56 

50.61 

72.43 

97.87 

126.75 

•  4 

.6 

2.10 

8.37 

18.77 

33.24 

51-66 

73-91 

99-83 

129.25 

.6 

.8 

2.14 

8.54 

19.16 

33.92 

52.71 

75-39 

101.80 

131-74 

.8 

10  0 

2.18 

8.72 

19-55 

34.6o 

53-75 

76.86 

103-75 

134  22 

10.0 

Degree 

I  Sta. 

2  Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 

(37) 


TABLE  VI.  —  (Continued) 


Degree 
of  curve 

I  Sta. 

2  Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 
of  curve 

10.0 

2.18 

8.72 

19  55 

34.6o 

53  75 

76.86 

103-75 

134  22 

10.0 

.2 

2.23 

8.89 

19.94 

35.28 

54-79 

78.33 

105  .  70 

136.68 

.2 

-4 

2.27 

9.06 

20.32 

35.96 

55-83 

79-79 

107.64 

139.14 

•  4 

.6 

2.31 

9-24 

20.71 

36.63 

56.87 

81.25 

109.57 

141.58 

.6 

.8 

2.36 

9-41 

21.10 

37-31 

57-91 

82.71 

in.  49 

144.00 

.8 

II.  O 

2.40 

9  59 

21.48 

37  99 

58.94 

84.16 

113-41 

146.41 

II.  O 

.2 

2.44 

9-76 

21.87 

38.66 

59-98 

85.61 

115-32. 

148.81 

.2 

•  4 

2.49 

9-93 

22.25 

39-34 

61.01 

87-05 

117.21 

151.20 

•  4 

.6 

2.53 

IO.II 

22.64 

40.01 

62.04 

88.49 

119.11 

153.57 

.6 

.8 

2.58 

10.28 

23.03 

40.68 

63.06 

89-92 

120.99 

155-93 

.8 

12.0 

2.62 

10.45 

2341 

41  36 

64-09 

91.36 

122.87 

158.27 

12  0 

.2 

2.66 

10.63 

23.80 

42.03 

65.11 

92.78 

124-73 

160.59 

.2 

•  4 

2.71 

10.80 

24.18 

42.70 

66.13 

94.20 

126.59 

162.91 

•  4 

.6 

2.75 

10.97 

24-57 

43-37 

67-14 

95-62 

128.43 

165.21 

.6 

.8 

2.80 

II.  IS 

24-95 

44-03 

68.16 

97-03 

130.27 

167.49 

.8 

13-0 

2.84 

11.32 

2533 

44.70 

69.17 

98.43 

132.10 

169.75 

13  .0 

.2 

2.88 

11-49 

25-72 

45-37 

70.18 

99-83 

133.92 

172.01 

.2 

•  4 

2.93 

11.67 

26.10 

46.03 

71.19 

101.23 

135-73 

174.24 

•  4 

.6 

2.97 

11.84 

26.48 

46.70 

72.19 

102.62 

137-53 

176.46 

.6 

.8 

3-01 

12.01 

26.87 

47.36 

73-20 

104.00 

139-33 

178.67 

.8 

14.0 

3-o6 

12.19 

27-25 

48.02 

74.20 

105-38 

141.11 

180.85 

14.0 

.2 

3.io 

12.36 

27.63 

48.69 

75-20 

106.76 

142.88 

183.02 

.2 

•  4 

3-15 

12.53 

28.01 

49-35 

76.19 

108.12 

144.64 

185-17 

•  4 

.6 

3-19 

12.71 

28.40 

50.01 

77-18 

109.49 

146.40 

187-31 

.6 

.8 

3-23 

12.88 

28.78 

50.66 

78.17 

110.85 

148.14 

189.43 

.8 

15  o 

3  28 

13  05 

29.16 

5i  32 

79-16 

112.  2O 

149  87 

191-53 

IS  o 

.2 

3-32 

13-23 

29-54 

51-98 

80.14 

113-54 

151-59 

193-62 

.2 

•  4 

3.36 

13-40 

29.92 

52.63 

81.12 

114.88 

153.30 

195-68 

•  4 

.6 

3  41 

13-57 

30.30 

53.29 

82.10 

II6.22 

I55.oo 

197-73 

.6 

.8 

3-45 

13-74 

30.68 

53-94 

83.08 

117-55 

156.69 

199.76 

.8 

16.0 

3  50 

13  92 

31.06 

54-59 

84-05 

II8.87 

158.37 

201.77 

16.0 

.2 

3-54 

14.09 

31-44 

55-24 

85.02 

120.19 

160.03 

203.77 

.2 

•  4 

3-58 

14.26 

31.82 

55-89 

85-99 

121.50 

161.69 

205.74 

.4 

.6 

3.63 

14-44 

32.20 

56-54 

86.95 

122.80 

163.33 

207.70 

.6 

.8 

3.67 

14.61 

32-57 

57-19 

87.91 

124.10 

164.96 

209.64 

.8 

17.0 

3  72 

14.78 

32.95 

57-83 

88.87 

125-39 

166.59 

211.55 

17.0 

.2 

3-76 

14-95 

33-33 

58.48 

89.83 

126.68 

168.20 

213.46 

.2 

.4 

3-8o 

15-13 

33-71 

59-12 

90.78 

127.96 

169.79 

215-33 

•  4 

.6 

3-85 

15-30 

34.08 

59.76 

91-73 

129.23 

171-38 

217.20 

.6 

.8 

3-89 

15-47 

34.46 

60.40 

92.67 

130-49 

172.95 

219.03 

.8 

18.0 

3  94 

15  64 

34-84 

61.04 

9362 

I3L75 

174-52 

220.86 

18.0 

.2 

3-98 

15.82 

35-21 

61.68 

94-55 

133-01 

176.07 

222.65 

.2 

•  4 

4-02 

15-99 

35-59 

62.32 

95-49 

134-25 

177-60 

224.43 

-4 

.6 

4.07 

16.16 

35.96 

62.96 

96.42 

135-49 

179-13 

226.20 

.6 

.8 

4-  II 

16.33 

36.34 

63-59 

97-35 

136.72 

180.64 

227.93 

.8 

19.0 

4.16 

16.51 

36.71 

64.22 

98.28 

137-95 

182.15 

229.65 

19.0 

.2 

4.20 

16.68 

37-09 

64-85 

99-20 

I39-I7 

183.64 

231.35 

.2 

•  4 

4-24 

16.85 

37.46 

65.48 

100.12 

140.38 

185.11 

233.03 

-4 

.6 

4.29 

'  17.02 

37.83 

66.ii 

101.03 

141.58 

186.57 

234.69 

.6 

.8 

4  33 

17-19 

38.20 

66.74 

101.95 

142.78 

188.02 

236.33 

.8 

20  0 

4  37 

17  37 

38.58 

67  37 

102.86 

143-97 

189-46 

237.94 

20.0 

Degree 

i  Sta. 

2  Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 

(38) 


CHAPTER  II 
THE  SPIRAL 

THE  railroad  spiral  is  a  curve  of  varying  radius  connecting  a  main 
or  central  curve  with  a  tangent  or  connecting  the  two  branches  of  a 
compound  curve.  If  it  is  a  true  spiral  its  change  in  "degree"  is  pro- 
portionate to  its  length.  Thus  at  the  point  of  junction  with  the  tan- 
gent (T.  S.  in  Fig.  22)  the  degree  is  zero;  at  the  junction  with  the  main 
or  central  curve  of  degree  D  (S.  C.  in  Fig.  22)  it  is  D;  at  its  mid- 
point it  is  |  Z)  ...  etc.  The  radius  is  closely  inversely  as  the 
length.  Knowing  the  degree  of  the  central  curve  the  first  quantity 
to  determine  is  the  length  L,  the  second  is  A,  the  central  angle  consumed 
by  the  spiral.  If  these  two  can  be  conveniently  chosen  the  other 
functions  can  be  had  from  tables. 

The  length  of  the  spiral  is  determined  as  follows:  For  curves  of  6° 
or  over  on  which  track  is  canted  8  inches,  L  =  240  feet  as  a  minimum. 

_0_ 

For  curves  flatter  than  6°  likely  sometime  to  limit  speed,  L  =  -—=feet, 

D  being  the  degree  of  the  central  curve.  For  minor  curves  not  likely 
to  limit  speed,  L  =  f  SE  or  30  E  in  feet,  in  which  S  is  speed  in  miles 
per  hour  and  E  is  the  difference  in  elevation  of  the  two  rails  in  inches. 

If  the  maximum  allowable  cant  is  6  inches,  L  =  ^-7=  feet  for  curves 

VD 

flatter  than  4.5°  likely  to  limit  speed.  For  curves  of  4.5°  and  over  the 
minimum  length  will  be  180  feet. 

For  minor  curves,  L  =  f  SE  or  30  E,  as  above. 

It  will  be  well  to  select  lengths  that  are  round  numbers  of  feet  not 
less  than  the  required  minimums  and  such  that  the  resulting  A  may  be 
whole  degrees  or  a  whole  number  of  tenths  of  a  degree  divisible  by  3. 
This  is  merely  for  convenience  in  computing. 


200 


39 


40  RAILROAD  FIELD  MANUAL 

Notation:   Referring  to  Fig.  22 


S.T. 


U                      '                   ' 

1 

x                      ! 

1 

T, 

FIG.  22. 

T.  S.  =  Tangent-Spiral.  5.  C.  =  Spiral-Curve. 

C.  S.  =  Curve-Spiral.  S.  T.  =  Spiral-Tangent. 

T.  C.  =  Tangent-Curve.  C.  T.  =  Curve-Tangent. 

A  =  central  angle  of  the  spiral. 

A  =  deflection  angle  T.  S.  to  S.  C. 

B  =  deflection  angle  S.  C.  to  T.  S. 

C  =  the  long  chord  of  the  spiral. 

X  =  abscissa  with  T.  S.  as  origin. 

Y  =  ordinate  with  T.  S.  as  origin. 

U  =  spiral  long  tangent. 

V  =  spiral  short  tangent. 

o  =  curve  offset. 

Z  =  distance  on  tangent  from  T.  S.  to  T.  C.  of  the  offset  curve. 
Tt  =  tangent  distance  of  the  spiraled  curve. 
E,  =  external  distance  of  the  spiraled  curve. 

R  =  radius  of  central  curve. 


THE   SPIRAL  41 

The  Chord  Spiral.  —  If  the  spiral  be  laid  out  by  equal  chords  it  is 
approximately  true  that  the  deflection  angles  from  the  tangent  at  the 
T.  S.  to  the  several  chord  points  are  as  the  squares  of  the  chord  num- 
bers, and  the  final  deflection  A  of  the  long  chord  is  one-third  the  central 
angle  A. 

If  the  spiral  be  divided  into  N  chords,  the  deflection  angle  for  the 

first  chord  will  closely  approximate  —  ^=  and  the  angles  that  the  several 

chords  (produced)  will  make  with  the  tangent  will  be  approximately 

A 
J»  7»  J9»  37»  61,  91,  127,  169,  217,  271,  etc.,  times  —  ™- 

The  chord  spiral  is  a  curve  passing  through  the  chord  points  of  a 
series  of  equal  chords  for  which  the  relations  of  the  preceding  para- 
graph are  exactly  true.  It  is  not  a  curve  of  uniformly  varying  radius 
or  degree,  but  differs  from  such  a  curve  by  an  inappreciable  amount. 

The  spiral  may  be  divided  into  any  number  of  chords.  Tables  for 
a  division  into  ten  chords  have  been  devised  by  Mr.  Jenks  B.  Jenkins 
for  the  American  Railway  Engineering  Association,  and  have  been 
approved  as  good  practice  by  that  association. 

Table  VIII  gives  values  for  the  quantities  noted  below.  Excepting 
o  and  Z  the  linear  quantities  vary  as  L  and  hence  the  tabular  quanti- 
ties are  coefficients  by  which  the  L's  of  any  given  cases  are  to  be  multi- 
plied to  find  the  functions  C,  X,  F,  £7,  and  V.  The  use  of  the  table 
to  get  o  and  Z  will  be  evident  from  the  table  headings. 

C    X     Y 

Referring  to  Fig.  22,  the  tabulated  quantities  are  A,  A,  T>   y->  T  . 

Lt      Li       Li 

U     V 

•j-i  y,  coefficients  for  o  and  Z.     The  following  formulas  give  these 

quantities: 

A  =  -  ,  A  =  \  A  —  0.000000825  A3,  B  =  A  —  A. 

2OO 
£ 

T  =  cos  0.3  A  -f-  0.004  exsec  f  A  (approx.). 

X  =  CcosA. 
Y  =  CsinA. 
Z  =  X  -tfsinA. 


sin  A 


sin  A 
o  =  7-^versA. 


42  RAILROAD   FIELD  MANUAL 


Exactly,  X  =  ^  (cos  -*-  +  7-±  +  cos  ^  +  cos  &*  +  cos 

10  V      300      300  300  n         300  n         300 


9iA  I27A  .  . 

+  cos  _  +  COS  —  +  COS  --  +  COS  -  +  COS 

Exactly,  F  =  £(«„£  +  s!n^  +  .  .  .  etc.). 

y 
Exactly,  tan  A  =  •=• 

^L 

The  following  formulas  give  the  tangent  distance  and  external  dis- 
tance of  the  curve: 


E8  =  (R  +  0}  exsec  \I  +  o. 

The  central  5  subtended  by  any  portion,  /  feet,  of  the  spiral  is  the 
average  "degree"  of  the  portion  multiplied  by  -  .  The  average 
"degree"  is  the  initial  and  final  degree  of  the  portion  divided  by  2. 
The  degree  at  any  point  distant  /  feet  from  the  T,  S.  is  y£>.  The 

jL» 

degree  at  the  end  of  any  chord  p  (p  being  the  number  of  the  chord) 

is  —  D  for  the  lo-chord  spiral  or^-,D  for  the  TV-chord  spiral. 
10  N 

For  precise  computation  of  positions  of  points  on  line,  A  should  be 
computed  from  A  =  I  A  —  0.000000825  A3  or  taken  from  Table  VIII, 
or  Tables  IX  to  XXIII.  The  deflection  01  for  the  first  chord  is  always 

-  for  the  lo-chord  spiral. 

For  field  use  the  deflection  from  the  T.  S.  to  any  chord  point  should 
be  taken  as  01  times  the  square  of  the  number  of  the  chord  point  to  be 
located  so  long  as  5  does  not  exceed  15°.  A  may  be  taken  as  1/3  A 
for  A^  15°.  When  A  is  more  than  15°  one  or  more  intermediate  transit 
points  should  be  used.  Such  points  should  be  so  chosen  that  the  5 
from  the  T.  S.  to  the  first  intermediate  point  shall  not  exceed  15°,  and 
so  that  5  from  any  occupied  point  to  the  next  transit  point  less  the  5 
from  the  T.  S.  to  the  occupied  point  shall  not  exceed  15°.  With  this 
procedure  the  deflections  from  the  tangent  at  any  intermediate  point 
may  be  taken  as  in  Table  VII,  which  gives  the  coefficients  by  which  a\ 
is  to  be  multiplied  to  give  deflections  to  points  both  forward  and  back 
as  indicated.  This  procedure  is  not  exact  but  results  in  angular  errors 
less  than  can  be  measured  by  the  transit.  It  is  probable  that  90  or 
more  per  cent  of  the  cases  in  practice  will  involve  As  of  less  than  10° 
and  an  error  of  3  seconds  or  less  than  0.001°  if  A  is  taken  as  \  A. 


THE  SPIRAL  43 

For  A  =  15°  the  error  is  10  seconds  or  less  than  0.003°.  H  it  is  desired 
to  find  the  deflection  from  the  T.  S.  to  any  point  to  which  the  5  exceeds 
15°  it  may  be  done  by  finding  the  5  and  then  the  corresponding  A 
from  Table  VIII.  If  convenient  spirals  have  been  chosen,  Tables  IX 
to  XXIII  may  be  used. 

To  Select  and  Lay  Out  the  Spiral.  —  Knowing  7  and  D,  determine 
L  and  A;  from  Table  VIII  find  coefficients  for  and  determine  o  and  Z 
and  substitute  in  the  equation  for  T8.  Knowing  the  P.  I.  the  station 
of  the  T.  S.  can  be  found.  There  are  now  four  ways  of  locating  the 
curve. 

1.  The  curve  may  be  run  from  the  T.  S.  to  the  S.  C.  by  deflection 
angles  and  chord  measurements,  using  Table  VII  for  multiples  of  a\ 
and  setting  on  intermediate  points  if  necessary  as  advised  in  the  pre- 
ceding article.     To  lay  out  by  5  chords  use  the  deflection  coefficients  for 
every  second  point  computing  a\  as  for  10  chords. 

2.  The  tangent  may  be  continued  from  the  T.  S.  for  Z  feet,  o  laid 
off  and  the  curve  D  run  in  for  the  full  central  angle  7,  using  an  offset 
back  sight  for  the  direction  of  the  offset  tangent,  locating  the  S.  C.  at 
a  distance  corresponding  to  A,  and  which  will  be  nearly  L  —  Z,  and  the 
C.  S.  at  a  distance  from  the  S.  C.  corresponding  to  7  —  2  A,  and  off- 
setting o  to  the  forward  tangent  and  proceeding,  locating  the  spirals 
later  by  deflection  angles,  or  by  offsets  as  in  4  below,  when  staking  out 
for  construction. 

3.  Measure  U  from  the  T.  S.',    establish  a  transit  point,  turn  the 
angle  A  and  measure  V  and  establish  the  S.  C. ;    run  the  spiral  by  de- 
flections from  either  end;  continue  the  central  curve  to  the  C.  S.;   lay 
out  V  and  U  to  get  the  S.  T.  and  run  in  the  final  spiral  by  deflections 
from  either  end. 

4.  Many  times  it  will  be  sufficiently  exact  after  running  the  central 
curve  as  in  2,  to  bisect  the  offset  o  for  a  point  on  the  spiral  and  then  set 
over  such  points  as  may  be  desired  from  tangent  and  curve  respectively, 
making  the  offsets  from  the  tangent  half  proportional  to  the  cube  of 
the  distance  from  T.  S.  and  from  the  curve  half  proportional  to  the 
cube  of  the  distance  from  the  S.  C.     Thus  the  quarter  points  would 
be  offset  1/8  of  \  o  or  0/16  from  tangent  and  curve  respectively. 

Time  may  be  saved  if  a  spiral  that  can  be  found  in  one  of  the  Tables 

IX  to  XXIII  can  be  chosen.     Thus  if  a  i.5-degree  curve  is  to  be  con- 
nected and  the  speed  to  be  considered  is  90  miles  an  hour  or  less,  Table 

X  gives  all  required  quantities  for  the  necessary  spiral  which  is  500 
feet  long.     It  may  be  laid  out  in  ten  chords  of  50  feet  each,  for  which 
deflection  angles  are  found  under  the  A  column*     If  pluses  are  to  be 


44  RAILROAD  FIELD  MANUAL 

located  they  may  be  interpolated  between  the  tabular  values  which 
are  given  for  each  10  feet  on  the  spiral.  But  if  the  speed  considered  is 
only  65  miles  an  hour  Table  XI 1 1  may  be  used,  the  length  of  the  spiral 
being  200  feet.  It  may  be  laid  out  in  10  chords  of  20  feet  for  which 
the  deflection  angles  or  coordinates  are  given  in  the  table  or  it  may  be 
laid  out  by  5  chords  of  40  feet.  Pluses  may  be  interpolated  as  indicated 
above.  If  the  speed  is  60  miles  an  hour,  Table  XIV  may  be  used  and 
the  length  of  spiral  will  be  found  to  be  150  feet.  It  may  be  laid  out  in 
10  chords  of  15  feet  interpolating  in  the  table,  or  better,  by  5  chords  of 
30  feet,  with  quantities  taken  directly  from  the  table.  Thus  each  table 
is  good  for  many  different  spiral  lengths  connecting  curves  of  various 
degrees.  Any  table  may  be  used  in  which  the  degree  of  the  central 
curve  can  be  found  in  the  column  headed  D  provided  the  speed  for 
which  the  table  is  adapted  is  that  for  which  the  curve  is  to  be  spiraled 
or  the  track  canted.  Shorter  spirals  found  in  tables  for  slower  maximum 
speed  than  that  for  which  the  track  is  canted  may  be  used  but  are  not 
recommended  except  where  it  is  necessary  materially  to  save  cost  of 
construction  or  to  fit  cramped  situations  in  cities  or  on  high  embank- 
ments or  in  deep  cuts  when  relining  old  track. 

Spiraling  a  Compound  Curve.  —  The  length  of  spiral  to  connect 
the  two  branches  of  a  compound  curve  may  be  found  just  as  for  a 
tangent  and  simple  curve  by  substituting 
the  difference  of  "degrees"  (A  —  D2)  in 
the  equation  for  length.  It  is  also  prac- 
tically true  that  the  deflections  at  the 
junction  points  with  the  two  branches  to 
the  various  chord  points  of  the  spiral  are 
the  same  as  for  corresponding  chord  points 
of  the  spiral  between  tangent  and  simple 
PIG  T  2-  curve  of  degree  (Dt  —  D2)  if  the  deflections 

are  considered  as  turned  from  equivalent 
chord  points  on  the  respective  curves  rather  than  from  the  tangent. 
Thus  in  Fig.  23,  the  deflection  from  chord  AB  to  chord  AC of  the  spiral  is 
\  A  (A  being  the  central  angle  for  spiral  of  length  L  connecting  a  tangent 
and  (Di  —  D2)°  curve)  if  arc  AB  =  L,  and  from  chord  CE  to  chord 
CA  it  is  the  same.  These  relations  are  closely  approximate.  The 
deflection  from  the  tangent  at  A  is,  if  D2  be  the  degree  of  the  larger 

radius   curve   and   DI  of   the   shorter,  —    -   +  f  A  —  C,    when    A  = 

- — — —  and  C  is  the  correction  to  be  used  when  necessary  or  when 

200 

A  is  more  than  15°.  Or  the  curve  may  be  considered  as  part  of  a  spiral 
from  a  tangent  to  the  curve  of  degree  Dt  and  the  deflection  coefficients 
of  Table  VII  may  be  used. 


THE  SPIRAL  45 

Illustrative  Example.  —  A  4°  curve  is  to  connect  with  an  8°  curve 
the  offset  coming  at  Sta.  464  of  the  4°  curve.     D2  =  4°;    D\  =  8°; 


For  computing  o  and  Z  we  use  D  =  A  —  D2  =  4°,  and  L  =  300, 
whence  A  =  6°,  and  from  the  tables  for  D  =  4,  L  =  300,  and  A  =  6° 
we  find  o  =  2.62  and  Z  =  149.92.  Therefore  C.  S.  =  Sta.  464  — 
149.92  ft.  =  Sta.  462  +  50.08.  If  the  300  feet  is  part  of  a  spiral 
connecting  a  tangent  and  an  8°  curve  and  covers  a  difference  of  4°  in 

o  7" 

its  length  the  whole  spiral  would  be  L8  =  •=:  -  ^-  =  2  L  =  600  feet 

JJi  —  L>2 

covering  a  A  of  24°.  Therefore  Sta.  462  +  50.08  =  C.  S.  is  the  fifth 
chord  point  of  the  spiral.  Since  the  central  angle  consumed  by  the 
spiral  to  be  run  is  18°  and  the  central  angle  up  to  the  fifth  point  of  the 
6oo-foot  spiral  is  6°,  the  difference  is  12°  or  less  than  15°  and  it  will  be 
proper  to  use  Table  VII  with  the  transit  at  the  fifth  chord  point.  Hence 
the  deflections  to  the  several  chord  points  are  16,  34,  54,  76,  and  100 

times  a\.  which  is  -  =  0.08°  or: 
300 

Chord  point  6          7  8  9         10 

Deflection  .................     1.28°  2.72°  4.32°  6.08°  8.00° 

The  chords  are  60  feet  and  the  deflections  from  tangent  at  A  to  the 
corresponding  points  on  the  4°  curve  extended  would  be: 

i.  20     2.40     3.60     4.80     6.00 
The  differences  .............     0.08°  0.32°  0.72°   1.28°  2.00° 

which  would  be  the  deflections  from  corresponding  chord  points  on  the 
DI  curve,  are  the  deflections  for  the  chord  points  of  a  five-chord  spiral 
of  300  feet  connecting  a  tangent  and  4°  =  (Di  —  DZ)  degree  curve. 

Setting  up  on  the  S.  C.,  the  compounding  point  with  the  8°  curve, 
the  deflection  from  the  long  chord  of  the  spiral  to  the  tangent  is  from 

Table  VII,  125  X  01  or  10°.     It  is  also  —  -  —  2°  or,  stated  otherwise, 

the  angle  between  the  long  chord  of  —  stations  of  curve  DZ  and  the 

chord  of  the  spiral  is  2°,  which  is  the  deflection  angle  of  a  3OO-foot  spiral 
connecting  a  tangent  and  4°  =  (D\  —  DZ)  degree  curve. 

Considering  the  whole  spiraled  curve,  and  referring  to  Fig.  24,  in 
which  RI  is  the  shorter  radius  and  RZ  is  the  longer  radius,  the  com- 
pound curve  is  supposed  connected  first  directly  to  the  tangents.  To 
introduce  the  spirals,  the  arc  of  RI  must  be  thrown  in  along  the  line 
of  common  radius  PP\  =  o\  sec  I\.  The  arc  of  RZ  must  be  thrown 
PPz  =  oz  sec  72.  PPi  —  PPz  must  equal  o',  the  proper  offset  ^>r 
the  connecting  spiral.  Therefore  determine  L*  to  find  0%  and  PP*',  t*> 


\ 


RAILROAD   FIELD  MANUAL 


previously  found  and  find  a  trial  value  for  o\  =  -  —  -  —  ; 

sec  /i 
too  small,   oz  or  o'  or  both  may  be  increased,    which   will 

or  L' 


PP2  add  o' 

if  found 

necessitate  increase  in 
or  both;  if  found  too  large  no 
harm  will  result  unless  in  relin- 
ing  track  the  shift  is  too  great. 
The  tangent  distances  are  in- 
creased by  o2  tan  A2  and  01  tan  AI, 
respectively. 

To  lessen  the  movement  of 
existing  track  the  following  pro- 
cedure may  be  had :  Conceive  the 
larger  radius  curve  moved  out- 
ward along  the  common  radius 
line,  and  the  smaller  radius  curve 
moved  inward,  each  by  \  o',  the 

proper  offset  for  the  chosen  spiral ;  find  new  radii  for  the  curves  such  that 

I  o'  cos  72  +  02 


r>  /  r> 

J\\      —  Jvi    — 


—0     COS 

-  - 

vers  7i 


Both  tangent  points  will  be  moved  toward  the  vertex  by 
/2  =  (R*  -  R*  +  I  o'}  sin  72 
/i  =  (R,  -  Rif  -  %  o')  sin  /L 

TABLE  VII.  —  COEFFICIENTS  OF  a\  FOR  DEFLECTION  ANGLES  TO 
CHORD  POINTS 


Deflection 

Transit  at  chord-point  number 

angle  to 
chord-point 

o 

IO 

number 

T.  S. 

i 

2 

3 

4 

5 

6 

7 

8 

9 

S.  C. 

oT.  5. 

0 

2 

8 

18 

32 

50 

72 

98 

128 

162 

200 

I 

i 

O 

5 

14 

27 

44 

65 

90 

119 

152 

189 

2 

4 

4 

o 

8 

20 

36 

56 

80 

108 

140 

176 

3 

9 

10 

7 

o 

II 

26 

45 

68 

95 

126 

161 

4 

16 

18 

16 

IO 

0 

14 

32 

54 

80 

no 

144 

5 

25 

28 

27 

22 

13 

0 

17 

38 

63 

92 

125 

6 

36 

40 

40 

36 

28 

16 

0 

20 

44 

72 

104 

7 

49 

54 

55 

52 

45 

34 

19 

o 

23 

50 

81 

8 

64 

70 

72 

70 

64 

54 

40 

22 

o 

26 

56 

9 

81 

88 

9i 

90 

85 

76 

63 

46 

25 

0 

29 

10  S.  C. 

IOO 

108 

112 

112 

108 

IOO 

88 

72 

52 

28 

0 

TABLE  VIII.  —  GENERAL  FUNCTIONS  —  TEN-CHORD  SPIRAL 


A 

C 

X 

Y 

U 

V 

o=mL—nD 

Z=mL-nD 

A 

A 

L 

L 

L\ 

L 

L 

m 

n 

m 

« 

0.0 

O.OOO 

I.OOOOO 

I.OOOOO 

.00000 

.66667 

•33333 

.00000 

.0000 

.50000 

.0000 

0.0 

.1 

.033 

.00000 

.00000 

.00058 

.66667 

.33333 

.00015 

.0000 

.50000 

.0001 

.1 

.2 

.067 

.00000 

.00000 

.00116 

.66667 

.33333 

.00029 

.0000 

.50000 

.0003 

.2 

•  3 

.100 

.00000 

.00000 

.00175 

.66667 

.33333 

.00044 

.0000 

.50000 

.0004 

•  3 

•  4 

.133 

.00000 

.00000 

.00233 

.66667 

.33333 

.00058 

.0000 

.  50000 

.0005 

.4 

•  5 

.167 

.00000 

0.99999 

.00291 

.66667 

.33334 

.00073 

.0000 

.50000 

.0006 

.5 

.6 

.200 

.00000 

•99999 

•00349 

.66667 

•  33334. 

.00087 

.0000 

.50000 

.0008 

.6 

.7 

.233 

•99999 

•99999 

.00407 

.66667 

•33334 

.00102 

.0000 

.50000 

.0009 

.7 

.8 

.267 

•99999 

.99998 

.00465 

.66667 

.33334 

.OOII6 

.0000 

.50000 

.0010 

.8 

•  9 

.300 

•99999 

•99998 

.00524 

.66668 

•33334 

.00131 

.0000 

.50000 

.0011 

•9 

1.0 

•  333 

•99999 

•99997 

.  00582 

.66668 

.33334 

.00145 

.0000 

.50000 

.0013 

1.0 

.1 

.36? 

.99998 

.99996 

.00640 

.66668 

.33335 

.00160 

.0000 

•49999 

.0014 

.1 

.2 

.400 

•99998 

.99996 

'.00698 

.66668 

.33335 

.00175 

.0000 

•49999 

.0015 

.2 

•  3 

•  433 

•99998 

•99995 

.00756 

.66668 

•33335 

.00189 

.0000 

•49999 

.0017 

•  3 

•  4 

.467 

•99997 

•99994 

.00814 

.66669 

.33335 

.00204 

.0000 

-49999 

.0018 

•  4 

•  5 

.500 

•99997 

•99993 

.00873 

.66669 

.33336 

.00218 

.0000 

•49999 

.0019 

•  5 

.6 

•  533 

•99997 

•99992 

.00931 

.66669 

.33336 

.00233 

.0000 

•49999 

.0020 

.6 

•  7 

.567 

.99996 

•99991 

.00989 

.66670 

.33336 

.00247 

.0000 

•49999 

.0022 

.7 

.8 

.600 

.99996 

.99990 

.01047 

.66670 

.33337 

.00262 

.0000 

.49998 

.0023 

.8 

•  9 

.633 

•  99995 

.99989 

.01105 

.66671 

.33337 

.00276 

.0000 

•49998 

.0024 

•9 

2.0 

.667 

•99995 

.99988 

.01163 

.66671 

•33337 

.  00291 

.0000 

.49998 

.0025 

2.0 

.1 

.700 

•99994 

•99987 

.01222 

.66671 

.33338 

.00305 

.0000 

.49998 

.0027 

.1 

.2 

•  733 

•99994 

•99985 

.01280 

.66672 

.33338 

.00320 

.0001 

•49998 

.0028 

.2 

•  3 

.767 

•99993 

.99984 

.01338 

.66672 

.33338 

.00335 

.0001 

•49997 

.0029 

•  3 

.4 

.800 

.99992 

.99983 

.01396 

.66673 

•33339 

.00349 

.0001 

•49997 

.0031 

•  4 

•  5 

.833 

.99992 

.99981 

.01454 

.66673 

•33339 

.00364 

.0001 

•49997 

.0032 

-5 

.6 

.867 

.99991 

.99980 

.01512 

.66674 

•33340 

.00378 

.0001 

•49997 

•0033 

.6 

.7 

.900 

.99990 

•99978 

.01571 

.66674 

•33340 

•00393 

.0001 

•49996 

.0034 

•  7 

.8 

.933 

.99990 

•99976 

.01629 

.66675 

•33341 

.00407 

.0001 

•49996 

•  0036 

.8 

•  9 

.967 

.99989 

•99975 

.01687 

.66676 

•33342 

.00422 

.0001 

.49996 

.0037 

•  9 

3.0 

I.OOO 

.99988 

•99973 

.01745 

.66676 

•33342 

•00436 

.0001 

•49996 

.0038 

3.0 

.1 

.033 

•99987 

•99971 

.01803 

.66677 

•33343 

.00451 

.0001 

•49995 

.0039 

.1 

.2 

.067 

.99986 

.99969 

.01861 

.66678 

•33343 

.00465 

.0001 

•49995 

.0041 

.2 

•  3 

.100 

.99985 

.99967 

.01919 

.66678 

•33344 

.00480 

.0001 

•49995 

.0042 

•  3 

.4 

.133 

.99985 

.99965 

.01978 

.66679 

•33345 

.00494 

.0001 

•49994 

•  0043 

•  4 

•  5 

.167 

.99984 

.99963 

.02036 

.66680 

•33345 

.00509 

.0001 

•49994 

.0045 

•  5 

.6 

.200 

.99983 

.99961 

.02094 

.66681 

•33346 

.00524 

.0001 

•49994 

.0046 

.6 

.7 

.233 

.99982 

•99959 

.02152 

.66681 

•33347 

.00538 

.0002 

•49993 

.0047 

.7 

.8 

.267 

.99981 

•99956 

.02210 

.66682 

•33347 

.00553 

.0002 

•49993 

.0048 

.8 

•  9 

.300 

.99980 

•99954 

.02268 

.66683 

.33348 

.00567 

.0002 

•49993 

•  0050 

•  9 

4.0 

.333 

.99979 

•99952 

.02326 

.66684 

•33349 

.00582 

.0002 

•49992 

.0051 

4.0 

.1 

.367 

•99978 

•99949 

.02384 

.66685 

•33350 

.00596 

.0002 

•49992 

.0052 

.1 

.2 

.400 

.99976 

•99947 

.02443 

.66686 

•33351 

.00611 

.0002 

•49991 

•  0053 

.2 

•  3 

•  433 

•99975 

•99944 

.02501 

.66686 

•33351 

.00625 

.0002 

•49991 

•  0055 

•  3 

•  4 

.467 

•99974 

•99941 

.02559 

.66687 

•33352 

.00640 

.0002 

•49991 

.0056 

•  4 

•  5 

.500 

•99973 

•99939 

.02617 

.66688 

•33353 

.00654 

.0002 

•49990 

.0057 

•  5 

.6 

.533 

•99972 

.99936 

.02675 

.66689 

•33354 

.00669 

.0002 

•49990 

.0059 

.6 

.7 

.567 

.99970 

•99933 

•02733 

.66690 

•33355 

.00683 

.0002 

.49989 

.0060 

•  7 

.8 

.600 

.99969 

•99930 

.02791 

.66691 

•33356 

.00698 

.0003 

.49989 

.0061 

.8 

•9 

.633 

.99968 

•99927 

.02849 

.66692 

•33357 

.00713 

.0003 

.49988 

.0062 

-9 

5.0 

1.667 

.99967 

.99924 

.02907 

.66693 

•33358 

.00727 

.0003 

.49988 

.0064 

5.0 

(47) 


TABLE   VIII.  —  (Continued^ 


A 

^| 

C 

X 

F 

U 

V 

o=mL—nD 

Z=mL-nD 

A 

L 

L 

L 

L 

L 

m 

n 

m 

n 

5^0 

1.667 

.99967 

-99924 

.02907 

.66693 

.33358 

.00727 

.0003 

.49988 

.0064 

5.0 

.1 

.700 

.99965 

.99921 

.02965 

.66695 

.33359 

.00742 

.0003 

.49987 

.0065 

.1 

.2 

-733 

.99964 

.99918 

.03023 

.66696 

.33360 

.00756 

.0003 

.49987 

.0066 

.2 

3 

.767 

.99962 

•99915 

.03082 

.66697 

.33361 

.00771 

.0003 

.49986 

.0067 

•3 

.4 

.800 

.9996i 

.99912 

.03140 

.66698 

.33362 

.00785 

.0003 

.49986 

.0069 

•  4 

•  5 

.833 

.9996o 

.99908 

.03198 

.66699 

.33363 

.00800 

.0003 

.49985 

.0070 

•  5 

.6 

.867 

.99958 

•99905 

.03256 

.66700 

.33364 

.00814 

.0003 

.49985 

.0071 

.6 

.7 

.900 

•99957 

.99902 

.03314 

.66702 

.33365 

.00829 

.0004 

.49984 

.0073 

.7 

.8 

•  933 

•99955 

.99898 

-03372 

.66703 

.33366 

.00843 

.0004 

.49984 

.0074 

.8 

•  9 

.967 

•99953 

.99895 

.03430 

.66704 

.33367 

.00858 

.0004 

.49983 

.0075 

-9 

6.0 

2.OOO 

•99952 

.99891 

.03488 

.66705 

.33369 

.00872 

.0004 

.49982 

.0076 

6.0 

.1 

2.033 

.99950 

-99887 

.03546 

.66707 

•33370 

.00887 

.0004 

.49982 

.0078 

.1 

.2 

2.067 

•99949 

.99884 

.03604 

.66708 

-33371 

.00901 

.0004 

.49981 

.0079 

.2 

•  3 

2.100 

•99947 

.99880 

.03662 

.66709 

•33372 

.00916 

.0004 

.49981 

.0080 

•  3 

•  4 

2.133 

•99945 

.99876 

.03720 

.66711 

•33373 

.00930 

.0005 

.4998o 

.0081 

•  4 

-5 

2.167 

•99944 

.99872 

•03778 

.66712 

•33375 

.00945 

.0005 

•49979 

.0083 

•  5 

.6 

2.200 

•99942 

.99868 

.03836 

.66713 

.33376 

.00959 

.0005 

•49979 

.0084 

.6 

•  7 

2.233 

-99940 

.99864 

.03894 

.66715 

•33377 

.00974 

.0005 

•49978 

.0085 

.7 

.8 

2.267 

.99938 

.99860 

•03952 

.66716 

•33379 

.00989 

.0005 

.49977 

.0086 

.8 

.9 

2.300 

.99936 

.99856 

.04010 

.66718 

.33380 

.01003 

.0005 

•49977 

.0088 

•  9 

7.0 

2-333 

•99935 

.99852 

.04068 

.66719 

.33381 

.01018 

.0005 

•49976 

.0089 

7.0 

.1 

2.367 

.99933 

.99847 

.04126 

.66721 

.33383 

.  01032 

.0006 

•49975 

.0090 

.1 

.2 

2.400 

•99931 

.99843 

.04184 

.66722 

•33384 

.01047 

.0006 

•49975 

.0091 

.2 

•  3 

2.433 

.99929 

.99839 

.04242 

.66724 

.33385 

.01061 

.0006 

•49974 

.0093 

•  3 

•  4 

2.467 

.99927 

.99834 

.04300 

.66725 

.33387 

.  01076 

.0006 

•49973 

.0094 

•  4 

•  5 

2.500 

.99925 

.99830 

.04358 

.66727 

•33388 

.01090 

.0006 

•49972 

.0095 

•  5 

.6 

2.533 

.99923 

.99825 

.04416 

.66729 

•33390 

.01105 

.0006 

•49972 

.0097 

.6 

-7 

2.567 

•99921 

.99821 

.04474 

.66730 

•33391 

.01119 

.0007 

•49971 

.0098 

-7 

.8 

2.600 

.99919 

.99816 

.04532 

.66732 

•33393 

.01134 

.0007 

•49970 

.0099 

.8 

.9 

2.633 

•99917 

.998n 

.04590 

.66734 

.33394 

.01148 

.0007 

.49969 

.0100 

•  9 

8.0 

2.666 

.99914 

.99806 

.04648 

-66735 

.33396 

.01163 

.0007 

.49969 

.0102 

8.0 

.1 

2.699 

.99912 

.99801 

.04706 

.66737 

.33398 

.01177 

.0007 

.49968 

.0103 

.1 

.2 

2.733 

•99910 

.99797 

.04764 

.66739 

•33399 

.01192 

.0007 

.49967 

.OIO4 

.2 

•  3 

2.766 

.99908 

•99792 

.04822 

.66741 

•33401 

.01206 

.0008 

.49966 

.OIO5 

•  3 

•  4 

2-799 

.99906 

.99786 

.04880 

.66742 

•33402 

.OI22I 

.0008 

.49965 

.0107 

•  4 

•  5 

2.833 

.99903 

.99781 

.04937 

.66744 

•33404 

.01235 

.0008 

•49965 

.0108 

•  5 

.6 

2.866 

.99901 

.99776 

.04995 

.66746 

.33406 

.01250 

.0008 

.49964 

.0109 

.6 

.7 

2.899 

.99899 

•99771 

.05053 

.66748 

•33407 

.01264 

.0008 

.49963 

.0110 

•  7 

.8 

2.933 

.99897 

.99766 

.05111 

.66750 

.33409 

.01279 

.0009 

.49962 

.0112 

.8 

.9 

2.966 

.99894 

.9976o 

.05169 

.66752 

•334II 

.01293 

.0009 

.4996i 

.0113 

•9 

9.0 

2.999 

.99892 

•99755 

.05227 

.66754 

•33413 

.01308 

.0009 

.4996o 

.0114 

9.0 

.1 

3-033 

.99889 

•99749 

.05285 

.66756 

•33414 

.OI322 

.0009 

•49959 

.OIl6 

.1 

.2 

3.066 

.99887 

.99744 

.05343 

,66758 

.33416 

.01337 

.0009 

•49959 

.OII7 

.2 

•3 

3.099 

.99884 

.99738 

.05400 

.66760 

•33418 

.01351 

.0010 

•49958 

.0118 

•  3 

•  4 

3-133 

.99882 

•99733 

.05458 

.66762 

.33420 

.01366 

.0010 

•49957 

.0119 

•  4 

•  5 

3-166 

.99879 

.99727 

.05516 

.66764 

•33422 

.01381 

.0010 

•49956 

.OI20 

•  5 

.6 

3.199 

.99877 

•99721 

•05574 

.66766 

.33424 

•01395 

.0010 

•49955 

.OI22 

.6 

.7 

3.232 

.99874 

-99715 

.05632 

.66768 

.33425 

.01410 

.0010 

•49954 

.0123 

.7 

.8 

3.266 

.99872 

.99709 

.05690 

.66770 

•33427 

.01424 

.0011 

•49953 

.OI24 

.8 

•  9 

3.299 

.99869 

.99704 

.05747 

.66772 

.33429 

.01439 

.OOII 

.49952 

.OI26 

•  9 

10.0 

3-332 

.99866 

.99698 

.  05805 

.66774 

-33431 

.01453 

.0011 

•49951 

.OI27 

10.0 

(48) 


TABLE  VIII.  —  (Continued) 


A 

C 

X 

F 

U 

V 

o=mL—nD 

Z=*mL—nD 

A 

/L 

L 

L 

L 

L 

L 

m 

n 

m 

n 

10.0 

3.332 

.99866 

.99698 

.05805 

.66774 

-33431 

.01453 

.0011 

•49951 

.0127 

10.0 

.1 

3.366 

.99864 

.99691 

.05863 

.66776 

.33433 

.01468 

.0011 

•49950 

.0128 

.1 

.2 

3.399 

.99861 

•99685 

.05921 

.66779 

•33435 

.01482 

.0012 

•49949 

.0129 

.2 

•3 

3.432 

.99858 

.99679 

.05979 

.66781 

•33437 

.01497 

.0012 

.49948 

.0131 

•  3 

•4 

3.466 

.99856 

.99673 

.06036 

.66783 

•33439 

.01511 

.0012 

•49947 

.0132 

4 

•  5 

3.499 

.99853 

.99667 

.06094 

.66785 

•33441 

.01526 

.0012 

.49946 

•  0133 

•  5 

.6 

3-532 

.99850 

.99660 

.06152 

.66787 

•33443 

.01540 

.0012 

•49945 

•  0134 

.6 

.7 

3-566 

.99847 

.99654 

.06210 

.66790 

•33446 

.01555 

.OOI3 

•49944 

.0136 

•  7 

.8 

3.599 

.99844 

.99647 

.06267 

.66792 

•33448 

.01569 

.0013 

•49943 

•  0137 

.8 

•  9 

3.632 

.99841 

.99641 

.06325 

•66794 

•33450 

.01584 

•  OOI3 

•49942 

.0138 

•  9 

11.0 

3.666 

.99838 

.99634 

.06383 

.66797 

.33452 

.01598 

.OOI3 

•49941 

.0139 

11.0 

.1 

3-699 

.99835 

.99627 

.06441 

.66799 

•33454 

.01612 

.0014 

•49940 

.0141 

.1 

.2 

3-732 

.99832 

.99621 

.06498 

.66802 

•33456 

.01627 

.OOI4 

•49939 

.0142 

.2 

•  3 

3.765 

.99829 

.99614 

.06556 

.66804 

•33459 

.01641 

.OOI4 

•49937 

•0143 

•  3 

•  4 

3-799 

.99826 

.99607 

.06614 

.66806 

.33461 

.  01656 

.OOI4 

•49936 

.0144 

•  4 

.5 

3.832 

.99823 

.99600 

.06671 

.66809 

.33463 

.01670 

.0015 

•49935 

.0146 

•  5 

.6 

3-865 

.99820 

•99593 

.06729 

.66811 

.33465 

.01685 

.0015 

•49934 

.0147 

.6 

.7 

3-899 

.99817 

.99586 

.06787 

.66814 

.33468 

.01699 

.OOI5 

•49933 

.0148 

•  7 

.8 

3-932 

.99814 

•99579 

.06844 

.66816 

•33470 

.01714 

.0015 

•49932 

.0149 

.8 

.9 

3.965 

.99811 

•99572 

.06902 

.66819 

•33472 

.01728 

.OOl6 

•49931 

.0151 

•  9 

12.0 

3-999 

.99808 

.99565 

.06960 

.66822 

•33475 

•01743 

.OOl6 

•49929 

.0152 

12.0 

.1 

4-032 

.99804 

.99557 

.  07017 

.66824 

•33477 

•01757 

.OOl6 

•49928 

•  0153 

.1 

.2 

4.065 

.99801 

•99550 

•07075 

.66827 

•33479 

.01772 

.OOl6 

•49927 

•  0154 

.2 

•  3 

4.098 

•99798 

•99543 

.07133 

.66830 

.33482 

.01786 

.001? 

•49926 

.0156 

•  3 

•4 

4-132 

•99795 

.99535 

.07190 

.66832 

.33484 

.01801 

.OOI7 

•49925 

.0157 

•  4 

•  5 

4.165 

•99791 

.99528 

.07248 

.66835 

.33487 

.01815 

.0017 

•49923 

.0158 

•  5 

.6 

4.198 

•99788 

•99520 

.07305 

.66838 

•33489 

.01830 

.O0l8 

•49922 

.0159 

.6 

.7 

4-232 

.99785 

•99513 

•07363 

.66840 

•33492 

.  01844 

.ooiJ 

•49921 

.0160 

.7 

.8 

4.265 

.99781 

.99505 

.07421 

.66843 

•33494 

.01859 

.0018 

-49920 

.0162 

.8 

•  9 

4.298 

.99778 

•99497 

.07478 

.66846 

•33497 

.01873 

.0018 

•49918 

•  0163 

•  9 

13.0 

4-331 

•99774 

.99489 

.07536 

.66849 

•33499 

.01888 

.0019 

.49917 

.0164 

13.0 

.1 

4.365 

•99771 

.99481 

•07593 

.66852 

•33502 

.01902 

.0019 

.49916 

.0165 

.1 

.2 

4.398 

.99767 

•99474 

.07651 

.66854 

•33504 

.01917 

.0019 

•49915 

.0167 

.2 

•  3 

4-431 

.99764 

.99467 

.07708 

•66857 

•33507 

.01931 

.0020 

•49913 

.0168 

3 

•  4 

4.465 

.99760 

•99457 

.07766 

.66860 

•33510 

.01946 

.0020 

•49912 

.0169 

•  4 

•  5 

4.498 

•99757 

•99449 

.07823 

.66863 

•33512 

.01960 

.OO20 

•499II 

.0170 

•  5 

.6 

4-531 

•99753 

•99441 

.07881 

.66866 

•33515 

.01974 

.0020 

•49909 

.0172 

.6 

.7 

4.564 

•99749 

•99433 

•07938 

.66869 

•33518 

.01989 

.0021 

.49908 

•  0173 

•  7 

.8 

4.598 

.99746 

•99425 

.07996 

.66872 

•33520 

.02003 

.0021 

•49907 

.0174 

.8 

•  9 

4-631 

•99742 

•99416 

.08053 

.66875 

•33523 

.02018 

.0021 

.49905 

•  0175 

•  9 

14.0 

4.664 

•99738 

.99408 

.0811 

.66878 

•33526 

.02032 

.0022 

•49904 

•0177 

14.0 

.1 

4.698 

•99735 

•99399 

.08168 

.66881 

•33529 

.02047 

.0022 

•49903 

.0178 

.1 

.2 

4-73 

•99731 

•99391 

.08226 

.66884 

•33531 

.02061 

.OO22 

•49901 

.0179 

.2 

3 

4.764 

•99727 

•99382 

.08283 

.66887 

•33534 

.02076 

.0023 

.49900 

.0180 

•  3 

•  4 

4-797 

•99723 

•99374 

.0834 

.66890 

•33537 

.02090 

.0023 

.49898 

.0182 

•  4 

•  5 

4.83 

•997IS 

.99365 

.0839 

.66893 

•33540 

.02105 

.0023 

•49897 

.0183 

•  S 

.6 

4.864 

•997IS 

•99356 

.0845 

.66897 

-33543 

.02119 

.OO2* 

.49896 

.0184 

.6 

.7 

4.89 

•9971 

•99347 

.0851 

.66900 

.33546 

.02134 

.0024 

.49894 

.0185 

-7 

.8 

4-93 

.99708 

•99339 

.0857 

.66903 

•33549 

.  0214* 

.OO24 

.49893 

.0186 

.8 

•  9 

4.96 

•  9970 

•99330 

.0862 

.66906 

•  3355 

.02162 

.O025 

.49891 

.0188 

•  9 

15.0 

4-99 

.9970 

-9932 

.0868 

.66909 

•  3355 

.0217 

.OO2S 

.49890 

.0189 

15  0 

(49) 


TABLE   VIII.  —  (Continued) 


A 

15  °0 

.1 

.2 
•3 

•  4 
•  5 
.6 

•  7 
.8 
•9 
16.0 
.1 

.2 
•  3 

•  4 

'.6 

.7 
.8 
•9 
17.0 
.1 

.2 

•3 

•4 
•  S 
.6 

.7 
.8 
•9 
18.0 
.1 

.2 
•3 

•4 
•  S 
.6 

.7 
.8 
>9 
19.0 
.1 

.2 

3 
•4 
•  5 
.6 

.7 
.8 
•  9 
20.0 

A 

4-997 

C 

X 

Y 

u 

V 

o=mL—nD  1  Z=mL—nD 

A 

15  0 
.1 

.2 

•3 

•4 
•  5 
.6 

•  7 
.8 
•  9 
16.0 
.1 

.2 

•  3 

•  4 
.5 
.6 

.7 
.8 
•  9 
17.0 
.1 

.2 

•  3 

•4 
•  5 
.6 

.7 
.8 
•  9 
18.0 
.1 

.2 

•3 

•4 
•  5 
.6 

•  7 
.8 
•9 
19.0 
.1 

.2 

•3 
•  4 
•  S 
.6 

•  7 
.8 
•  9 
20.0 

.99700 

•33555 

m 

.02177 

— 

.OO25 

m 

.49890 

n 

•99321 

.08685 

.66909 

.0189 

5-030 
5.064 
.5.097 
5.130 
5.163 
5-197 
5.230 
5.263 
5.296 

.99696 
.99692 
•99687 
.99683 
.99679 
.99675 
.99671 
.99667 
.99662 

•99312 
•99302 
.99293 
.99284 
.99275 
.99265 
.99256 
.99246 
.99237 

.08742 
.08799 
.08857 
.08914 
.08971 
.09028 
.09086 
•09143 
.09200 

.66913 
.66916 
.66919 

.66923 
.66926 
.66929 

.66933 
.66936 
.66940 

•33558 
.33561 
•33564 
•33567 
•33570 
•33573 
.33576 
•33579 
-33582 

.02191 
.  02206 

.  O2220 
.02235 
.02249 
.  O2264 
.02278 
.  O2292 
.02307 

.OO25 
.O026 
.0026 
.0026 
.C027 
.O027 
.OO27 
.0028 
.OO28 

.49888 
.49887 
.49885 

.49884 
.49882 
•49881 

.49879 
.49878 
.49876 

.0190 
.0191 
•  0193 
•  0194 
.0195 
.0196 

.0198 
.0199 

.0200 

5-330 

.99658 

.99227 

.09257 

.66943 

.33585 

.O232I 

.0028 

•49875 

.0201 

5.363 
5.396 
5.429 
5.463 
5-496 
5.529 
5.563 
5.596 
5.629 

.99654 
.99650 
.99645 
.99641 
.99637 
.99632 
.99628 
.99623 
.996i9 

.99218 
.99208 
.99198 
.99188 
.99178 
.99169 
•99159 
.99148 
.99138 

.09315 
.09372 
.09429 

.  09486 
•09543 
.09600 

.09658 
.09715 
.09772 

-66947 
.66950 
.66954 

.66957 
.66961 
.66964 
.66968 
.66972 
.66975 

•33588 
.33592 
•33595 
•33598 
.33601 
.33605 
.33608 
.33611 
.33615 

.02336 
.02350 
.02365 
.02379 
.02393 
.  024O8 
.O2422 
.02437 
.02451 

.O029 
.OO29 
.O029 
.0030 
.OO3O 
.OO3O 
.0031 
.OO3I 
.0032 

.49873 
.49872 
.49870 
.49868 
.49867 
.49865 
.49863 
.49862 
.49860 

.O202 

.O204 
.0205 
.0206 
.0207 
.0209 
.O2IO 
.O2II 
.O2I2 

5.662 

.99614 

.99128 

.09829 

.66979 

.33618 

.  02466 

.0032 

.49859 

.0213 

5.696 
5.729 
5.762 

5.796 
5.829 
5.862 

5.896 
5.929 
5.962 

.99610 
.99605 
.99601 

•99596 
•99591 
.99587 
.99582 
•99577 
•99572 

.99"8 
.99108 
.99097 
.99087 
.99076 
.99066 

.99055 

.99044 
•99034 

.09886 
.09943 
.10000 

.10057 
.10114 
.10171 
.10228 
.10285 
.  10342 

.66983 
.66986 
.66990 
.66994 
.66998 
.67002 

.67005 
.67009 
.67013 

.33621 
.33625 
.33628 
.33632 
.33635 
.33639 
.33642 
•33646 
.33649 

.02480 
.02494 
.02509 
.02523 
.02538 
.02552 

.02567 
.02581 
.02595 

.0032 
.0033 
•  0033 
.0033 
.0034 
.0034 
.0035 
.0035 
•  0035 

.49857 
.49855 
.49853 
.49852 
.49850 
.49848 
.49847 
•49845 
.49843 

.O2I5 
.0216 
.O2I7 
.0218 
.0220 
.O22I 
.O222 
.0223 
.0224 

5-995 

.99568 

.99023 

.10399 

.67017 

.33653 

.O26lO 

.0036 

•49841 

.0226 

6.028 
6.062 
6.095 
6.128 
6.161 
6.194 
6.228 
6.261 
6.294 

.99563 
.99558 
•99553 
.99548 
.99543 
.99538 

.99533 
.99528 
.99523 

.99012 
.99001 
.98990 

98979 
.98968 
.98957 
.98946 
.98935 
.98923 

.10456 
.10513 
.10570 
.  10627 
.10684 
.10741 
.10798 
.10855 
.10912 

.67021 
.67025 
.67029 

.67033 
.67037 
.67041 

.67045 
.67049 
.67053 

.33657 
.33660 
.33664 
.33667 
.33671 
.33675 

.33679 
.33682 
.33686 

.  02624 
.02639 
.02653 

.02667 
.02682 
.02696 
.O27II 
.02725 
.02739 

.0036 
•  0037 
.0037 

.0037 
.0038 
.0038 

.0039 
.0039 
•  C039 

.49840 
.49838 
.49836 
.49834 
.49833 
.49831 
.49829 
.49827 
.49825 

.O227 
.0228 
.O229 
.0230 
.0232 
.0233 
.0234 
•0235 
.0236 

6.328 

.99518 

.98912 

.  10968 

.67058 

-33690 

.02754 

.0040 

.49823 

.0238 

6.361 
6.394 
6.427 
6.461 
6.494 
6.527 
6.560 
6.594 
6.627 

.99513 
.99508 
•99503 
.99498 
•99493 
.99487 
.99482 
•99477 
-99472 

.98901 
.98889 
.98878 
.98866 
.98854 
.98843 
.98831 
.98819 
.98807 

.11025 
.11082 
•III39 
.11196 
.11252 
.11309 
.11366 
.11423 
.11479 

.67062 
.67066 
.67070 

.67074 
.67079 
.67083 

.67087 
.67092 
.67096 

.33694 
.33697 
•33701 
.33705 
.33709 
.33713 
.33717 
•33721 
.33725 

.02768 
.02783 
.02797 
.02811 
.02826 
.02840 
.02854 
.02869 
.02883 

.0040 
.0041 
.0041 
.0041 
.0042 
.0042 
.0043 
.0043 
.0044 

.49821 
.49820 
.49818 
.49816 
.49814 
.49812 

.49810 
.49808 
.49806 

•  0239 
.0240 
.0241 
.0242 
.0244 
.0245 
.0246 
.0247 
.0248 

6.660 

.99466 

.98795 

.11536 

.67100 

.33729 

.02898 

.0044 

.49804 

.0250 

(50) 


TABLE  VIII.  —  (Continued) 


A 

20  °0 

.1 

.2 

•3 
•4 
•  5 
.6 

•  7 
.8 
•  9 
21.0 
.1 

.2 

•  3 

•  4 
•  5 
.6 

•  7 
.8 
•  9 
22.0 
.1 

.2 
•3 
•  4 
•  5 
.6 

.7 
.8 
-9 
23.0 
.1 

.2 

3 

•4 
•5 
.6 

•  7 
.8 
-9 
24.0 
.1 

.2 

•3 

•4 
•5 
.6 

•  7 
.8 
•9 
25.0 

A 
6.660 

C 

X 

F 

U 

V 

o=mL—nD 

Z=mL—nD 

A 

20!  o 

.1 

.2 

•  3 

•  4 
•  5 
.6 

•  7 
.8 
-9 
21.0 
.1 

.2 

•  3 
•  4 
•  5 
.6 

•  7 
.8 
9 
22.0 
.1 

.2 

•  3 

•  4 
-5 
.6 

-7 
.8 
•9 
23.0 

.1 

.2 

•  3 

-4 
-5 
.6 

•  7 
.8 
•9 
24.0 
.1 

.2 

3 

•  4 
•  5 
.6 

-7 
.8 
•  9 
25.0 

L 

.99466 

L 

L 

.11536 

L 

.67100 

L 

m 

n 

.0044 

m 
.49804 

n 

.0250 

.98795 

.33729 

.02898 

6.693 
6.727 
6.759 

6.793 
6.826 
6.859 
6.892 
6.926 
6-959 

.99461 
-99456 
•99450 
•99445 
•99439 
•99434 
.99428 
•99423 
.99417 

.98783 
.98771 
.98759 
.98747 
.98734 
.98722 

.98710 
.98697 
.98685 

.11593 
.11649 
.  11706 

•11763 
.11819 
.11876 
.H932 
.11989 
.  12046 

.67105 
.67109 
.67114 
.67118 
.67123 
.67127 
.67132 
.67136 
.67141 

•33733 
•33737 
•33741 
•33745 
•33749 
•33753 

•33757 
.33762 
.33766 

.02912 
.02926 
.02941 
.02955 
.02969 
.02984 
.02998 
.03013 
.03027 

.0044 
.0045 
.0045 
.0046 
.0046 
.0047 
.0047 
.0048 
.0048 

.49802 
.49800 
.49798 
.49796 
•49794 
.49792 
•49790 
.49788 
•49786 

.0251 
.0252 
•  0253 

.0254 
.0256 
.0257 
.0258 
•  0259 
.0260 

6.992 

•99412 

.98672 

.  I2IO2 

.67145 

•33770 

.03041 

.0048 

.49784 

.0262 

7.026 
7.059 
7.092 

7-125 
7-158 
7.192 
7.225 
7-258 
7.291 

.99406 
.99400 
•99395 
.99389 
.99383 
•99378 
•99372 
.99366 
.9936o 

.98660 
.98647 
.98634 
.98622 
.98609 
•98596 
-98583 
.98570 
.98557 
.98544 

•I2I59 
.12215 
.  12272 
.12328 
.12385 
.12441 

.12497 

.12554 
.12610 

.67150 
.67155 
•67159 
.67164 
.67169 
•67173 
.67178 
.67183 
.67188 

•33774 
.33778 
.33783 
.33787 
•33791 
.33796 
.33800 
.33804 
.33809 

.03056 
.03070 
.03084 

.03099 
.03113 
.03127 

.03142 
.03156 
.03170 

.0049 
.0049 
.0050 

.0050 
.0051 
.0051 
.0052 
.0052 
.0053 

.49782 
.49780 
•49778 
.49776 
•49774 
.49772 
•49770 
.49768 
.49765 

.0263 
.0264 
.0265 
.0266 
.0267 
.0269 
.0270 
.0271 
.0272 

7-324 

-99354 

.12667 

.67193 

.33813 

.03185 

•  0053 

.49763 

•  0273 

7-358 
7-391 
7.424 

7-458 
7-491 
7.524 
7-557 
7-590 
7.623 

•99349 
•99343 
•99337 
•99331 
.99325 
•99319 
•99313 
.99307 
-99301 

.98531 
.98517 
.98504 
.98491 
.98477 
.98464 
.98450 
.98437 
-98423 

.12723 
.12779 
.12836 
.12892 
.12948 
.13005 
.  13061 
.13117 
.13173 

.67197 
.67202 
.67207 
.67212 
.67217 
.67222 
.67227 
.67232 
•67237 

.33818 
.33822 
•33827 

.33831 
.33836 
.33840 
.33845 
.33849 
.33854 

•03199 
•03213 
.03228 
.03242 
.03256 
.03271 
.03285 
.03299 
.03314 

.0054 
.0054 
•  0055 

•0055 
.0056 
.0056 

.0057 
.0057 
.0058 

.49761 
•49759 
•49757 
.49755 
•49752 
•49750 
.49748 
.49746 
•49744 

.0275 
.0276 
.0277 
.0278 
.0279 
.0281 
.0282 
.0283 
.0284 

7.657 

.99295 

.98409 

.13230 

.67242 

.33859 

.03328 

.0058 

•49741 

.0285 

7.690 
7-723 
7.756 

7.789 

7.822 
7.856 
7.889 
7.922 
7-955 

.99288 
.99282 
.99276 

.99270 
.99264 
•99257 
.99251 
.99245 
.99238 

.98396 
.98382 
.98368 

.98354 
.98340 
.98326 

.98312 
.98298 
.98283 

.  13286 
.13342 
.13398 

.13454 
.13510 
.13567 
.13623 
.13679 
.13735 

.67247 
.67252 
.67258 

.67263 
.67268 
•67273 
.67278 
.67284 
.67289 

.33863 
.33868 
.33873 

.33877 
.33882 
.33887 
.33892 
.33896 
•33901 

.03342 
.03357 
.03371 

.03385 
.03400 
.03414 
.03428 
.03443 
.03457 

•  0059 
.0059 
.0060 
.0060 
.0061 
.0061 
.0062 
.0062 
.0063 

•49739 
•49737 
•49735 
•49732 

.49730 
.49728 

.49725 
.49723 
•49721 

.0286 
.0288 
.0289 
.0290 
.0291 
.0292 

.0293 
•  0295 
.0296 

7.989 

.99232 

.98269 

.13791 

.67294 

.33906 

-03471 

.0063 

.49718 

.0297 

8.022 

8.055 
8.088 

8.  121 

8.154 
8.188 

8.221 

8.254 
8.287 

.99226 
•99219 
.99213 
.99206 
.99200 
•99193 

.99187 
.99180 
•99174 

.98255 
.98240 
.98226 
.98211 
.98197 
.98182 

.98167 
.98153 
.98138 

.13847 
.13903 
.13959 
.14015 
.14071 
•  14127 
.14183 
.14239 
.14295 

.67300 
.67305 
.67310 

.67316 
.67321 
.67327 

.67332 
.67338 
.67343 

•339II 
.33916 
•33921 
.33926 
•33931 
•33936 

•33941 
.33946 
•33951 

.03485 
.03500 
.03514 
.03528 
.03543 
•03557 
.03571 
.03585 
.03600 

.0064 
.0064 
.0065 
.0065 
.0066 
.0066 
.0067 
.0067 
.0068 

.49716 
•49714 
•497II 
.49709 
.49707 
•49704 
•49702 
.49699 
.49697 

.0298 
.0299 
.0300 
.0302 
.0303 
.0304 
.0305 
.0306 
.0307 

8.321 

.99167 

.98123 

.14350 

.67349 

.33956 

.0361* 

.0068 

.49695 

.0309 

(51) 


TABLE   VIII.  —  (Continued) 


A 

25°0 

.1 

.2 

•3 

•4 
•  5 
.6 

•  7 
.8 
.9 
26.0 
.1 

.2 

•  3 

•4 

'.6 

.7 
.8 
•9 
27.0 
.1 

.2 
3 

•4 
•  5 
.6 

•  7 
.8 
•  9 
28.0 
.1 

.2 

.3 

.4 
•  5 
.6 

.7 
.8 
•  9 
29.0 

.1 

.2 

-3 

•  4 
•  5 
.6 

.7 
.8 
•  9 
30.0 

A 
8.321 

C 
L 

.99167 

X 

Y 

U 

V 

o=mL—nD 

Z=mL-nD 

A 

L 

L 

L 

L 

.33956 

m 
.03614 

n 

m 

n 
.0309 

.98123 

•14350 

.67349 

.0068 

.49695 

25°.  0 

.1 

.2 

•  3 

.4 

'.6 

•  7 
.8 
•  9 
26.0 

.1 

.2 
•3 

•4 
•  5 
.6 

•  7 
.8 
•9 
27.0 
.1 

.2 
•3 
•4 
•  5 
.6 

•  7 
.8 
•  9 
28.0 

.1 

.2 
•3 

•  4 
•  5 
.6 

•  7 
.8 
•  9 
29.0 
.1 

.2 
•3 

•4 
•  5 
.6 

•  7 
.8 
•9 
30.0 

8.354 
8.387 
8.420 

8.453 
8.486 
8.519 

8.553 
8.586 
8.619 

.99160 
.99154 
.99147 
.99140 
..99133 
.99127 
.99120 
.99113 
.99106 

.98108 
.98093 
.98078 

.98063 
.98048 
.98033 
.98017 
.98002 
.97987 
•97971 

.14406 
.  14462 
•14518 

•14574 
.14629 
.14685 
•I474I 
•14797 
.14852 

.67354 
.67360 
.67365 
.67371 
.67377 
.67382 

.67388 
.67394 
.67400 

•33961 
•33966 
-33971 
.33976 
.33982 
.33987 
.33992 
-33997 
.34002 

.03628 
.03643 
.03657 
.03671 
.03685 
.03700 

.03714 
.03728 
.03742 

.0069 
.0069 
.0070 
.0071 
.0071 
.0072 
.0072 
.0073 
.0073 

.49692 
.49690 
•49687 

.49685 
.49682 
.49680 

.49677 
.49675 
.49672 

.0310 
.0311 
.0312 

.0313 
.0314 
.0315 

.0317 
.0318 
.0319 

8.652 

.90099 

.14908 

.67405 

.34008 

.03757 

.0074 

•49670 

.0320 

8.685 
8.719 
8.752 

8.785 
8.818 
8.851 
8.884 
8.917 
8.951 

.99092 
.99085 
.99078 
.99071 
.99064 
•99057 
.99050 
•99043 
.99036 

.97956 
•97940 
.97925 
.97909 
.97893 
.97878 
.97862 
.97846 
-97830 

.14964 
.15019 
.15075 

.15131 
.15186 
.15242 
.15297 
•15353 
.15408 

.67411 
.67417 
.67423 
.67429 
.67435 
.67441 

.67447 
.67452 
.67458 

-34013 
.34018 
.34024 
.34029 
.34035 
.34040 

.34045 
.34051 
.34056 

.03771 
.03785 
.03800 

.03814 
.03828 
.03842 

.03857 
.03871 
.03885 

.0074 
.0075 
.0076 
.0076 
.0077 
.0077 
.0078 
.0078 
.0079 

.49667 
.49665 
.49662 

.49660 
.49657 
.49654 
.49652 
.49649 
.49647 

.0321 
.0322 
.0323 

.0325 
.0326 
.0327 
.0328 
.0329 
.0330 

8.984 

.99029 

.97814 

.15464 

.67465 

.34062 

.03899 

.0080 

.49644 

.0331 

9.017 
9-050 
9.083 
9.116 
9-149 
9-183 
9.216 
9-249 
9.282 

.99022 
•99014 
.99007 
.99000 
.98993 
•98985 
.98978 
.98971 
•98963 

•97798 
.97782 
.97766 

•97749 
•97733 
.97717 
.97700 
.97684 
.97667 

.15519 
•15575 
.15630 
.15686 
.15741 
.15796 
.15852 
.15907 
.15962 

.67471 
.67477 
.67483 
.67489 
.67495 
.67501 

•67507 
•67514 
.67520 

•34067 
•34073 
.34079 
.34084 
•34090 
.34095 
.34101 
•34107 
.34113 

.03913 
.03929 
.03942 
.03956 
.03970 
.03985 

.03999 
.04013 
.04027 

.0080 
.0081 
.0081 
.0082 
.0082 
.0083 
.0084 
.0084 
.0085 

.49641 
.49639 
.49636 

.49633 
.49631 
•49629 
.49625 
•49623 
.49620 

.0333 
.0334 
.0335 
•  0336 
•  0337 
.0338 

•  0339 
.0340 
•  0342 

9-315 

.98956 

.97651 

.16018 

.67526 

.34118 

.04041 

.0085 

.49617 

.0343 

9-348 
9.381 
9-415 
9-448 
9.481 
9-514 

9-547 
9.58o 
9.613 

.98948 
.98941 
.98933 
.98926 
.98918 
.98911 
.98903 
.98895 
.98888 

.97634 
.97617 
.97601 

.97584 
.97567 
•97550 

•97533 
-97SI6 
•97499 

.  16073 
.16128 
.16183 

.16239 
.16294 
.16349 
.16404 
.16459 
.16514 

.67532 
.67539 
.67545 
.67551 
.67558 
.67564 
.67571 
.67577 
.67584 

.34124 
.34130 
.34136 

.34141 

.34147 
•34153 
.34159 
.34165 
.34171 

.04056 
.04070 
.04084 
.04098 
.04113 
.04127 
.04141 
.04155 
.04169 

.0086 
.0087 
.0087 
.0088 
.0088 
.0089 
.0090 
.0090 
.0091 

.49615 
.49612 
.49609 
.49606 
.49604 
.49601 

.49598 
•49595 
•49592 

.0344 
.0345 
.0346 

•  0347 
.0348 
.0349 
•  0351 
.0352 
.0353 

9.647 

.98880 

.97482 

.16569 

.67590 

.34177 

.04184 

.0092 

.49590 

.0354 

9.680 
9-713 
9.746 

9-779 
9.812 
9-845 
9.878 
9-9II 
9-945 

.98872 
.98865 
.98857 
.98849 
.98841 
.98833 
.98826 
.98818 
.98810 

.97465 
•97447 
•97430 
.97413 
•97395 
•97378 
.97360 
•97343 
•97325 

.16624 
.16679 
.16734 
.16789 
.16844 
.16899 

.16954 
.17009 
.17064 

.67597 
.67603 
.67610 
.67616 
.67623 
.67630 
.67636 
.67643 
.67650 

.34183 
.34189 
.34195 
.34201 
.34207 
•34213 
.34219 
.34225 
.34232 

.04198 
.04212 
.04226 
.04240 
.04254 
.04269 

.04283 

.04297 
.04311 

.0092 
.0093 
.0093 
.0094 
.0095 
.0095 
.0096 
.0097 
.0097 

.49587 
.49584 
.49581 
.49578 
•49575 
•49573 
•49570 
.49567 
.49564 

.0355 
.0356 
.0357 
.0358 
.0359 
.0361 

.0362 
.0363 
.0364 

9-978 

,98802 

-97307 

.I7H9 

.67657 

.34238 

.04325 

.0098 

.49561 

.0365 

(52) 


TABLE  VIII.  —  (Continued^ 


A 

30  °0 
.1 
.2 
•3 
•  4 
•  5 
.6 

•  7 
.8 
•  9 
31.0 
.1 

.2 

•3 
•4 
•  5 
.6 

.7 
.8 
•  9 
32.0 
.1 

.2 

•  3 
•  4 
•  5 
.6 

.7 
.8 
•  9 
33.0 
.1 

.2 

•  3 

•  4 

'.6 

•  7 
.8 
•9 
34.0 
.1 

.2 

•3 

•  4 
•  5 
.6 

•  7 
.8 
•9 
35.0 

A 
9.978 

C 
L 

.98802 

X 

F 

U 

V 

o—mL—nD 

Z=mL-nD 

A 

30  ."0 
.1 

.2 
•3 

•  4 
5 
.6 

'.8 
•9 
31.0 
.1 

.2 

•3 

•  4 
•  5 
.6 

•  7 
.8 
•9 
32.0 

.1 

..2 

•3 

•  4 
•  5 
.6 

•  7 
.8 
•  9 
33.0 

.1 

.2 

•3 

•  4 
•  5 
.6 

•  7 
.8 
•  9 
34.0 
.1 

.2 
•3 
.4 
•  5 
.6 

•  7 
.8 
•  9 
35.0 

L 

.97307 

L 

.17119 

L 

-67657 

L 

.34238 

m 
.04325 

« 
.0098 

m 

.49561 

n 
.0365 

IO.OII 

10.044 
10.077 

10.  IIO 
10.143 
10.176 

10.209 
10.242 
10.276 

-98794 
.98786 
.98778 
.98770 
.98762 
.98754 
.98745 
.98737 
.98729 

.97290 
.97272 
•97254 
.97236 
.97218 
.97200 
.97182 
•  97164 
.97146 

.17174 
.  17229 
.17283 
.17338 
.17393 
.17448 
.17502 
•17557 
.17612 

.67663 
.67670 
.67677 
.67684 
.67691 
.67698 

.67705 
.67712 
.67719 

.34244 
.34250 
•34257 
.34263 
•34269 
•34276 
.34282 
.34288 
.34295 

•04339 
•04354 
.04368 

.04382 
.04396 
.04410 

.04424 
.04439 
•04453 

.0098 
.0099 

.0100 

.0100 

.0101 
.0102 
.0102 
•  OIO3 
.OIO4 

.49558 
•49555 
.49552 

•49549 
•49546 
•49543 
•49540 
•49537 
.49534 

.0366 
.0367 
.0368 

.0369 
•0371 
.0372 

.0373 

•  0374 
•  0375 

10.309 

.98721 

.97127 

.17666 

.67726 

.34301 

.04467 

.OI04 

•49531 

•  0376 

10.342 
10.375 
10.408 
10.441 
10.474 
10.507 
10.540 
10.573 
10.607 

.98713 
.98704 
.98696 
.98688 
.98680 
.98671 
.98663 
.98654 
.98646 

.97109 
.97091 
.97072 

.97054 
-97035 
.97017 

.96998 
.96979 
.96960 

.  17721 
•  17776 
.17830 
.17885 
•17939 
•17994 
.  18048 
.  18103 
.18157 

.67733 
.67740 
•67747 

.67754 
.67761 
.67768 

•67775 
.67783 
.67790 

.34308 
•34314 
•34321 

•34327 
•34334 

•34340 

•34347 
•34353 
.34360 

.04481 
•04495 
.04509 

•04523 
.04538 
•04552 
.04566 
.04580 
•04594 

.0105 
.0106 
.OIO6 
.OIO7 
.OIO8 
.0108 
.0109 
.0110 
.OIIO 

•49528 
•49525 
•49522 

•49519 
.49516 
•49513 
•49510 
•49507 
•49504 

•  0377 
•  0378 
•  0379 
.0380 
.0381 
.0383 
•  0384 
.0385 
.0386 

10.640 

•98637 

.96942 

.18212 

.67797 

.34367 

.04608 

.OIII 

•49501 

.0387 

10.673 
10.706 
10.739 
10.772 
10.805 
10.838 
10.871 
10.904 
10.937 

.98629 
.98620 
.98612 
.98603 
•98595 
.98586 

.98577 
.98569 
.98560 

.96923 
.96904 
.96885 
.96866 
.96847 
.96828 
.96808 
.96789 
•96770 

.18266 
.18320 
.18375 
.18429 
.18483 
.18538 
.18592 
.18646 
.18700 

.67804 
.67812 
.67819 
.67826 
•67834 
.67841 

.67849 
.67856 
.67864 

•34373 
•34380 
.34387 

•34394 
.34400 
•34407 

.34414 
.34421 
.34428 

.04622 
.04636 
.04650 

.04665 
.04679 
•04693 
.04707 
.04721 
•04735 

.0112 
.0112 
.0113 
.OII4 
.0114 
.0115 
.0116 
.0116 
.Oil? 

.49498 
.49495 
•49491 
.49488 
.49485 
.49482 

•49479 
-49476 
•49473 

.0388 
.0389 
.0390 

.0391 
.0392 
•  0393 
•  0394 
•  0395 
•  0397 

10.970 

.98551 

•96750 

.18754 

.67871 

•34435 

•04749 

.0118 

.49469 

.0398 

11.003 
11.036 
11.069 

11.103 
11.136 
11.169 
n.  202 
11.235 
11.268 

.98543 
•98534 
.98525 
.98516 
.98507 
.98499 
.98490 
.98481 
.98472 

.96731 
.96712 
.96692 
.96672 
.96653 
.96633 
.96613 
.96593 
.96574 

.18809 
.18863 
.18917 
.18971 
.19025 
.19079 

.19133 
.19187 
.19241 

.67879 
.67886 
.67894 
.67901 
.67909 
.67917 
.67925 
.67932 
.67940 

•34442 
-34448 
•34455 
.34462 
.34469 
•34477 
.34484 
•34491 
•34498 

•04763 
.04777 
•04791 
.04805 
.04820 
.04834 
.04848 
.04862 
.04876 

.0118 
.0119 
.OI20 
.0121 
.OI2I 
.OI22 
.OI23 
.0123 
.OI24 

.49466 
.49463 
.49460 

•49457 
•49453 
.49450 

•49447 
•49443 
.49440 

•0399 
.0400 
.0401 
.0402 
.0403 
.0404 
.0405 
.0406 
.0407 

11.301 

.98463 

.96554 

.19295 

.67948 

•34505 

.04890 

.OI25 

•49437 

.0408 

11.334 
11.367 
11.400 

11.433 
11.466 
".499 
11-532 
II-565 
"•598 

.98454 
.98445 
.98436 
.98427 
.98417 
.98408 

.98399 
.98390 
.98381 

.96534 
.96514 
.96494 
.96473 
.96453 
.96433 
.96413 
.96392 
.96372 

.19349 
.19403 
•19457 
•I95IO 
.19564 
.19618 

.19672 
.19726 
•19779 

.67956 
.67963 
.67971 
.67979 
.67987 
•67995 
.68003 
.68011 
.68019 

•34512 
•34519 
•34527 
•34534 
•34541 
•34548 
.34556 
.34563 
•34570 

.04904 
.04918 
•04932 
.04946 
.04960 
.04974 
.04988 
.05002 
.05016 

.0126 
.OI26 
.0127 
.0128 
.0128 
.0129 
.0130 
.0131 
.0131 

.49434 
•49430 
•49427 
.49424 
.49420 
.49417 
.49414 
•49410 
.49407 

.0409 
.0410 
.0411 
.0412 
.0413 
.0415 
.0416 
.0417 
.041? 

11.631 

.98371 

.96351 

.19833 

.68027 

•34578 

.05030 

.0132 

.49404 

.0419 

(53) 


TABLE   VIII.  —  (Continued} 


A 

C 

X 

F 

U 

V 

o=mL—nD 

Z=mL—nD 

A 

L 

L 

L 

L 

L 

m 

n 

m 

n 

A 

35.0 

11.631 

.98371 

.96351 

•  19833 

.68027 

.34578 

.05030 

.0132 

.49404 

.0419 

35  °0 

.1 

11.664 

.98362 

.96331 

.  19887 

.68035 

.34585 

.05044 

.0133 

.49400 

.0420 

.1 

.2 

11.698 

.98353 

.96310 

.19940 

.68043 

•34593 

.05058 

•  0133 

•49397 

.0421 

.2 

•3 

11.731 

.98344 

.96290 

•19994 

.68051 

.34600 

.05072 

.0134 

•49393 

.0422 

•3 

•4 

11.764 

.98334 

.96269 

.20047 

.68059 

.34608 

.05086 

•  0135 

.49390 

.0423 

.4 

•  5 

11.797 

.98325 

.96248 

.20IOI 

.68068 

.34615 

.05100 

.0136 

.49387 

.0424 

•  5 

.6 

11.830 

•98315 

.96227 

•20155 

.68076 

.34623 

•05115 

.0136 

.49383 

.0425 

.6 

.7 

11.863 

.98306 

.96207 

.20208 

.68084 

.34630 

.05129 

.0137 

.49380 

.0426 

.7 

.8 

11.896 

.98297 

.96186 

.  2O262 

.68092 

.34638 

•05143 

.0138 

•49376 

.0427 

.8 

•  9 

11.929 

.98287 

.96165 

.20315 

.68101 

.34645 

•05157 

•  0139 

•49373 

.0428 

•  9 

36.0 

11.961 

.98278 

.96144 

.20368 

.68109 

.34653 

.05171 

•  0139 

.49369 

.0429 

36.0 

.1 

11.994 

.98268 

•96123 

.  2O422 

.68117 

.34661 

•05185 

.0140 

.49366 

.0430 

.1 

.2 

12.027 

.98259 

.96102 

•20475 

.68126 

.34668 

•05199 

.0141 

.49362 

.0431 

.2 

•3 

12.061 

.98249 

.96080 

.20529 

.68134 

.34676 

.05213 

.0142 

•49359 

.0432 

•  3 

•4 

12.094 

•98239 

•96059 

.20582 

.68142 

.34684 

.05227 

.0142 

•49355 

•  0433 

•  4 

•  5 

12.127 

.98230 

.96038 

.20635 

.68151 

•34692 

.05241 

•  0143 

•49352 

•  0434 

•  5 

.6 

12.159 

.98220 

.96017 

.20689 

.68159 

•34699 

•05255 

.0144 

.49348 

•  0435 

.6 

•  7 

12.192 

.98210 

•95995 

.20742 

.68168 

•34707 

.05269 

•  0145 

•49345 

.0436 

•  7 

.8 

12.226 

.98201 

•95974 

•20795 

.68176 

•34715 

.05282 

.0145 

•49341 

•  0437 

.8 

-9 

12.259 

.98191 

•95952 

.20848 

.68185 

•34723 

.05296 

.0146 

.49338 

.0438 

•  9 

37.0 

12  .  292 

.98181 

•95931 

.  2O9OI 

.68194 

•34731 

.05310 

.0147 

•49334 

.0439 

37.0 

.1 

12.324 

.98171 

.95909 

•20955 

.68202 

•34739 

•05324 

.0148 

•49330 

.0440 

.1 

.2 

12.358 

.98162 

.95887 

.21008 

.68211 

•34747 

.05338 

.0149 

.49327 

.0441 

.2 

•3 

12.391 

.98152 

.95866 

.21061 

.68219 

•34754 

•05352 

.0149 

•49323 

.0442 

•  3 

•  4 

12.424 

.98142 

.95844 

.21114 

.68228 

.34762 

.05366 

.0150 

•49320 

•  0443 

•  4 

•  5 

12.456 

.98132 

.95822 

.21167 

.68237 

•34770 

.05380 

.0151 

.49316 

•  0444 

•  5 

.6 

12.489 

.98122 

.95800 

.21220 

.68246 

•34779 

•05394 

.0152 

.49312 

•  0445 

.6 

•  7 

12.523 

.98112 

.95778 

.21273 

.68254 

.34787 

.05408 

.0152 

•49309 

.0446 

.7 

.8 

12-556 

.98102 

•95756 

.21326 

.68263 

•34795 

.05422 

.0153 

.49305 

.0447 

.8 

•9 

12.588 

.98092 

•95734 

.21379 

.68272 

•34803 

.05436 

.0154 

-49302 

.0448 

•  9 

38.0 

12.621 

.98082 

•95712 

.21432 

.68281 

•34811 

.05450 

.0155 

.49298 

.0449 

38.0 

.1 

12.654 

.98072 

.95690 

.21485 

.  68290 

.34819 

.05464 

.0156 

.49294 

.0450 

.1 

.2 

12.687 

.98062 

.95668 

•21537 

.68299 

•34827 

•05478 

.0156 

.49291 

.0451 

.2 

•3 

12  .  72O 

.98052 

.95646 

.21590 

.68307 

.34835 

•05492 

.0157 

.49287 

.0452 

•3 

.4 

12.753 

.98042 

.95623 

.21643 

.68316 

.34844 

.05506 

.0158 

.49283 

•  0453 

•4 

•  5 

12.786 

.98032 

.956oi 

.21696 

.68325 

.34852 

.05520 

•  0159 

•49279 

•  0454 

•  5 

.6 

12.819 

.98022 

•95578 

.21749 

.68334 

.34860 

.05534 

•  0159 

.49276 

•  0455 

.6 

•  7 

12.852 

.98011 

.95556 

.  21801 

-68343 

•34869 

.05548 

.0160 

.49272 

.0456 

.7 

.8 

12.885 

.98001 

•95533 

.21854 

.68353 

.34877 

.05561 

.0161 

.49268 

.0457 

.8 

.8 

12.918 

.97991 

•95511 

.21907 

.68362 

.34885 

•05575 

.0162 

.49265 

.0458 

•  9 

39.0 

12.951 

.9798i 

.95488 

.21959 

.68371 

.34894 

.05589 

.0163 

.49261 

.0459 

39.0 

.1 

12.984 

•97970 

.95466 

.22012 

.68380 

.34902 

•05603 

.0163 

.49257 

.0460 

.1 

.2 

13.017 

.9796o 

•95443 

.22065 

.68389 

•349II 

.05617 

.0164 

.49253 

.0461 

.2 

•3 

13-050 

•97950 

•95420 

.22117 

.68398 

.34919 

.05631 

.0165 

.49250 

.0462 

•3 

.4 

13.083 

•97939 

•95397 

.22I7O 

.68408 

.34928 

.05645 

.0166 

.49246 

.0463 

•  4 

•  5 

13.116 

.97929 

•95374 

.22222 

.68417 

.34936 

.05659 

.0167 

.49242 

.0464 

•  5 

.6 

I3.U9 

.97919 

•95351 

.22275 

.68426 

•34945 

.05673 

.0168 

.49238 

.0465 

.6 

•  7 

13.182 

.97908 

•95328 

.22327 

•68435 

•34953 

.05687 

.0168 

.49234 

.0466 

•  7 

.8 

13-215 

.97898 

•95305 

.22379 

.68445 

.34962 

.05701 

.0169 

.49231 

.0467 

.8 

•  9 

13-247 

.97887 

.95282 

.22432 

.68454 

•34970 

.05714 

.0170 

.  49227 

.0468 

•  9 

40.0 

13.281 

.97877 

•95259 

.22484 

.68464 

•34979 

.05728 

.0171 

.49223 

.0469 

40.0 

(54) 


TABLE  IX.  —  SPIRAL  FUNCTIONS  FOR  CHANGE  OF  0.2°  PER  100  FEET 

SUITABLE  FOR  SPEEDS  OF  104  MILES  AN  HOUR  OR  LESS  AND 

CURVES  OF  i°  OR  LESS 


L 

D 

A 

A 

z 

0 

C 

X 

Y 

U 

V 

10 

0 

O.O2 

O.OOI 

o.ooo 

5.00 

o.oo 

10.00 

10.00 

0.00 

6.67 

3-33 

20 

.04 

.004 

.001 

IO.OO 

.00 

20.00 

20.00 

.00 

13  33 

6.6? 

30 

.06 

.009 

.003 

15.00 

.00 

30.00 

30.00 

.00 

20.00 

10.00 

40 

.08 

.016 

.005 

20.00 

.00 

40.00 

40.00 

.00 

26.67 

13-33 

50 

.IO 

.025 

.008 

25.00 

.00 

50.00 

50.00 

.01 

33-33 

16.67 

60 

.12 

.036 

.012 

30.00 

.00 

60.00 

60.00 

.01 

40.00 

20.00 

70 

•  14 

.049 

.016 

35-00 

.00 

70.00 

70.00 

.02 

46.67 

23-33 

80 

.16 

.064 

.021 

40.00 

.01 

80.00 

80.00 

•  03 

53-33 

26.67 

90 

.18 

.081 

.027 

45.00 

.01 

90.00 

90.00 

.04 

60.00 

30.OO 

100 

.20 

.100 

•  033 

50.00 

.01 

IOO.OO 

IOO.OO 

.06 

66.67 

33-33 

10 

.22 

.121 

.040 

55-00 

.02 

10.00 

10.00 

.08 

73-33 

36.67 

20 

•24 

•  144 

.048 

60.00 

•03 

20.00 

20.00 

.10 

80.00 

40.00 

30 

.26 

.169 

.056 

65.00 

.03 

30.00 

30.00 

.13 

86.67 

43-33 

40 

.28 

.196 

.065 

70.00 

.04 

40.00 

40.00 

.16 

93-33 

46.67 

50 

•30 

.225 

•  075 

75-00 

.05 

50.00 

50.00 

.20 

IOO.OO 

50.00 

60 

•  32 

.256 

.085 

80.00 

.06 

60.00 

60.00 

-24 

06.67 

53-33 

70 

•  34 

.289 

.096 

85.00 

.07 

70.00 

70.00 

.28 

13.33 

56.67 

80 

•  36 

•  324 

.108 

90.00 

.08 

80.00 

80.00 

-34 

20.00 

60.00 

90 

•  38 

.361 

.120 

95-00 

.10 

90.00 

90.00 

.40 

26.67 

63.33 

200 

•  40 

.400 

.133 

100.00 

.12 

200.00 

200.00 

-47 

133.33 

66.67 

10 

.42 

•  441 

.147 

105.00 

-13 

IO.OO 

IO.OO 

-54 

40.00 

70.00 

20 

•  44 

•  484 

.161 

110.00 

.15 

20.00 

20.00 

.62 

46.67 

73-33 

30 

-46 

•  529 

.176 

115.00 

.18 

30.00 

30.00 

•  71 

53.33 

76.67 

40 

.48 

.576 

.192 

120.  OO 

.20 

40.00 

40.00 

.80 

60.00 

80.00 

50 

•  SO 

.625 

.208 

125.00 

-23 

50.00 

50.00 

-91 

66.67 

83.33 

60 

•52 

.676 

.225 

130.00 

.26 

60.00 

60.00 

.02 

73.33 

86.67 

70 

•  54 

.729 

.243 

135.00 

.29 

70.00 

70.00 

-14 

80.00 

90.00 

80 

•  56 

•  784 

.261 

140.00 

.32 

80.00 

79-99 

.28 

86.67 

93-34 

90 

•  58 

.841 

.280 

145.00 

•  35 

90.00 

89.99 

•  42 

93.33 

96.67 

300 

.60 

.900 

.300 

150.00 

•  39 

300.00 

99.99 

-57 

200.00 

IOO.OO 

10 

.62 

.961 

.320 

155.00 

-43 

10.00 

309.99 

-73 

06.67 

103.34 

20 

.64 

.024 

•341 

160.00 

.48 

20.00 

19.99 

•  91 

13.33 

106.67 

30 

.66 

.089 

.363 

165.00 

•  52 

29.99 

29.99 

.09 

20.00 

110.00 

40 

.68 

.156 

.385 

170.00 

•  57 

39.99 

39.99 

-29 

26.67 

113.34 

50 

.70 

.225 

.408 

175.00 

.62 

49.99 

49.98 

•  49 

33.34 

116.67 

60 

•  72 

.296 

•  432 

180.00 

.68 

59.99 

59.98 

2.71 

40.01 

120.01 

70 

•  74 

.369 

.456 

185.00 

•  74 

69.99 

69.98 

2.95 

46.67 

123.34 

80 

.76 

•  444 

.481 

189.99 

.80 

79-99 

79.98 

3.19 

53-34 

126.67 

90 

•  78 

.521 

j  -507 

194.99 

.86 

89.99 

89.97 

3-45 

60.  01 

130.01 

400 

.80 

.600 

•  533 

199.99 

•  93 

99.99 

99.97 

3-72 

266.68 

133.34 

10 

.82 

.681 

.560 

204.99 

.00 

409.98 

409.96 

4.01 

73-35 

136.68 

20 

.84 

•  764 

.588 

209.99 

.08 

19.98 

19.96 

4-31 

80.02 

140.01 

30 

.86 

-849 

.618 

214.99 

.16 

29.98 

29.96 

4-63 

86.68 

143.35 

40 

.88 

.936 

.645 

219.99 

.24 

39.98 

39.95 

4-96 

93-35 

146.68 

So 

.90 

.025 

.675 

224.99 

•  33 

49.98 

49.94 

5-30 

300.02 

150  .  02 

60 

•92 

.116 

•  70S 

229.99 

-42 

59.97 

59-94 

5-66 

06.69 

153.35 

70 

•  94 

.209 

•736 

234.99 

•  51 

69.97 

69.93 

6.04 

13.36 

156.69 

80 

•  96 

.304 

.768 

239.98 

.61 

79.97 

79-92 

6.43 

20.03 

160.02 

90 

•  98 

2.401 

.800 

244.98 

•  71 

89.96 

89-91 

6.84 

26.70 

163.36 

500 

I.OO 

2.500 

.833 

249.98 

1.82 

499.96 

499-91 

7.27 

333-37 

166.70 

(55) 


TABLE  X.  — SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  0.3°  PER  100 

FEET.     SUITABLE  FOR  SPEEDS  OF  91  MILES  AN  HOUR  OR 
LESS,  OR  CURVES  OF  1.5°  OR  LESS 


L 

D 

A 

A 

Z 

o 

C 

X 

Y 

U 

V 

10 

0.03 

O.OOI 

O.OOI 

5.00 

o.oo 

10.00 

IO.OO 

o.oo 

6.67 

3-33 

20 

.06 

.006 

.002 

10.  OO 

.00 

20.00 

20.00 

.00 

13-33 

6.6? 

30 

.09 

.013 

.005 

15.00 

.00 

30.00 

30.00 

.00 

20.00 

10.00 

40 

.12 

.024 

.008 

20.00 

.00 

40.00 

40.00 

.00 

26.67 

13.33 

50 

•  IS 

.037 

.013 

25.00 

.00 

50.00 

50.00 

.01 

33-33 

16.67 

60 

.18 

•  054 

.018 

30.00 

.00 

60.00 

60.00 

.02 

40.00 

20.00 

70 

.21 

•  073 

.025 

35-00 

.01 

70.00 

70.00 

.03 

46.67 

23-33 

80 

.24 

.096 

.032 

40.00 

.01 

80.00 

80.00 

.04 

53-33 

26.67 

90 

•  27 

.121 

.041 

45-00 

.02 

90.00 

90.00 

.06 

60.00 

3O.OO 

100 

.30 

•  ISO 

.050 

50.00 

.02 

100.00 

100.00 

.09 

66.67 

33-33 

10 

•  33 

.I8l 

.061 

55-00 

.03 

IIO.OO 

IIO.OO 

.12 

73-33 

36.67 

20 

.36 

.216 

.072 

60.00 

.04 

120.  OO 

120.00 

.15 

80.00 

40.00 

30 

•39 

•253 

.085 

65.00 

.05 

130.00 

130.00 

•  19 

86.67 

43-33 

40 

•  42 

.294 

.098 

70.00 

.06 

140.00 

140  .  oo 

.24 

93-33 

46.67 

50 

•  45 

.337 

.113 

75-00 

•  07 

150.00 

150.00 

.29 

IOO.OO 

50.00 

60 

.48 

.384 

.128 

80.00 

•09 

160.00 

160.00 

.36 

106.67 

53-33 

70 

•  SI 

•  433 

.145 

85.00 

.11 

170.00 

170.00 

•  43 

113.33 

56.67 

80 

•  54 

.486 

.162 

90.00 

•  13 

180.00 

180.00 

•  51 

I2O.OO 

60.00 

90 

•57 

•  541 

.181 

95-oo 

.15 

190.00 

190.00 

.60 

126.67 

63.33 

200 

.60 

.600 

.200 

IOO.OO 

•  17 

200.00 

200.00 

•  70 

133.33 

66.67 

10 

.63 

.661 

.221 

105.00 

.20 

210.00 

2IO.OO 

.81 

140.00 

70.00 

20 

.66 

.726 

.242 

IIO.OO 

-23 

220.00 

220.00 

•  93 

146.67 

73.33 

30 

.69 

•  793 

.265 

115.00 

•  27 

230.OO 

230.00 

1.  06 

153.33 

76.67 

40 

•  72 

.864 

.288 

120.  OO 

.30 

24O.OO 

240  .  oo 

1.  21 

160.00 

8o.OO 

50 

•  75 

•937 

.313 

125.00 

•  34 

250.00 

250  .  oo 

1.36 

166.67 

83.34 

60 

.78 

1.014 

•338 

130.00 

•  38 

26O.OO 

259-99 

1-53 

173.34 

86.67 

70 

.81 

1.093 

-365 

135-00 

•  43 

269.99 

269.99 

1.72 

180.00 

90.00 

80 

•  84 

1.176 

•  392 

140  .  oo 

.48 

279-99 

279.99 

1.92 

186.67 

93-34 

90 

•  87 

1.261 

.421 

145.00 

•  53 

289.99 

289.99 

2.13 

193.34 

96.67 

300 

.90 

1.350 

•  450 

150.00 

.59 

299-99 

299.98 

2.36 

20O.OI 

100.01 

10 

•  93 

1.441 

.481 

155-00 

.65 

309-99 

309.98 

2.60 

206.67 

103.34 

20 

•  96 

1.536 

•  512 

160.00 

•  7i 

319-99 

319.98 

2.86 

213-34 

106.67 

30 

•99 

1.633 

•  545 

165.00 

•  79 

329.99 

329.97 

3-14 

22O.OI 

110.  01 

40 

1.02 

1.734 

.578 

170.00 

.86 

339-99 

339-97 

3-43 

226.68 

113.34 

50 

1.05 

1.837 

.613 

175-00 

•93 

349-99 

349-96 

3-74 

233-35 

116.68 

60 

1.  08 

1-944 

.648 

180.00 

1.02 

359-98 

359-96 

4.07 

240.02 

120.01 

70 

I.  II 

2.053 

.685 

184.99 

I.  II 

369.98 

369.95 

4-42 

246.68 

123-35 

80 

1.  14 

2.166 

.722 

189.99 

1.20 

379-98 

379-94 

4-79 

253-35 

126.68 

90 

1.  17 

2.281 

.761 

194-98 

1.29 

389.97 

389.94 

5-i8 

260.02 

130.02 

400 

1.20 

2.400 

.800 

199-98 

1.40 

399-97 

399-93 

5-58 

266.69 

133.36 

10 

1.23 

2.521 

.841 

204.98 

1-50 

409.96 

409.92 

6.01 

273-36 

136.69 

20 

1.26 

2.646 

.882 

209.98 

1.62 

419.96 

419-91 

6.46 

280.03 

140.03 

30 

1.29 

2.773 

.925 

214.98 

1-74 

429.96 

429.90 

6-94 

286.70 

143-37 

40 

1.32 

2.904 

.968 

219.98 

1.86 

439-95 

439-89 

7-43 

293-37 

146.70 

50 

1.35 

3-037 

1.013 

224.98 

1.98 

449-95 

449-87 

7-95 

300.04 

I50.0/) 

60 

1.38 

3-174 

1.058 

229.97 

2.13 

459-94 

459-86 

8.49 

306.72 

153.38 

70 

1.41 

3.313 

1.105 

234-97 

2.27 

469.93 

469-84 

9.06 

313-39 

156.72 

80 

1.44 

3.456 

1.152 

239-96 

2.41 

479-92 

479-83 

9-65 

320.06 

160.06 

90 

1-47 

3-6oi 

I.  201 

244.96 

2-57 

489.92 

489.81 

10.27 

326.74 

163.40 

500 

1.50 

3.7<>0 

1.250 

249.96 

2.72 

499.90 

499-79 

10.91 

333-41 

166.74 

(56) 


TABLE  XL  — SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  0.4°  PER  100 

FEET.    SUITABLE  FOR  SPEEDS  OF  83  MILES  AN  HOUR  OR 
LESS,  OR  CURVES  OF  2.0°  OR  LESS 


L 

D 

A 

A 

Z 

o 

C 

X 

Y 

U 

V 

10 

0.04 

o 
O.O02 

O.OOI 

S-oo 

o.oo 

10.  OO 

IO.OO 

o.oo 

6.67 

3-33 

20 

.08 

.008 

.003 

10.00 

.00 

20.00 

20.00 

.00 

13-33 

6.67 

30^ 

.12 

.018 

.006 

15.00 

.00 

30.00 

30.00 

.00 

20.00 

10.00 

40 

.16 

.032 

.on 

20.00 

.00 

40.00 

40.00 

.01 

26.67 

13.33 

So 

.20 

.050 

.016 

25.00 

.00 

50.00 

50.00 

.02 

33-33 

16.67 

60 

•  24 

.072 

.024 

30.OO 

.01 

60.00 

60.00 

.03 

40.00 

20.00 

70 

.28 

.008 

.033 

35.00 

.01 

70.00 

70.00 

•  04 

46.67 

23-33 

80 

.32 

.128 

.043 

40.00 

.01 

80.00 

80.00 

.06 

53-33 

26.67 

90 

.36 

.162 

.054 

45-00 

.02 

90.00 

90.00 

.08 

60.00 

30.00 

100 

.40 

.200 

.067 

50.00 

.03 

100.00 

100.00 

.12 

66.67 

33-33 

10 

•  44 

.242 

.081 

55-00 

.04 

IIO.OO 

IIO.OO 

.16 

73-33 

36.67 

20 

•  48 

.288 

.096 

60.00 

.05 

120.00 

I2O.OO 

.20 

80.00 

40.00 

30 

•  52 

.338 

.113 

65.00 

.06 

130.00 

130.00 

.26 

86.67 

43-33 

40 

.56 

.392 

.131 

70.00 

.08 

140.00 

140.00 

•  32 

93-33 

46.67 

So 

.60 

•450 

.150 

75-00 

.10 

150.00 

150.00 

•39 

IOO.OO 

5O.OO 

60 

.64 

.512 

.171 

80.00 

.12 

160.00 

160.00 

.48 

106.67 

53-33 

70 

.68 

.578 

.193 

85.00 

•  14 

170.00 

170.00 

•  57 

113.33 

56.67 

80 

.72 

.648 

.216 

90.00 

.17 

180.00 

180.00 

.68 

120.  OO 

60.00 

90 

•  76 

.722 

.241 

95-00 

.20 

190.00 

190.00 

.80 

126.67 

63.33 

200 

.80 

.800 

.267 

IOO.OO 

.23 

200.00 

200.00 

•93 

133-33 

66.67 

10 

.84 

.882 

.294 

105  .  oo 

.27 

2IO.OO 

210.  OO 

i.  08 

I40.OO 

70.00 

20 

.88 

.968 

•  323 

IIO.OO 

.31 

22O  .  OO 

219-99 

1.24 

146.67 

73-33 

30 

.92 

1.058 

•  353 

115.00 

•  35 

230.00 

229.99 

1.41 

153-34 

76.67 

40 

•  96 

1.  152 

.384 

I2O.OO 

.40 

24O.OO 

239-99 

1.61 

I60.00 

80.00 

50 

1.  00 

1.250 

.417 

125.00 

.46 

250.00 

249-99 

1.82 

166.67 

83.34 

60 

1.04 

I.3S2 

•  451 

130.00 

.51 

259-99 

259.98 

2.04 

173-34 

86.67 

70 

1.  08 

1.458 

.486 

135.00 

•  57 

269.99 

269.98 

2.29 

ISO.OI 

90.01 

80 

1.  12 

1.568 

•  523 

140.00 

.64 

279-99 

279.98 

2.55 

186.67 

93-34 

90 

1.16 

1.682 

.561 

144.99 

•  71 

289.99 

289.97 

2.84 

193.34 

96.67 

300 

1.20 

1.800 

.600 

149.99 

•  79 

299-99 

299-97 

3.14 

2OO.OI 

IOO.OI 

10 

1.24 

1.922 

.641 

154.99 

.86 

309-98 

309.97 

3-47 

206.68 

103.34 

20 

1.28 

2.048 

.683 

159.99 

•  95 

319.98 

319  96 

3.8z 

213-35 

106.68 

30 

1.32 

2.178 

.726 

164.99 

1.05 

329.98 

329.95 

4-18 

220.02 

110.02 

40 

1.36 

2.312 

•  771 

169.99 

1.14 

339-98 

339.95 

4-57 

226.68 

113-35 

So 

1.40 

2.450 

.817 

174.98 

1.25 

349-97 

349.94 

4-99 

233.36 

II6.69 

60 

1.44 

2.592 

.864 

179.98 

1.36 

359-97 

359-93 

5-43 

240.03 

120.02 

70 

1.48 

2.738 

.913 

184.98 

1.48 

369.96 

369.91 

5.89 

246.69 

123.36 

80 

I.S2 

2.888 

.963 

189.98 

i.  60 

379-96 

379-90 

6.38 

253-37 

126.70 

90 

1-56 

3.042 

1.014 

194.98 

1.72 

389.95 

389-89 

6.90 

260.04 

130.03 

400 

1.  60 

3.200 

1.067 

199.97 

1.86 

399-94 

399-88 

7-44 

266.71 

133-37 

10 

1.64 

3.362 

1.  121 

204.97 

2.OO 

409.94 

409.86 

8.02 

273.38 

136.71 

20 

1.68 

3-528 

I.I76 

209.97 

2.  IS 

419.93 

419.84 

8.61 

280.06 

140.05 

30 

1.72 

3.698 

1.233 

214.96 

2.31 

429-92 

429.82 

9-25 

286.73 

143-39 

40 

1.76 

3.872 

I.29I 

219.96 

2.48 

439-91 

439-80 

9.90 

293.41 

146.73 

So 

i.  80 

4.050 

1.350 

224.95 

2.65 

449-90 

449-78 

10.  60 

300.08 

ISO.O? 

60 

1.84 

4.232 

1.  411 

229.95 

2.83 

459-89 

459-75 

11.32 

306.76 

153-41 

70 

1.88 

4.418 

1.473 

234.95 

3-02 

469.88 

469.72 

12.07 

313.43 

156.75 

80 

1.92 

4.608 

1.533 

239.94 

3-22 

479-87 

479.69 

12.86 

320.11 

160.10 

90 

1.96 

4.802 

1.601 

244.93 

3-42 

489-85 

489.66 

13-68 

326.79 

163.44 

500 

2.00 

5.000 

1.667 

249.93 

3-63 

499.84 

499.62 

14.54 

333  •  47 

166.79 

(57) 


TABLE  XII.  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  0.5°  PER  100 

FEET.    SUITABLE  FOR  SPEEDS  OF  77  MFLES  AN  HOUR  OR 

LESS,  OR  CURVES  OF  2.0°  OR  LESS 


L 

D 

A 

A 

Z 

o 

C 

X 

Y 

U 

V 

10 

0 

0.05 

0 

O.002 

o 
O.OOI 

5-00 

o.oo 

IO.OO 

10.00 

0.00 

6.67 

3-33 

20 

.10 

.OIO 

.003 

IO.OO 

.00 

20.00 

20.00 

.00 

13-33 

6.67 

30 

•  IS 

.025 

.008 

15.00 

.00 

30.00 

30.00 

.00 

20.00 

10.00 

40 

.20 

.040 

.013 

20.00 

.00 

40.00 

40.00 

.01 

26.67 

13-33 

So 

•25 

.062 

.021 

25.00 

.00 

50.00 

50.00 

.02 

33-33 

16.67 

60 

.30 

.000 

.030 

30.00 

.01 

60.00 

60.00 

.03 

40.00 

20.00 

70 

•  35 

.122 

.041 

35-00 

.01 

70.00 

70.00 

•  05 

46.67 

23-33 

80 

.40 

.100 

.053 

40.00 

.02 

80.00 

80.00 

.07 

53.33 

26.67 

90 

•  45 

.202 

.067 

45-00 

•03 

90.00 

90.00 

.11 

60.00 

30.00 

100 

•  50 

.250 

.083 

50.00 

.04 

IOO.OO 

IOO.OO 

.15 

66.67 

33-33 

10 

•  55 

-302 

.101 

55-00 

.05 

IIO.OO 

IIO.OO 

•  19 

73-33 

36.67 

20 

.60 

.360 

.120 

60.00 

.06 

I2O.OO 

120.00 

.25 

80.00 

40.00 

30 

.65 

.422 

.141 

65.00 

.08 

130.00 

130.00 

•  32 

86.67 

43-33 

40 

•  70 

•490 

.163 

70.00 

.10 

140.00 

140.00 

•  40 

93  33 

46.67 

50 

•  75 

.562 

.I87 

75-00 

.12 

150.00 

150.00 

•  49 

100.00 

50.00 

60 

.80 

.640 

.213 

80.00 

•  IS 

160.00 

160  .  oo 

.60 

106.67 

53-33 

70 

.85 

.722 

.241 

85.00 

.18 

170.00 

170.00 

•  71 

113.33 

56.67 

80 

.90 

.8lO 

.270 

90.00 

.21 

180.00 

180.00 

.85 

I2O.OO 

60.00 

90 

•  95 

.002 

.301 

95-00 

.25 

190.00 

189.99 

I.OO 

126.67 

63.33 

200 

I.OO 

I.  000 

•  333 

IOO.OO 

.29 

200.00 

199.99 

1.16 

133.34 

66.67 

10 

.05 

1.  102 

.367 

105.00 

•  34 

210.00 

209.99 

.35 

140.00; 

70.00 

20 

.10 

I.2IO 

•  403 

IIO.OO 

•  39 

220.00 

219.99 

.55 

146.67 

73-34 

30 

.15 

1-322 

.441 

115.00 

•  44 

230.00 

229.99 

•  77 

153.34 

76.67 

40 

.20 

1.440 

.480 

120.  OO 

•  So 

239-99 

239.99 

.01 

160.01 

80.00 

50 

•25 

1.562 

.521 

125.00 

•  57 

249-99 

249.98 

.27 

166.67 

83.34 

60 

.30 

I.60X) 

.563 

129.99 

.64 

259-99 

259.98 

.56 

173.34 

86.67 

70 

•  35 

1.822 

.607 

134.99 

.72 

269.99 

269.97 

2.86 

180.01 

90.01 

80 

•  40 

1.960 

•  653 

139.99 

.80 

279-99 

279.97 

3-19 

186.68 

93-34 

90 

•  45 

2.IO2 

.701 

144.99 

.88 

289.98 

289.96 

3-55 

193.35 

96.68 

300 

1-50 

2.250 

•  750 

149.99 

•  98 

299.98 

299.96 

3-93 

20O  .  02 

IOO.OI 

10 

•  55 

2.4O2 

.801 

154.99 

1.  08 

309.98 

309.95 

4-33 

206.69 

103.35 

20 

.60 

2.560 

.853 

159.98 

1.  19 

319.97 

319.94 

4-76 

213.36 

106.69 

30 

•  65 

2.722 

.907 

164.98 

1.31 

329.97 

329.93 

5-23 

220  .  02 

110.02 

40 

.70 

2.890 

.963 

169.98 

1-43 

339.96 

339.92 

5-72 

226.70 

113.36 

50 

•  75 

3.O62 

.021 

174.98 

1.56 

349.96 

349.90 

6.23 

233-37 

II6.70 

60 

.80 

3.240 

.080 

179.97 

1.70 

359-95 

359-88 

6.78 

240.04 

120.03 

70 

.85 

3-422 

.141 

184.97 

1.84 

369.94 

369.87 

7-37 

246.71 

123.38 

80 

.90 

3.6lO 

.203 

189.97 

2.OO 

379-94 

379-85 

7-98 

253-39 

126.71 

90 

•  95 

3.8O2 

.267 

194.96 

2.16 

389.93 

389.83 

8.63 

260  .  06 

130.05 

400 

2.00 

4.000 

1.333 

199.96 

2-33 

399-92 

399-81 

9-30 

266.74 

133-40 

(58) 


TABLE  XIII.  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  0.75°  PER 
100  FEET.     SUITABLE  FOR  SPEEDS  OF  67  MILES  AN  HOUR 
OR  LESS,  OR  CURVES  OF  3.0°  OR  LESS 


L 

D 

A 

A 

Z 

0 

c 

X 

Y 

U 

V 

10 

0.075 

0.004 

O.OOI 

5.00 

o.oo 

IO.OO 

IO.OO 

o.oo 

6.67 

3  33 

20 

•  ISO 

.015 

.005 

10.  OO 

.00 

20.00 

20.00 

.00 

13-33 

6.67 

30 

.225 

•  034 

.012 

15.00 

.00 

30.00 

30.00 

.01 

20.00 

10.00 

40 

.300 

.060 

.020 

20.00 

.00 

40.00 

4O.OO 

.01 

26.67 

13.33 

50 

•  375 

.094 

.031 

25.00 

.01 

50.00 

50.OO 

.03 

33-33 

16.67 

60 

•  450 

.135 

.045 

30.00 

.01 

60.00 

60.00 

.05 

40.00 

20.00 

70 

.525 

.184 

.061 

35-00 

.02 

70.00 

7O.OO 

.07 

46-67 

23-33 

80 

.600 

.240 

.080 

40.00 

.03 

80.00 

8O.OO 

.11 

53-33 

26.67 

90 

.675 

.304 

.101 

45-00 

.04 

90.00 

90.OO 

.16 

60.00 

30.CO 

100 

•  750 

•  375 

•125 

50.00 

.06 

IOO.OO 

IOO  .  CO 

.22 

66.67 

33-33 

10 

.825 

•  454 

.151 

55-00 

•°7 

IIC.  00 

110.00 

•29 

73-33 

36.67 

20 

.900 

.540 

.180 

60.00 

.09 

120.00 

120.00 

.38 

80.00 

40.OO 

30 

•  975 

.634 

.211 

65.00 

.12 

130.00 

130.00 

.48 

86.67 

43-33 

40 

1.050 

.735 

•  245 

70.00 

.15 

140.00 

140  .  oo 

.60 

93-33 

46.67 

So 

1.125 

.844 

.281 

75-00 

.18 

150  .  oo 

150.00 

•  74 

100.00 

50.OO 

60 

1.200 

.960 

.320 

80.00 

.22 

160.00 

160.00 

.89 

106.67 

53-33 

70 

1-275 

1.084 

.361 

85.00 

.27 

170  .  co 

169.99 

1.07 

113.33 

56.67 

80 

1.350 

1.215 

.405 

90.00 

.32 

180.00 

179.99 

1.27 

120.  OO 

60.00 

90 

1.425 

1.354 

•  451 

95-00 

.37 

189.99 

189.99 

1.50 

126.67 

63.34 

200 

I.5OO 

1.500 

.500 

IOO.OO 

•  44 

199.99 

199.99 

1-75 

133.34 

66.67 

10 

I  575 

1.654 

•  551 

104.99 

•  Si 

209.99 

209.98 

2.  02 

140.01 

70.01 

20 

1.650 

1.815 

.60S 

109.99 

-58 

219.99 

219.98 

2.32 

146.67 

73-34 

30 

1.725 

1.984 

.661 

114.99 

.66 

229.99 

229.97 

2.65 

153.34 

76.68 

40 

1.800 

2.160 

.720 

119.99 

•  73 

239-99 

239.97 

3-02 

160.01 

80.01 

So 

1.875 

2.344 

.781 

124.99 

.85 

249.98 

249.96 

3.41 

166.68 

83.34 

60 

1-950 

2.535 

•845 

129.99 

.96 

259-98 

259-95 

3.84 

173.35 

86.68 

70 

2.025 

2.734 

.911 

134.98 

1.07 

269.97 

269.94 

4.30 

180.02 

90.02 

80 

2.100 

2.940 

.980 

139.98 

1.20 

279.97 

279-93 

4-79 

186.69 

93.36 

90 

2.175 

3-154 

I.O5I 

144.98 

1.33 

289.96 

289.91 

5-32 

193.37 

96.69 

300 

2.25O 

3-375 

1.  125 

149.97 

1-47 

299.96 

299-90 

5.86 

200.04 

100.03 

10 

2.325 

3.604 

.201 

154.97 

1.63 

309.95 

309-88 

6.50 

206.71 

103-37 

20 

2.400 

3.840 

.280 

159.97 

1.79 

319.94 

319.86 

7-15 

213.38 

106.71 

30 

2.475 

4.084 

.361 

164.96 

1.96 

329.93 

329-83 

7-84 

220.06 

110.04 

40 

2.550 

4-335 

.445 

169.96 

2.14 

339.92 

339-81 

8.57 

226.73 

113-39 

50 

2.625 

4-594 

•531 

174.95 

2.34 

349.90 

349.78 

9-35 

233.41 

116.74 

60 

2.700 

4.860 

.620 

179.94 

2.54 

359-88 

359-74 

10.17 

240.09 

120.09 

70 

2.775 

5-134 

.711 

184.93 

2.76 

369-87 

369-70 

11.04 

246.77 

123-43 

80 

2.850 

5.415 

.805 

189.93 

2.99 

379-85 

379.67 

11.97 

253.45 

126.78 

90 

2.925 

5.704 

.901 

194.92 

3-24 

389.83 

389-62 

12-93 

260.14 

130.12 

400 

3-000 

6.000 

2.OOO 

199.91 

3-49 

399-81 

399-56 

13-95 

266.82 

138.34 

(59) 


TABLE  XIV.  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  1.0°  PER 

100  FEET.      SUITABLE  FOR  SPEEDS  OF  61  MILES  AN 

HOUR  OR  LESS,  OR  CURVES  OF  4.0°  OR  LESS 


L 

D 

A 

A 

Z 

o 

C 

X 

Y 

U 

V 

10 

O.IO 

0.005 

O.O02 

5-co 

o.oo 

IO.OO 

IO.OO 

.00 

6.67 

3-33 

20 

.20 

.020 

.007 

IO.OO 

.00 

20.00 

20.00 

.00 

13-33 

6.66 

30 

•  30 

.045 

.015 

15.00 

.00 

30.00 

30.00 

.01 

20.00 

IO.OO 

40 

.40 

.080 

.027 

20.00 

.00 

40.00 

40.00 

.02 

26.67 

13.33 

50 

•  SO 

.125 

.042 

25.00 

.01 

50.00 

50.00 

.04 

33-33 

16.67 

60 

.60 

.180 

.060 

30.00 

.02 

60.00 

60.00 

.06 

40.00 

20.00 

70 

.70 

.245 

.082 

35.00 

.03 

70.00 

70.00 

.10 

46.67 

23-33 

80 

.80 

.320 

.107 

40.00 

.03 

80.00 

80.00 

.15 

53-33 

26.67 

90 

.90 

.405 

•  135 

45-00 

.05 

90.00 

90.00 

.21 

60.00 

3O.OO 

100 

I.OO 

.500 

.167 

50.00 

.07 

IOO.OO 

IOO.OO 

•29 

66.67 

33-33 

10 

1.  10 

.605 

.202 

55-00 

.10 

no.oo 

110.00 

•  39 

73-33 

36.67 

20 

1.20 

.720 

.240 

60.00 

.13 

120.  OO 

I2O.OO 

•  So 

80.00 

40.00 

30 

1-30 

.845 

.282 

65.00 

.16 

130.00 

130.00 

.64 

86.67 

43-33 

40 

1.40 

.980 

.327 

70.00 

.20 

140.00 

140.00 

.80 

93-34 

46.67 

50 

I.SO 

1.  125 

•  375 

75-00 

.25 

150.00 

149.99 

-98 

100.00 

50.00 

60 

1.  60 

1.280 

.427 

80.00 

•  30 

160.00 

159.99 

1.19 

106.67 

53-34 

70 

1.70 

1.  445 

.482 

85.00 

.36 

169.99 

169.99 

1-43 

113.34 

56.67 

80 

1.  80 

1.620 

•  540 

90.00 

.42 

179.99 

179.99 

1.70 

120.  OO 

60.00 

90 

I.QO 

1.805 

.602 

94-99 

•  50 

189.99 

189.98 

1.99 

126.67 

63.34 

200 

2.OO 

2.000 

.667 

99-99 

.58 

199.99 

199.98 

2.33 

133.34 

66.67 

10 

2.10 

2.205 

•  735 

104.99 

.67 

209.99 

209.97 

2.69 

140.01 

70.01 

20 

2.20 

2.420 

.807 

109.99 

•  77 

219.98 

219.96 

3-10 

146.68 

73-35 

30 

2.30 

2.645 

.882 

114-99 

.89 

229.98 

229.95 

3-54 

153.35 

76.68 

40 

2.40 

2.880 

.960 

119.98 

.01 

239.97 

239.94 

4-02 

160.02 

80.02 

So 

2.SO 

3-125 

1.042 

124.98 

•  14 

249.97 

249.93 

4-54 

166.69 

83.36 

60 

2.60 

3-380 

1.127 

129.97 

.28 

259.96 

259.91 

5-  ii 

173.37 

86.70 

70 

2.70 

3.645 

1.  215 

134-97 

•  43 

269.95 

269.89 

5-72 

180.04 

90.03 

80 

2.80 

3-920 

1.307 

139-97 

.60 

279.94 

279.87 

6.38 

186.71 

93-37 

90 

2.90 

4.205 

1.402 

144-96 

•  77 

289.93 

289.85 

7.09 

193.39 

96.72 

300 

3-00 

4-500 

1.500 

149-95 

1.96 

299.92 

299.82 

7-85 

200.06 

100.06 

10 

3.10 

4-805 

1.602 

154-95 

2.16 

309.90 

309.78 

8.66 

206.74 

103.40 

20 

3-20 

5.120 

1.707 

159-94 

2.38 

319.89 

319.75 

9-53 

213.42 

106.75 

30 

3-30 

5-445 

1.815 

164-93 

2.61 

329.87 

329.70 

10.44 

220.10 

110.09 

40 

3-40 

5.78o 

1.927 

169.92 

2.86 

339.85 

339-66 

11.42 

226.79 

113-44 

50 

3-50 

6.125 

2.042 

174.91 

3.12 

349.82 

349-6o 

12.46 

233-47 

116.80 

60 

3.6o 

6.480 

2.160 

179.89 

3-39 

359.80 

359-54 

13.56 

240.16 

120.15 

70 

3-70 

6.845 

2.282 

184.88 

3.68 

369.77 

369.47 

14.71 

246.85 

123.50 

80 

3.8o 

7.220 

2.407 

189.87 

3-99 

379.73 

379-40 

15-94 

253.54 

126.86 

90 

3.90 

7-605 

2.535 

194.85 

4-31 

389.70 

389-32 

17-23 

260.24 

I3O  .  22 

400 

4.00 

8.000 

2.667 

199.84 

4.65 

399-66 

399-22 

18.59 

266.94 

133-58 

(60) 


THE   SPIRAL 


61 


TABLE  XV.  — SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  i$°  PER 

100  FEET.    SUITABLE  FOR  A  SPEED  OF  55  MILES  AN 

HOUR  OR  LESS,  OR  CURVES  OF  4.0°  OR  LESS 


L 

D 

A 

A 

Z 

o 

C 

X 

Y 

U 

V 

10 

0.133 

0.007 

0.002 

5-00 

o.oo 

IO.OO 

IO.OO 

o.oo 

6.67 

3-33 

20 

.267 

.027 

.009 

10.00 

.00 

20.00 

20.00 

.00 

13-33 

6.6? 

30 

.400 

.060 

.O2O 

15.00 

.00 

30.00 

30.00 

.01 

20.00 

IO.OO 

40 

•  533 

.107 

.036 

20.00 

.01 

40.00 

40.00 

.02 

26.67 

13.33 

50 

.667 

.167 

.056 

25.00 

.01 

50.00 

50.00 

.05 

33-33 

16.67 

60 

.800 

.240 

.080 

30.00 

.02 

60.00 

60.00 

.08 

40.00 

20.00 

70 

•  933 

.327 

.109 

35-00 

.03 

70.00 

70.00 

•  13 

46-67 

23-33 

80 

1.067 

.427 

.142 

40.00 

.05 

80.00 

80.00 

.20 

53-33 

26.67 

90 

1.  200 

•  540 

.180 

45-00 

.07 

90.00 

90.00 

.28 

60.00 

30.00 

100 

1-333 

.667 

.222 

50.00 

.10 

IOO.OO 

IOO.OO 

-39 

66.67 

33-33 

10 

1.467 

.807 

.269 

55-00 

•  13 

110.00 

IIO.OO 

.52 

73-33 

36.67 

10 

1.  600 

.960 

.320 

60.00 

.17 

120.00 

I2O.OO 

.67 

80.00 

40.00 

30 

1-733 

1.127 

.376 

65.00 

.21 

130.00 

129.99 

.85 

86.67 

43-34 

40 

1.867 

I.307 

.436 

70.00 

.27 

140.00 

139.99 

.06 

93-34 

46.67 

So 

2.OOO 

1.500 

.500 

74-99 

-33 

150.00 

149.99 

-31 

100.00 

50.00 

60 

2.133 

1.707 

.569 

79-99 

.40 

159.99 

159.99 

-59 

106.67 

53-34 

70 

2.267 

1.927 

.642 

84-99 

.48 

169.99 

169.98 

91 

113.34 

56.67 

80 

2.400 

2.160 

.720 

89-99 

•  57 

179-99 

179.97 

.26 

120.  OI 

60.  oi 

90 

2.533 

2.407 

.802 

94-99 

.66 

189.98 

189.97 

2.66 

126.68 

63.34 

200 

2.667 

2.667 

.889 

99-98 

•  78 

199.98 

199.96 

3.10 

133-35 

66.68 

10 

2.800 

2.940 

.980 

104.98 

.90 

209.97 

209.94 

3-59 

I4O.O2 

70.02 

20 

2.933 

3-227 

.  076 

109.98 

1.03 

219-97 

219.93 

4.12 

146.69 

73-35 

30 

3.067 

3.527 

.176 

H4-97 

1.18 

229.95 

229.91 

4-71 

153.36 

76.69 

40 

3.200 

3.840 

.280 

119-97 

1-34 

239-95 

239.89 

5-35 

160.04 

80.03 

So 

3-333 

4.167 

.389 

124.96 

I.  Si 

249-94 

249.87 

6.05 

166.72 

83.38 

60 

3.467 

4.507 

•  502 

129.95 

1.70 

259-93 

259.84 

6.81 

173-39 

86.72 

70 

3.6oo 

4.860 

.620 

134-95 

1.91 

269.91 

269.81 

7.62 

180.07 

90.06 

80 

3-733 

5-227 

•  742 

139-94 

2.13 

279-90 

279.77 

8.50 

186.75 

93-41 

90 

3-867 

5.607 

.869 

144-94 

2.36 

289.88 

289.72 

9-43 

193-43 

96.76 

300 

4.000 

6.000 

2.000 

149-92 

2.61 

299-86 

299.67 

10.46 

200.12 

loo.n 

62 


RAILROAD   FIELD  MANUAL 


TABLE  XVI.  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  1.5°  PER 
100  FEET.    SUITABLE  FOR  SPEEDS  OF  53  MILES  AN  HOUR 
OR  LESS,  OR  CURVES  OF  4.5°  OR  LESS 


L 

D 

A 

A 

z 

0 

c 

X 

Y 

U 

V 

10 

0.15 

0.008 

O.O02 

S.oo 

o.oo 

IO.OO 

IO.OO 

o.oo 

6.67 

3-33 

20 

-30 

.030 

.OIO 

IO.OO 

.00 

20.00 

20.00 

.00 

13-33 

6.67 

30 

•  45 

.068 

.022 

15.00 

.00 

30.00 

30.00 

.01 

20.00 

IO.OO 

40 

.60 

.120 

.040 

20,00 

.01 

40.00 

40.00 

.03 

26.67 

13.33 

So 

•  75 

.188 

.062 

25.00 

.01 

50.00 

50.00 

•  05 

33-33 

16.67 

60 

•  90 

.270 

.090 

30.00 

.02 

60.00 

60.00 

.09 

40.00 

20.00 

70 

1.05 

.368 

.122 

35-00 

.04 

70.00 

70.00 

.15 

46.67 

23.33 

80 

1.20 

.480 

.160 

40.00 

.06 

80.00 

80.00 

.22 

53-33 

26.67 

90 

1.35 

.608 

.202 

45-00 

.08 

90.00 

90.00 

•32 

60.00 

30.00 

100 

1.50 

•  750 

.250 

50.00 

.11 

IOO.OO 

IOO.OO 

•44 

66.67 

33-33 

10 

1.65 

.908 

.302 

55-00 

•  IS 

IIO.OO 

IIO.OO 

•  58 

73-33 

36.67 

20 

i.  80 

1.080 

.360 

60.00 

•  19 

120.  OO 

120.  OO 

•  75 

80.00 

40.00 

30 

1-95 

1.268 

.422 

65.00 

.24 

130.00 

129.99 

-96 

86.67 

43-34 

40 

2.10 

1.470 

•  490 

69.99 

•  30 

140.00 

139.99 

1.  20 

93-34 

46.67 

50 

2.  25 

1.688 

.562 

74-99 

•  37 

149.99 

149.99 

1.47 

IOO.OO 

50.OO 

60 

2.40 

1.920 

.640 

79-99 

•  45 

159.99 

159.98 

1-79 

106.67 

53-34 

70 

2.55 

2.168 

.722 

84.99 

•  54 

169.99 

169.97 

2.14 

113.34 

56.67 

80 

2.70 

2.430 

.810 

89-99 

.64 

179.99 

179.97 

2.54 

I2O.OI 

60.  01 

90 

2.85 

2.708 

.902 

94-98 

•  75 

189.98 

189.96 

2-99 

126.68 

63.35 

200 

3-00 

3.000 

I.OOO 

99.98 

-87 

199.98 

199-95 

3.49 

133-35 

66.68 

10 

3-15 

3.308 

.102 

104.98 

I.OI 

209.97 

209.93 

4.04 

140.02 

70.02 

20 

3-30 

3  630 

.2IO 

109.97 

1.16 

219.96 

219.91 

4.64 

146.70 

73.36 

30 

3-45 

3-968 

.322 

114-96 

1-33 

229.95 

229.89 

5-30 

153-37 

76.70 

40 

3-60 

4.320 

.440 

119.96 

•  51 

239-94 

239-87 

6.03 

I6O.O5 

80.04 

50 

3-75 

4-688 

.562 

124-95 

.70 

249-93 

249-83 

6.8l 

166.73 

83.39 

60 

3-90 

5.070 

.600 

129-94 

.92 

259-91 

259-80 

7.66 

I73-4I 

86.73 

70 

4-05 

5.468 

.822 

134-93 

.15 

269.89 

269.76 

8.58 

I80.09 

90.08 

80 

4.20 

5-880 

.960 

139  92 

•  39 

279-87 

279-71 

9-55 

186.77 

93-43 

90 

4-35 

6.308 

.102 

144.91 

2.66 

289.85 

289.65 

10.  61 

193.46 

96.78 

300 

4-50 

6.750 

2.25O 

149.90 

2.94 

299-82 

299-59 

11-77 

200.15 

100.13 

THE   SPIRAL 


TABLE  XVII. —SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  2.0°  PER 

100  FEET.    SUITABLE  FOR  A  SPEED  OF  48  MILES  AN  HOUR 

OR  LESS,  AND  CURVES  OF  6.0°  OR  LESS 


L 

D 

A 

A 

Z 

0 

C 

X 

Y 

U 

V 

10 

O.2O 

O.OIO 

0.003 

5.00 

o.oo 

10.  OO 

IO.OO 

o.oo 

6.97 

3-33 

20 

.40 

.040 

.013 

10.  OO 

.00 

20.00 

20.00 

.00 

13-33 

6.67 

30 

.60 

.090 

.030 

15.00 

.00 

30.00 

30.00 

.02 

20.00 

10.00 

40 

.80 

.160 

.053 

20.00 

.01 

40.00 

40.00 

.04 

26.67 

13-33 

50 

I.OO 

.250 

.083 

25.00 

.02 

50.00 

50.00 

.07 

33-33 

16.67 

60 

.20 

.360 

.120 

30.00 

•03 

60.00 

60.00 

.13 

40.00 

20.00 

70 

.40 

.490 

.163 

35-00 

.05 

70.00 

70.00 

.20 

46.67 

23-33 

So 

.60 

.640 

.213 

40.00 

.07 

80.00 

80.00 

.30 

53-33 

26.67 

90 

.80 

.810 

.270 

45-00 

.11 

90.00 

90.00 

.42 

60.00 

30.00 

100 

2.OO 

I.OOO 

.333 

50.00 

•  14 

IOO.OO 

IOO.OO 

.58 

66.67 

33-33 

10 

.20 

I.2IO 

•  403 

55-00 

•  19 

IIO.OO 

109.99 

•  77 

73-33 

36.67 

20 

.40 

1.440 

.480 

59-99 

.25 

I2O.OO 

119.99 

I.OO 

80.00 

40.00 

30 

.60 

1.690 

.563 

64.99 

.34 

129.99 

129.99 

1.28 

86.67 

43-34 

40 

.80 

1.960 

.653 

69-99 

•  40 

139.99 

139.98 

1.  60 

93-34 

46.67 

So 

3.00 

2.250 

•  750 

74-99 

•  49 

149.99 

149.98 

1.96 

IOO.OI 

50.01 

60 

.20 

2.560 

.853 

79.98 

.60 

159.99 

159.97 

2.38 

106.68 

53-34 

70 

.40 

2.890 

.963 

84.98 

•  71 

169.98 

169.96 

2.86 

113.35 

56.68 

80 

.60 

3.240 

1.080 

89.98 

.85 

179.97 

179.94 

3.39 

120.  O2 

'  60.02 

90 

.80 

3.6lO 

1.  203 

94-97 

I.OO 

189.97 

189.93 

3.99 

126.69 

63.36 

200 

4.00 

4.000 

1.333 

99.96 

1.16 

199.96 

199.90 

4.65 

133-37 

66.70 

10 

.20 

4.410 

1.470 

104.96 

1.35 

209.95 

209.88 

5.38 

140.04 

70.04 

20 

.40 

4.840 

1.613 

109.95 

1.55 

219.93 

219.84 

6.19 

146.72 

73.38 

30 

.60 

5.290 

1.763 

114.94 

1.77 

229.91 

229.80 

7.07 

153-40 

76.73 

40 

.80 

5.760 

1.920 

"9-93 

2.01 

239.89 

239.76 

8.03 

l6o.09 

80.08 

50 

S.oo 

6.25O 

2.083 

124.91 

2.27 

249.87 

249.70 

9.08 

166.77 

83.43 

60 

.20 

6.760 

2.253 

129.90 

2.55 

259.84 

259.64 

10.21 

173.46 

86.78 

70 

.40 

7.290 

2.430 

134-88 

2.86 

269.81 

269.57 

11.44 

ISO.IS 

90.14 

80 

.60 

7.840 

2.613 

139-86 

3.19 

279.77 

279.48 

12.75 

186.85 

93.50 

90 

.80 

8.410 

2.802 

144.84 

3-54 

289.73 

289.38 

14.17 

193-55 

96.87 

300 

6.00 

9-OOO 

2.999 

I49-8I 

3-92 

299.68 

299.26 

15-68 

200.26 

100.24 

RAILROAD   FIELD   MANUAL 


TABLE  XVIII.  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  2.5° 

PER  100  FEET.    SUITABLE  FOR  SPEEDS  OF  45  MILES  AN 

HOUR  OR  LESS,  AND  CURVES  OF  7.5°  OR  LESS 


L 

D 

A 

A 

Z 

0 

c 

X 

Y 

u 

V 

10 

0.25 

O.OI2 

0.004 

S.oo 

o.oo 

10.00 

10.00 

0.00 

6.67 

3-33 

20 

•  So 

.050 

.017 

10.00 

.00 

20.00 

20.00 

.01 

13-33 

6.67 

30 

•  75 

.112 

.037 

15.00 

.00 

30.00 

30.00 

.02 

20.00 

IO.OO 

40 

1.  00 

.200 

.067 

20.00 

.01 

40.00 

40.00 

.05 

26.67 

13.33 

So 

.25 

-312 

.104 

25.00 

.02 

50.00 

50.00 

.09 

33-33 

'16.67 

60 

•  So 

•450 

•  ISO 

30.00 

.04 

60.00 

60.00 

.16 

40.00 

20.00 

70 

•  75 

.612 

.204 

35.00 

.06 

70.00 

70.00 

.21 

46.67 

23.33 

80 

2.0O 

.800 

.267 

40.00 

.09, 

80.00 

80.00 

•  37 

53-33 

26.67 

90 

.25 

1.  012 

•  337 

45-00 

.13 

90.00 

90.00 

.53 

60.00 

30.00 

100 

.50 

1.250 

•  417 

50.00 

.18 

IOO.OO 

100.00 

.73 

66.67 

33.34 

10 

.75 

I.5I2 

.504 

54-99 

.24 

IIO.OO 

109.99 

•  97 

73-34 

36.67 

20 

3-00 

1.800 

.600 

59-99 

•  31 

I2O.OO 

119.99 

1.26 

80.00 

40.00 

30 

•  25 

2.  112 

.704 

64.99 

•  40 

129.99 

129.98 

i.  60 

86.67 

43.34 

40 

•  50 

2.450 

.817 

69.98 

•  50 

139.99 

139.97 

2.OO 

93-34 

46.67 

50 

•  75 

2.812 

•937 

74.98 

.61 

149.98 

149.96 

2.45 

IOO.OI 

50.01 

60 

4.00 

3.200 

1.067 

79-98 

•  74 

159.98 

159.95 

2.98 

106.68 

53.35 

70 

.25 

3.612 

1.204 

84-97 

.89 

169.97 

169.93 

3-57 

113.36 

56.69 

80 

•  50 

4.050 

1.350 

89.96 

1.  06 

179.96 

179.91 

4.24 

120.03 

60.03 

90 

.75 

4.512 

1.504 

94-95 

1.25 

189.95 

189.88 

4-99 

126.71 

63.37 

200 

S.oo 

5.000 

1.667 

99-94 

1.45 

199.93 

199.85 

5.8i 

133.39 

66.72 

10 

•25 

5.512 

1-837 

104-93 

1.68 

209.91 

209.81 

6-73 

140.07 

70.06 

20 

.50 

6.050 

2.017 

109.92 

1-93 

219.89 

219.76 

7-74 

146.76 

73.41 

30 

•  75 

6.612 

2.204 

114.90 

2.21 

229.87 

229.70 

8.84 

153.44 

76.76 

40 

6.00 

7.200 

2.400 

119.89 

2.51 

239.83 

239.62 

10.04 

160.13 

80.12 

50 

.25 

7.812 

2.604 

124.86 

2.84 

249.80 

249.54 

11.35 

166.83 

83.48 

60 

.50 

8.450 

2.816 

129.84 

3-19 

259.75 

259.44 

12.76 

173.53 

86.85 

70 

•  75 

9.112 

3-036 

134-81 

3-57 

269.70 

269.32 

14.29 

180.24 

90.22 

80 

7.00 

9.800 

3.266 

139.78 

3.98 

279.64 

279.19 

15-93 

186.96 

93.60 

90 

.25 

10.512 

3.503 

144.75 

4.42 

289.57 

289.03 

17-69 

193.68 

96.98 

300 

7-50 

11.250 

3-749 

149-71 

4-89 

299.49 

298.85 

19.58 

200.41 

100.37 

THE   SPIRAL 


TABLE  XIX.  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  3.0° 

PER  100  FEET.    SUITABLE  FOR  SPEEDS  OF  41  MILES  AN 

HOUR  OR  LESS,  AND  CURVES  OF  9.0°  OR  LESS 


L 

D 

A 

A 

Z 

0 

C 

X 

Y 

u 

V 

10 

o 

0.30 

0.015 

0.005 

S.oo 

0.00 

10.00 

10.00 

0.00 

6.67 

3-33 

20 

.60 

.060 

.020 

10.00 

.00 

20.00 

20.00 

.01 

13-33 

6.67 

30 

.90 

.135 

.045 

15.00 

.01 

30.00 

30.00 

.02 

20.OO 

IO.OO 

40 

1.20 

.240 

.080 

20.00 

.01 

40.00 

40.00 

.06 

26.67 

13.33 

So 

•  50 

•  375 

-125 

25.OO 

.03 

50.00 

5O.OO 

.11 

33-33 

16.67 

60 

.80 

•  540 

.180 

30.OO 

.05 

60.00 

60.00 

-19 

40.00 

20.00 

70 

2.10 

•  735 

-245 

35-00 

.07 

70.00 

7O.OO 

•  30 

46.67 

23  33 

80 

.40 

.960 

-320 

40.00 

.11 

80.00 

80.00 

•  45 

53-34 

26.67 

90 

•  70 

1.  215 

-405 

45-00 

.16 

90.00 

9O.OO 

.64 

60.00 

30.00 

100 

3-00 

1.500 

.500 

49-99 

.22 

100.00 

99-99 

.87 

66.67 

33-34 

10 

•  30 

1.815 

.605 

54-99 

.29 

109.99 

109.99 

1.16 

73-34 

36.67 

20 

.60 

2.160 

.720 

59-99 

.36 

119.99 

119.98 

I.  Si 

80.01 

40.01 

30 

.90 

2.535 

.845 

64.98 

.48 

129.99 

129.98 

1.92 

86.67 

43-34 

40 

4.20 

2.940 

.980 

69-98 

.60 

139-98 

139.96 

2.39 

93-35 

46.68 

So 

•  So 

3-375 

1.125 

74-97 

•  74 

149.98 

149-95 

2.94 

100.02 

50.02 

60 

.80 

3.840 

1.280 

79-97 

.89 

159-97 

159-93 

3-57 

106.69 

53.36 

70 

5.10 

4-335 

1-445 

84.96 

1.07 

169.96 

169.90 

4.28 

113-37 

56.70 

80 

•  40 

4.860 

1.620 

89-95 

1.27 

179-94 

I79-87 

5.08 

120.05 

60.04 

90 

.70 

5-415 

1.805 

94-93 

1.49 

189.92 

189.83 

5-98 

126.73 

63.39 

200 

6.00 

6.000 

2.000 

99.92 

1-74 

199-90 

199.78 

6.98 

133-41 

66.74 

10 

•  30 

6.615 

2.205 

104.90 

2.02 

209.88 

209.72 

8.06 

I4O.IO 

70.09 

20 

.60 

7.260 

2.420 

109.88 

2.32 

219.85 

219.65 

9.26 

146.79 

73-45 

30 

.90 

7-935 

2.645 

114.86 

2.65 

229.81 

229.56 

10.59 

153-49 

76.81 

40 

7.20 

8.640 

2.879 

119-83 

3.01 

239.76 

239.46 

12.04 

160.19 

80.17 

So 

•  50 

9-375 

3-124 

124.80 

3-40 

249-71 

249-34 

13-60 

166.90 

83-55 

60 

.80 

10.140 

3-379 

129.77 

3-82 

259-64 

259-19 

15-30 

173-62 

86.93 

70 

8.10 

10.935 

3.644 

134-73 

4.28 

269.57 

269.03 

17.11 

180.35 

90.32 

80 

.40 

11.760 

3.919 

139.69 

4-77 

279.48 

278.83 

19.08 

187.08 

93-71 

90 

•  70 

12.615 

4-203 

144.64 

5.30 

289.39 

288.61 

21.20 

193.83 

97.12 

300 

9.00 

13-500 

4.498 

149.58 

5-86 

298.70 

298.35 

23-47 

200.59 

100.54 

66 


RAILROAD   FIELD  MANUAL 


TABLE  XX. —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  4.0° 

PER  100  FEET.    SUITABLE  FOR  SPEEDS  OF  35  MILES  AN 

HOUR  OR  LESS,  OR  CURVES  OF  10.0°  OR  LESS 


L 

D 

A 

A 

Z 

o 

C 

X 

Y 

u 

V 

10 

0.40 

o 
O.O20 

0.007 

5.00 

o.oo 

IO.OO 

IO.OO 

o.oo 

6.67 

3-33 

20 

.80 

.080 

.027 

IO.OO 

.00 

20.00 

20.00 

.01 

13-33 

6.67 

30 

1.20 

.180 

.060 

15.00 

.01 

30.00 

30.00 

.03 

20.00 

IO.OO 

40 

.60 

.320 

.107 

20.00 

.02 

40.00 

40.00 

.07 

26.67 

13.33 

50 

2.OO 

.500 

.167 

25.00 

.04 

50.00 

50.00 

-IS 

33-33 

16.67 

60 

.40 

.720 

.240 

30.00 

.06 

60.00 

60.00 

-25 

40.00 

20.00 

70 

.80 

.980 

•  327 

35.00 

.10 

70.00 

70.00 

.40 

46.67 

23.33 

80 

3-20 

1.280 

.427 

39.99 

.15 

80.00 

80.00 

.60 

53-33 

26.67 

90 

.60 

1.620 

•  540 

44.99 

.21 

90.00 

89.99 

.85 

60.00 

30.00 

100 

4.00 

2.OOO 

.667 

49.99 

.29 

99-99 

99.99 

1.16 

66.67 

33.34 

10 

•  40 

2.420 

.807 

54.98 

•39 

109-99 

109.98 

1.55 

73-33 

36.67 

20 

.80 

2.880 

.060 

59.98 

-50 

119.99 

119.97 

1.84 

80.01 

40.01 

30 

5-20 

3.380 

1.127 

64.97 

.64 

129.98 

129.95 

2.56 

86.68 

43.35 

40 

.60 

3.920 

•  307 

69.96 

.80 

139-97 

139.93 

3-19 

93.36 

46.69 

50 

6.00 

4.500 

.500 

74-95 

.98 

149.96 

149.91 

3-93 

100.03 

50.03 

60 

•  40 

5.120 

.707 

79-94 

1.  19 

159-94 

159-87 

4-76 

106.71 

53.37 

70 

.80 

5.780 

.927 

84.92 

1.43 

169.92 

169.83 

5-71 

113.40 

56.72 

80 

7.20 

6.480 

.160 

89.90 

1.77 

179.90 

179.77 

6.78 

120.08 

60.08 

90 

.60 

7.220 

.407 

94-88 

1.99 

189.87 

189.70 

7-97 

126.77 

63.43 

200 

8.00 

8.000 

2.667 

99-86 

2.32 

199.83 

199.61 

9-30 

133-47 

66.79 

10 

.40 

8.820 

2.939 

104.83 

2.68 

209.78 

209.51 

10.76 

140.18 

70.  ie 

20 

.80 

9.680 

3.222 

109.79 

3-09 

219.72 

219.38 

12.38 

146.89 

73-54 

30 

9.20 

10.580 

3.526 

114-75 

3-52 

229.66 

229.22 

14.11 

I53.6I 

76.92 

40 

.60 

11.520 

3.839 

119.70 

4.00 

239-57 

239.03 

6.03 

160.34 

80.31 

250 

10.00 

12.500 

4-165 

124.65 

4-52 

249.48 

248.82 

8.12 

167.09 

83.72 

THE   SPIRAL 


67 


TABLE  XXL  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  5.0° 

PER  100  FEET.    SUITABLE  FOR  SPEEDS  OF  32  MILES  AN 

HOUR  OR  LESS,  OR  CURVES  OF  12.5°  OR  LESS 


L 

D 

A 

A 

Z 

o 

C 

X 

Y 

u 

V 

10 

0.50 

0.025 

0.008 

5.00 

o.oo 

10.00 

10.00 

0.00 

6.67 

3-33 

20 

I.OO 

.100 

.033 

IO.OO 

•  OO 

20.00 

20.00 

.01 

13.33 

6.67 

30 

•So 

.225 

.075 

15.00 

.01 

30.00 

30.00 

.04 

20.00 

IO.OO 

40 

3.00 

.400 

.133 

20.00 

.02 

40.00 

40.00 

.09 

26.67 

13.33 

So 

•50 

.625 

.208 

25.00 

.05 

50.00 

50.00 

.18 

33.33 

16.67 

60 

3-00 

.900 

.300 

30.00 

.08 

60.00 

60.00 

.31 

40.00 

20.00 

70 

•50 

1.225 

.408 

34.99 

.13 

70.00 

70.00 

.50 

46.67 

23-33 

80 

4.00 

1.  600 

•  533 

39.99 

.19 

80.00 

79-99 

.74 

53-34 

26.67 

90 

•  SO 

2.025 

.675 

44.99 

.27 

90.00 

89-99 

1.  06 

60.  OQ 

3O.OO 

100 

S.oo 

2.500 

.833 

49.98 

.36 

99.99 

99-98 

1.45 

66.67 

33-34 

10 

•  SO 

3-025 

.008 

54.97 

.48 

109.99 

109.97 

1-93 

73-34 

36.68 

20 

6.00 

3.600 

.200 

59.97 

.63 

119.98 

H9.95 

2.51 

80.02 

40.O2 

30 

•  So 

4-225 

.408 

64.95 

.80 

129.97 

129.93 

3-19 

86.69 

43.36 

40 

7.00 

4.900 

.633 

69.94 

.00 

139.96 

139.90 

3-99 

93-37 

46.70 

So 

•  So 

5-625 

.875 

74.92 

.20 

149.94 

149-86 

4.90 

100.05 

50.05 

60 

8.00 

6.400 

2.133 

79.90 

.48 

159.91 

159-80 

5-94 

106.74 

53-40 

7o 

•  50 

7.225 

2.408 

84.88 

.78 

169.88 

169.73 

7-13 

113-43 

56.75 

80 

9.00 

8.100 

2.699 

89.85 

.11 

179-84 

179-64 

8.46 

120.13 

6b.  12 

90 

•  50 

9-025 

3.008 

94.82 

.48 

189.79 

189.53 

9-95 

126.83 

63.48 

200 

10.00 

IO.OOO 

3-332 

99.78 

2.90 

199.73 

199.40 

ii.  61 

133-55 

66.86 

10 

.50 

11.025 

3.674 

104.73 

3.35 

209  .  66 

209.23 

13.41 

140.27 

70.25 

20 

II.  OO 

12.100 

4.032 

109.67 

3.82 

219-57 

219.04 

15.42 

147-01 

73.65 

30 

.50 

13.225 

4.406 

114.61 

4.40 

229.46 

228.79 

17.62 

153.76 

77-06 

40 

12.  OO 

14.400 

4-797 

119.54 

5-99 

239-34 

238.50 

20.02 

160.54 

80.49 

260 

12.50 

15.625 

5-205 

124.46 

5.64 

249.18 

248.16 

22.62 

167.32 

83.94 

68 


RAILROAD   FIELD   MANUAL 


TABLE  XXII.  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  7.5° 

PER  100  FEET.    SUITABLE  FOR  A  SPEED  OF  26  MILES  AN 

HOUR  OR  LESS,  OR  A  CURVE  OF  18.0°  OR  LESS 


L 

D 

A 

A 

Z 

0 

C 

X 

Y 

u 

V 

10 

• 

0.75 

0.0375 

O.OI2 

5.00 

o.oo 

IO.OO 

IO.OO 

o.oo 

6.67 

3-33 

20 

1.50 

.1500 

.050 

10.  OO 

.00 

20.00 

20.00 

.02 

13-33 

6.67 

30 

2.25 

•  3375 

.113 

15.00 

.01 

30.00 

30.00 

.06 

20.00 

10.00 

40 

3  oo 

.6000 

.200 

20.00 

.03 

40.00 

40.00 

.14 

26.67 

13.33 

50 

3-75 

•  9375 

•  313 

25.0O 

.07 

50.00 

50.00 

.27 

33-33 

16.67 

60 

4-50 

1.3500 

•  450 

29-99 

.12 

60.00 

60.00 

.47 

40.00 

20.00 

70 

5-25 

1-8375 

.613 

34-99 

.19 

70.00 

69.99 

•  75 

46.67 

23-34 

80 

6.00 

2.4000 

.800 

39-98 

.28 

79-99 

79-99 

1.  12 

53-34 

26.67 

90 

6.75 

3-0375 

1.013 

44-97 

.40 

89-99 

89-97 

1.59 

60.  01 

30.01 

100 

7-50 

3-7500 

1.250 

49.96 

.54 

99.98 

99.96 

2.18 

66.68 

33-35 

10 

8.25 

4-5375 

I.5I3 

54-94 

•  7i 

109.97 

109.93 

2.90 

73.36 

36.69 

20 

9.00 

5.4000 

I.Soo 

59-92 

•  94 

"9-95 

119-89 

3-77 

80.04 

40.03 

30 

9-75 

6.3375 

2.  113 

64.90 

1.  19 

129-93 

129.84 

4-78 

86.72 

43-38 

40 

10.50 

7-3500 

2.450 

69.86 

1.49 

139-90 

139-77 

5-98 

93-41 

46-74 

50 

11.25 

8.4375 

2.812 

74-83 

1.83 

149-86 

149-68 

7-35 

IOO.II 

50.10 

60 

12.  OO 

9.6000 

3.199 

79.78 

2.22 

159-80 

159-55 

8.92 

106.83 

53-48 

70 

12.75 

10.8375 

3.612 

84-73 

2.66 

169-73 

169.40 

10.67 

H3-55 

56.86 

80 

13-50 

12.1500 

4.049 

89.66 

3-15 

179-64 

179-20 

12.66 

120.29 

60.26 

90 

14-25 

13-5375 

4.511 

94-59 

3-51 

189.54 

188.95 

14-89 

127.04 

63.68 

200 

15.00 

15.0000 

4-997 

99-50 

4-32 

199.40 

198.64 

17-37 

133  82 

67.11 

10 

15-75 

16.5375 

5.509 

104.40 

4-99 

209.23 

208.27 

19.86 

140.62 

70-57 

20 

16.50 

18.1500 

6.045 

109.27 

5-73 

219.03 

217.82 

22.72 

147-45 

74-05 

30 

17-25 

I9-8375 

6.607 

114-13 

6.54 

228.79 

227  .  28 

25-91 

I54-3I 

77.56 

240 

18.00 

21.6000 

7.192 

118.97 

7-41 

238.51 

236.63 

30.01 

161.22 

81.11 

THE   SPIRAL 


69 


TABLE  XXIII.  —  SPIRAL  FUNCTIONS  FOR  A  CHANGE  OF  10.0° 

PER  100  FEET.    SUITABLE  FOR  SPEEDS  OF  22  MILES  AN 

HOUR  OR  LESS,  OR  CURVES  OF  25.0°  OR  LESS 


L 

D 

A 

A 

Z 

o 

C 

X 

Y 

U 

V 

10 

• 

1.  00 

0.050 

o 
O.OI7 

S.oo 

o.oo 

10.00 

IO.OO 

o.oo 

6.67 

3-33 

20 

2.00 

.200 

.067 

10.00 

.01 

20.00 

20.00 

.02 

13-33 

6.67 

30 

3.00 

•450 

•ISO 

15.00 

.02 

30.00 

30.  co 

.08 

20.00 

10.00 

40 

4.00 

.800 

.267 

20.00 

.05 

40.00 

40.00 

.19 

26.67 

13  33 

So 

5.00 

1.250 

•417 

24-99 

.09 

50.00 

50.00 

.36 

33-33 

16.67 

60 

6.00 

1.800 

.600 

29.98 

.16 

60.00 

59.99 

.63 

40.00 

20.00 

70 

7.00 

2.450 

.817 

34-98 

.25 

69.99 

69.99 

.98 

46.67 

23-34 

80 

8.00 

3.200 

I.O67 

39-96 

•  37 

79-99 

79.97 

1.49 

53-34 

26.67 

90 

9.00 

4.050 

1-350 

44-95 

•  53 

89.98 

89.96 

2.12 

60.02 

30.OI 

100 

IO.OO 

5.000 

1.667 

49-92 

•  72 

99-97 

99.92 

2.91 

66.69 

33.36 

10 

II.  OO 

6.050 

2.OI7 

54.89 

•98 

109-95 

109.88 

3-87 

73-38 

36.71 

20 

12.  CO 

7.200 

2.400 

59-86 

1.25 

119  92 

119.81 

5-02 

80.07 

40.06 

30 

13-00 

8.450 

2.816 

64.81 

1.59 

129.88 

129.72 

6.38 

86.77 

43-42 

40 

14.00 

9.800 

3-266 

69.76 

1.98 

139-82 

139.59 

7.97 

93.48 

46.80 

50 

15-00 

11.250 

3-749 

74.69 

2-43 

149-74 

149.43 

9.78 

IO0.2O 

50.19 

60 

16.00 

I2.80C 

4-265 

79.6l 

2-95 

159.65 

159.21 

11.87 

106.95 

53-59 

70 

17.00 

14.450 

4-814 

84.52 

3-53 

169.53 

168.93 

14.21 

113.72 

57-01 

80 

18.00 

16.200 

5.396 

89.40 

4.18 

179-37 

178.57 

16.87 

120.45 

60.47 

90 

19.00 

18.050 

6.012 

94.26 

4-91 

189.18 

188.13 

19.78 

127-34 

63.94 

200 

20.00 

20.000 

6.660 

99-H 

5-71 

198.93 

197.59 

23.07 

134-20 

67.46 

10 

21.00 

22.050 

7.341 

103.92 

6.69 

208  .  64 

206.93 

26.60 

I4I.II 

71.01 

20 

22.OO 

24.200 

8.055 

108.71 

7-56 

218.28 

216.13 

30.59 

148.07 

74-62 

30 

23.00 

26.450 

8.802 

113.46 

8.SI 

227.86 

225.17 

34-77 

155.09 

78.27 

40 

24.00 

28.800 

9-58o 

118.18 

9-76 

237-35 

234.04 

39-50 

I62.I8 

82.00 

250 

25.00 

31.250 

10.392 

122.86 

10.99 

246.75 

242.70  . 

44.67 

169.36 

85-79 

CHAPTER   III 

LOGARITHMS  AND  TRIGONOMETRIC  FUNCTIONS 
TABLE  XXIV.  —  COMMON  LOGARITHMS  OF  NUMBERS 

USE  OF  THE  TABLE  OF  LOGARITHMS 

THE  logarithm  of  a  number  is  the  exponent  denoting  the  power  to 
which  some  fixed  base  number  must  be  raised  to  equal  the  number 
whose  logarithm  is  considered.  There  are  two  base  numbers  in  use, 
but  almost  all  operations  are  performed  by  one  system,  known  as  Com- 
mon Logarithms,  in  which  the  base  is  10.  The  logarithm  of  I  in  any 
system  is  o  because  any  number  raised  to  the  o  power  is  I.  Thus 

_  =  £i-i=  $0=  i.      The  logarithm  of  10  in  the  common  system  is  i; 

of  100,  2;  of  1000,  3;  etc.,  since  lo1  =  10,  io2  =  100,  io3  =  1000,  etc. 
Numbers  between  i  and  io,  io  and  100,  100  and  1000,  etc.,  will  have 
fractional  logarithms.  Thus,  the  logarithm  of  8  is  0.90309;  of  13  is 
1.11394;  of  126  is  2.10037,  etc.,  since  lo0-90309  =  8,  jo1-11394  =  13,  io2-10037 
=  126,  etc.  The  fraction  is  called  the  mantissa  and  is  always  the  same 
for  the  same  sequence  of  figures  and  is  incommensurable,  being  given 
to  3,  5,  6,  7>  or  io  decimal  places,  according  to  the  precision  required. 
Thus  log  1.263  =  0.10140;  log  12.63  =  1.10140;  and  log  126.3  = 
2.10140,  all  of  5  decimal  places.  The  whole  number,  called  the  charac- 
teristic, varies.  The  characteristic  is  always  I  less  than  the  number  of 
digits  to  the  left  of  the  decimal  point  of  the  number  whose  logarithm 
is  being  found.  In  the  tables  only  the  mantissas  are  given.  The  whole 
number  must  be  known  by  the  computer  from  the  number  of  digits  in 
the  number  whose  logarithm  is  wanted. 

To  find  the  logarithm  of  a  number  look  in  the  table  for  the  mantissa 
and  prefix  the  proper  characteristic,  determined  from  the  number  of 
digits  to  the  left  of  the  decimal  point  in  the  number  in  question.  Thus, 
on  page  76,  line  27,  we  find  the  mantissa  for  the  sequence  1263  in  the 
fifth  column  to  be  0.10140;  then  for  1.263  the  log  is  0.10140;  for 
12.63  and  126.3  as  given  above. 

70 


LOGARITHMS  AND  TRIGONOMETRIC   FUNCTIONS       71 

In  the  table  the  first  three  figures  of  a  four-figure  number  appear  in 
the  first  column,  the  fourth  figure  at  the  heads  of  the  10  numbered  col- 
umns. The  first  two  figures  of  the  mantissa  appear  in  the  second 
column,  the  last  three  in  the  column  under  the  fourth  digit  of  the  num- 
ber whose  logarithm  is  sought.  If  the  first  two  figures  change  in  going 
across  the  page,  that  fact  is  indicated  by  an  asterisk;  which,  to  economize 
space,  stands  for  the  first  two  figures  of  the  second  column  in  the  line 
below  the  asterisk.  Thus,  the  logarithm  of  1445  (see  p.  76)  is  3-15987, 
while  that  of  1446  is  3.16017.  For  numbers  of  3  figures  or  less,  the 
mantissa  is  found  in  the  column  headed  o,  since  the  mantissas  for  I, 
10,  100,  or  for  2,  20,  200,  or  for  15,  150,  1500,  etc.,  are  respectively  the 
same. 

The  logarithm  of  a  number  of  more  than  four  figures  is  found  as  in- 
dicated in  the  following  example:  What  is  the  log  of  382.568?  On 
page  81,  line  33,  columns  2  and  7,  find  log  382.5  to  be  2.58263.  Note 
that  log  382.6  is  2.59274,  a  difference  of  u  in  the  log  for  a  difference  of 
I  in  the  last  place  of  the  sequence  in  the  number.  Assuming  that  the 
log  increases  in  proportion  to  the  number,  the  log  of  382.568  may  be 
said  to  be  T%V  of  n  larger  than  log  382.5  since  382.568  is  ffa  of  I  in 
the  last  place  (the  place  of  the  5)  greater  than  382.5.  To  facilitate  this 
computation,  a  table  of  proportional  parts  is  found  alongside  the  log 
table.  Thus,  in  the  case  just  given,  for  a  difference  of  n  we  find,  from 
the  table  of  proportional  parts,  that  an  increase  of  0.6  of  one  in  the  last 
place  of  the  number  makes  a  difference  in  the  log  of  6.6,  an  increase  of 
0.08  in  the  number  increases  the  log  by  0.88,  found  by  moving  the  dec- 
imal point  i  digit  to  the  left  in  the  tabular  value  for  0.8,  so  that  an  in- 
crease of  0.68  of  i  in  the  last  place  increases  the  log  of  382.5  by  6.6  + 
0.88,  or  7.48;  or,  since  we  make  the  fifth  figure  the  nearest  whole  num- 
ber, we  find  log  382.568  =  2.58263  +  7  =  2.58270. 

To  find  the  number  corresponding  to  a  given  logarithm  we  reverse  the 
process.  Thus,  the  number  corresponding  to  the  logarithm  2.58270  is 
found  as  follows:  The  next  smaller  mantissa  130.58263  for  the  sequence 
3825  and  it  is  smaller  than  0.58270  by  7.  The  difference  for  a  whole 
unit  in  the  last  place  is  1 1  and  in  the  table  of  proportional  parts  under 
1 1  find  6.6,  corresponding  to  O.6  of  I  in  the  last  place  of  the  number,  as 
the  next  smaller  difference  to  7,  leaving  still  a  difference  of  7  —  6.6  = 
0.4  to  be  used,  which,  by  moving  the  decimal  point  one  digit  to  the  left, 
is  found  to  correspond  most  nearly  to  0.04  of  i  in  the  last  place  of  the 
number.  Therefore,  the  whole  number  is  382.564.  But  we  found  that 
2.58270  is  the  logarithm  of  382.568.  We  see  by  this  that  this  table 
cannot  be  depended  on  to  give  more  than  a  sequence  of  5  significant 


72  RAILROAD  FIELD   MANUAL 

figures  correctly.  This  is  true  of  all  tables  of  logarithms:  that  as  many 
significant  figures  in  sequence  may  be  correctly  determined  as  there 
are  decimal  places  in  the  tabular  mantissas.  A  5-place  table  gives  five 
significant  figures,  a  6-place  table,  six  significant  figures,  etc. 

To  multiply  a  by  &  we  add  the  logarithms  of  a  and  b,  written  log  a 
and  log  b,  and  find  the  number  corresponding  to  the  sum. 

To  divide  a  by  b,  we  subtract  log  b  from  log  a  and  find  the  number 
corresponding  to  the  difference. 

It  may  often  occur  in  computations  that  the  fifth  place  in  a  resulting 
logarithm,  found  by  adding  two  or  more  logarithms,  may  be  in  error 
by  one  unit,  thus  making  the  quantity  determined  certain  to  one  less 
significant  figure  than  the  number  of  places  in  the  logarithm. 

To  find  the  product  a?b3.  Find  the  logarithm  of  a  and  multiply  it  by 
2;  find  the  logarithm  of  b  and  multiply  it  by  3;  add  the  two  results 
for  the  logarithm  of  the  product  and  find  the  corresponding  number. 
Thus: 

What  is  the  product  1.2*  X  4-33? 

p.  76,  line  21,  col.  2,  log  1.2  =  0.07918  X  2  =  0.15836 

p.  82,  line  31,  col.  2,  log  4.3  =  0.63347  X  3  =  1.90041 

p.  76,  line  15,  col.  6  and  7  =  2.05877  =  log  114.49. 

Ans. 

This  example,  checked  by  a  7-place  table,  gives  the  same  result  to  the 
fifth  significant  figure  even  though  both  logarithms  were  multiplied 
and  then  added. 

The  following  example,  worked  by  5-place  and  7-place  logarithms, 
shows  the  uncertainty  of  the  last  figure  in  computations  made  by  any 
set  of  tables,  by  showing  the  uncertainty  of  the  fifth  figure  in  the  com- 
putations made  with  the  5-place  tables.  Required  the  product  1.652  X 
I.83. 

5-Place 

Log  1.65  =  0.21748  X  2  =  0.43496 
Log  1.8    =  0.25527  X  3  =  0.76581 

1.20077  =  log  15. 877.     Ans. 

7-Place    , 

Log  1.65  =  0.2174839  X  2  =  0.4349678 
Log  1.8    =  0.2552725  X  3  =  0.7658175 

1.2007853  =  log  15-8776.     Ans. 

Thus  15.878  is  nearer  right  than  15.877,  although  the  error  of  the  latter 
is  only  about  0.6  of  one  in  the  last  place  and  the  error  of  the  former  is 


LOGARITHMS  AND  TRIGONOMETRIC   FUNCTIONS       73 

about  0.4  of  one  in  the  last  place.  Greater  differences  can  occur  so 
that  the  fifth  place  is  not  certain  within  I  unit. 

Logarithms  oj  jr actions.  The  logarithm  of  I  =  |£  =  io1-1  =  10°  is 
o.ooooo.  Similarly  the  logarithm  of  o.i  =  ^  =  lo0"1  is  —  i.ooooo; 
the  logarithm  of  3foj  is  —2;  of  T^u  is  —3;  etc.  Therefore,  if  the 
sequence  is  all  fractional  the  characteristic  is  minus  and  with  a  nu- 
merical value  expressed  by  the  number  of  the  place  on  the  right  of  the 
decimal  point  in  which  the  first  significant  figure  appears.  Thus  the 
logarithm  of  0.00126  is  —3  -f  0.10037,  usually  written  3.10037.  The 
mantissa  is  not  minus,  only  the  characteristic  is  minus.  This  some- 
times gives  the  beginner  trouble,  but  need  not  if  he  remembers  that  the 
mantissa  is  always  plus,  while  the  characteristic  is  plus  or  minus  accord- 
ing as  the  number  corresponding  is  equal  to  or  greater  than  I  or  is  less 
than  i,  and  that  in  general  the  two  must  be  treated  separately.  The 
following  examples  will  make  the  use  of  the  signs  clear: 

Required  the  product  43.0  X  0.43. 

Log  43          =1.63347  1-63347 

Log    0.43     =  1.63347  0.63347  ~  I 

Log  18.49     =  1-26694  2.26694  —  I  =  1.26694 

Required  the  product  43.0  X  O.432. 

Log  43.0       =  1.63347  Log  0.432  =  1.63347  X  2 

Log  0.432      =  1.26694  =  2  +  1.26694  =  1-26694 

Log  7.951     =  0.90041 

Required  the  product  43.0  X  0.43*. 

Log  0.43*  =  1.63347  -4-  2  =  1.816735  found 

Log  43.0      =  1.63347  thus:    Add  10  to  the  characteristic  and 

Log  0.43*    =  7.81674  subtract  10  before  dividing  by  2,  getting 

Log  28.207  ==  1.45021  9'  334J  ~    -  =4.816735-5,  or  1.816735. 

Instead  of  adding  and  subtracting  10  in  the  preceding  example,  only 
enough  may  be  added  and  subtracted  to  make  the  negative  character- 
istic divisible  by  the  divisor.  Thus:  In  the  foregoing  example  add  and 
subtract  i,  getting  '-63347  -  I  +  I  _5  +  1.63347  .  ;Jl6yMt  as 

before,  without  the  necessity  of  considering  the  4  and  —5.  If  the 
1/3  power  has  been  required,  the  divisor  would  have  been  3,  and  2 

should  be  added  and  subtracted  getting  1'63347  -2+2  =  3  +2.63347 

3  3 

=  1.877823  +.     This  work  need  not  be  written  out  in  full  in  an  exam- 


74  RAILROAD  FIELD  MANUAL 

pie,  as  the  computer  can  see  the  figures  mentally.  Thus,  he  knows  the 
characteristic  will  be  I  so  he  writes  this  down  and  then  imagines  a  2, 
or  whatever  number  is  to  be  added,  at  the  left  of  the  decimal  and  at 
once  writes  down  the  quotient  after  the  I.  In  handling  very  small 
numbers  when  the  negative  characteristic  is  large,  it  may  be  necessary 
to  write  out  the  operation  to  guard  against  error. 

In  making  the  tables,  when  the  remainder  after  the  fifth  figure  was 
more  than  0.5,  the  fifth  figure  was  increased  by  i;  when  less  than  0.5, 
the  fifth  figure  was  not  changed. 

When  the  computer  is  finding  a  logarithm,  and  the  operation  brings 
a  5  in  the  place  following  the  last  place  of  the  table  (as  the  sixth  place 
when  using  the  tables  of  this  book)  and  the  5  is  followed  by  ciphers, 
a  good  rule  to  adopt  is  to  make  the  last  place  the  nearest  even  number. 
Thus  in  getting  log  0.43'  in  the  example  above  we  add  5  in  the  sixth 
place.  This  rule  will  tend  to  balance  inaccuracies  in  a  long  series  of 
computations. 

To  divide  3.68  X  4.21  we  find  (page  81)  log  3.68  =  0.56585 

(page  82)  log  4.21  =  0.62428 

Now  to  subtract,  we  may  add  and  subtract 

10  from  the  log  3.68,  getting    10.56585  —  10 

o. 62428 

9.94157  -  10  =  1.94157 
or,  we  may  add  the  arithmetical  complement  of  log  4.21  instead  of 

subtracting  the  log  4.21.     That  is,  we  may  multiply  by  instead 

of  dividing  by  4.21.     The  logarithm  of  is  o.ooooo  —  0.62428,  or 

4.21 

1.37572  and  is  called  the  arithmetical  complement  of  the  log  4.21.  It 
is  the  logarithm  of  the  reciprocal  of  4.21.  In  a  series  of  operations, 
where  several  factors  are  to  be  multiplied  and  the  product  divided  by 
the  product  of  several  factors,  the  arithmetical  complements  of  the 
divisor  factors  are  used  to  avoid  the  double  operation  of  two  additions 
and  one  subtraction,  since  the  arithmetical  complements  may  be 
written  down  from  the  logs  almost  as  readily  as  the  logs  themselves. 
Each  digit  of  the  mantissa  of  the  log  is  subtracted  from  9  except  the 
last,  which  is  subtracted  from  10.  The  "characteristic  is  negative  and 
one  greater  than  the  characteristic  of  the  log  when  the  log  character- 
istic is  positive;  and  is  positive  and  one  less  than  the  characteristic 
of  the  log  if  that  characteristic  is  negative.  Thus: 

Log  8.364  is  0.92241 ;      its  complement  is  1.07759 
Log  83.64  is  1.92241 ;      its  complement  is  2.07759 


LOGARITHMS  AND  TRIGONOMETRIC  FUNCTIONS       75 

Log  836.4  is  2.92241 ;  its  complement  is  3.07759 
Log  0.8364  is  1.92241 ;  its  complement  is  0.07759 
Log  0.08364  is  2.92241;  its  complement  is  1.07759 

Instead  of  thinking  of  the  characteristic  by  the  rule  above,  the  log 
may  be  subtracted  from  10  instead  of  zero  when  a  characteristic  of  9 
in  the  complement  will  correspond  to  T;  8  to  2,  etc.  And  the  computer 
can  as  readily  think  of  9  as  indicating  that  the  first  significant  figure  of 
the  result  is  in  the  first  or  tenths'  place  of  the  decimal;  8,  that  it  is 
in  the  second  or  hundredths'  place,  etc.,  and  this  will  cause  no  confusion 
unless  very  large  quantities  are  being  dealt  with,  so  that  the  8  or  9 
might  sometimes  be  a  positive  characteristic  not  standing  in  the  place 
of  a  2  or  T;  but  this  difficulty  is  not  likely  to  arise  in  using  5-  or  6-place 
tables,  since  such  tables  would  not  be  used  with  such  large  numbers. 

When  the  first  figures  are  small.  When  the  first  three  figures  of  a 
number  of  five  or  more  places  are  between  100  and  no  inclusive  use 
pages  94  and  95,  which  give  7-place  logarithms  for  five  digits  directly. 


N 

L  O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

P  P 

100 

087 

130 

17 

217 

260 

303 

346 

389 

IOI 
IO2 
103 
104 

i  OS 

1  06 

107 
108 
109 

432 
860 
oi  284 

703 

02  119 

53i 
938 
03  342 
743 

475 
903 
326 

745 
1  60 
572 

979 
383 
782 

945 
368 

787 

202 

612 

423 
822 

988 
410 
828 
243 
653 
*o6o 
463 
862 

604 
"030 
45 
870 
284 
694 

*IOO 

503 
902 

*072 

494 
912 
325 
735 
*Hi 
543 
941 

689 
*H5 
536 

953 
366 
776 
*i8i 
583 
981 

578 

995 
407 
816 

*222 
623 
*02I 

620 
*o36 
449 
857 

*262 

663 

*o6o 

817 

*242 
662 
*078 
490 
898 
*302 

*7°3 

*IOO 

44   43   42 

I  4-4   4-3   4-2 
2  8.8   8.6   8.4 
3  13-2  12.9  12.6 
4  17-6  17.2  16.8 
522.0  21.5  21.0 
626.4  25.8  25.2 
730.8  30.1  29.4 
835.2  34-4  33-6 

110 

04  139 

179 

218 

258 

297 

336 

376 

415 

454 

493 

III 

112 
"3 
114 
"5 
116 

117 
118 
119 

532 
922 
05  308 
690 
06  070 
446 
819 
07  1  88 
555 

57i 
961 
346 

729 
108 
483 
856 
225 
59i 

610 
999 
385 
767 
145 

893 
262 
628 

650 
*o38 
423 
805 
183 
558 
930 
298 
664 

689 
*o77 
461 

843 

221 

595 
967 
335 
700 

727 
*"S 
500 

88  1 
258 
633 

*°°4 
372 
737 

766 
*I54 
538 
918 
296 
670 

*04I 

408 
773 

80S 
*I92 
576 
956 

333 
707 

*o78 
445 
809 

844 

*23I 

6i4 

994 
37i 
744 

*«S 
482 
846 

*883 
652 

*032 

408 

781 

*i5i 
882 

41   40   39 

i  4.1   4-0   3-9 

2  8.2   8.0   7.8 

312.3  12.0  ii.  7 
4  16.4  16.0  15.6 
5  20.5  20.0  19.5 
624.6  24.0  23.4 
728.7  28.0  27.3 
832.8  32.0  31.2 
936.9  36.0  35.1 

120 

918 

954 

990 

*027 

uyy 

'171 

'207 

*243 

121 
122 

123 
124 
125 
126 

127 

128 
129 

08  279 
636 
991 
09  342 
691 
10  037 
380 
721 
ii  059 

314 
672 

*026 

377 
726 
072 

415 
755 
093 

350 
707 
*o6i 
412 
760 
106 

449 
789 
126 

386 

743 
*096 

447 
795 
140 

483 
823 
1  60 

422 
^778 

482 
830 
175 
517 
857 
193 

458 
814 
*i67 

517 
864 
209 

551 
890 
227 

493 
849 

*202 

552 
899 
243 
585 
924 
261 

is 

*237 
587 
934 
278 

619 

958 
294 

565 
*92° 

62! 
968 
312 

653 
992 
327 

600 
*9SS 

656 

"003 
346 
687 
"025 

361 

38   37   36 

i  3-8   3-7   36 
2  7.6   7.4   7.2 
3  11.4  ii.  i  10.8 
415-2  14.8  14.4 
5  19.0  18.5  18.0 

322.8  22.2  21.6 

726.6  25.9  25.2 
830.4  29.6  28.8 
934-2  33-3  32.4 

130 

394 

428 

461 

494 

528 

56i 

594 

628 

661 

694 

131 
132 
133 
134 
135 
136 

137 
138 
139 

727 
12  057 
385 
710 
13  033 
354 
672 
988 
14  301 

760 
090 
418 

743 
066 
386 

*7°4 
333 

793 
123 
450 

775 
098 
418 

*735 
364 

826 
156 
483 
808 
130 
450 
767 

*082 

395 

860 
189 

840 
162 
481 

*799 
426 

893 

222 
548 
872 
194 
513 
830 

*i45 
457 

926 
254 

90S 
226 
545 
862 
*i76 
489 

959 
287 
613 

937 
258 
577 
893 

*208 

520 

992 
320 
646 

969 
290 
609 

925 
*239 
551 

*024 

352 
678 

*OOI 

322 

640 

956 

*270 

582 

35   34   33 

i  3-5  3.4  3-3 
2  7.0   6.8   6.6 
3  10.5  10.2   9.9 
414.0  13.6  13-2 
517.5  17.0  16.5 
52i.o  20.4  19.8 
724.5  23.8  23.1 
3  28  .  o  27  .  2  26  .  4 
?3i-5  30.6  29.7 

140 

613 

644 

675 

706 

737 

768 

799 

829 

860 

891 

141 
142 
143 
144 
145 
146 

III 
149 

922 
15  229 
534 
836 
1  6  137 
435 
732 
17  026 
319 

953 
259 
564 
866 
167 
465 
76! 
056 
348 

983 
290 
594 

897 
197 

495 
791 
085 
377 

*oi4 
320 
625 

927 

227 

524 
820 
114 
406 

*045 
35i 
655 
957 
256 
554 
850 
143 
435 

°8i 
685 

987 
286 
584 
879 
173 
464 

*io6 
412 
715 
*OI7 
316 
613 
909 

202 
493 

*i37 
442 
746 

346 
643 
938 
231 
522 

*i68 
473 
776 

376 
673 
967 
260 

"198 
503 
806 

406 
702 

997 
289 
58o 

32   31   30 

I  3-2   3-1   30 
z  6.4   6.2   6.0 
J  9-6   93   9-0 
[  12.8   12.4   12.  0 

>  16.0  15.5  15.0 
)  19.2  18.6  18.0 

J  22.4   21.7   21.0 

525.6  24.8  24.0 
)  28.8  27.9  27.0 

ISO 

17  609 

863 

667 

696 

725 

754 

782 

811 

84o 

869 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

p  p 

(76) 


N 

L  O 

1 

2 

3 

4 

5 

6 

7 

8 

9 

PP 

150 

17  609 

638 

667 

696 

725 

754 

782 

811 

840 

869 

151 
152 
153 
154 
155 
156 

157 
158 
159 

898 
18  184 
469 
752 
19  033 
312 
590 
866 

20  140 

926 
213 
498 
780 
061 
340 
618 
893 
167 

955 
241 
526 
808 
089 
368 

645 
921 
194 

984 
270 
554 

837 
117 
396 

673 
948 

222 

"013 
298 
583 
865 
145 
424 

700 
976 
249 

*04I 

327 
611 

893 

728 
"003 
276 

*070 

355 
639 
921 

2OI 

479 
*756 
303 

"099 
384 
667 

949 
229 

507 

783 
"058 
330 

*I27 

412 
696 

977 

257 
535 
811 
*o8S 
358 

441 
724 
"005 
285 
562 

838 

*II2 
385 

I 

2 

3 

4 
5 
6 
7 
8 
9 

2.9   2.8 
5.8   5-6 
8.7   8.4 
II.  6  II.  2 

14-5  14-0 
17.4  16.8 
20.3  19.6 
23.2  22.4 
26.1  25.2 

160 

412 

439 

466 

493 

520 

548 

575 

602 

629 

656 

97     96 

161 
162 
163 
164 
165 
1  66 

167 
1  68 
169 

683 
952 
21  219 

484 
748 
22  OH 

272 
531 
789 

710 
978 
245 

775 
037 
298 
557 
814 

737 
*ooS 
272 

537 
801 
063 

324 
583 
840 

,763 
*032 
299 

564 
827 
089 

350 
608 

866 

790 
*059 
325 
590 
854 
"5 
376 
634 
891 

817 
*o85 
352 
6I7 
880 
141 
401 
660 
917 

844 

*II2 
378 

643 
906 
I67 
427 

686 
943 

871 
*I39 
4°5 
669 
932 
194 

453 
712 
968 

898 
"165 
43i 
696 

958 

220 

479 
737 
994 

925 
*I92 
458 
722 
985 
246 

505 

2 

3 

4 
5 
6 
7 
8 
9 

2.7  2.6 
5-4   5-2 
8.1   7-8 
10.8  10.4 
13-5  13-0 
16.2  15.6 
18.9  18.2 

21.6  20.8 

24.3  23.4 

170 

23  045 

070 

096 

121 

147 

172 

198 

223 

249 

274 

OK 

171 
172 
173 
174 

175 
176 

177 
178 
179 

300 

553 
805 

24  055 
304 

797 
25  042 
285 

325 
578 
830 
080 
329 
576 
822 
066 

350 
603 
855 
105 
353 
601 

846 
091 
334 

376 
629 
880 

130 
378 
625 

87I 
358 

401 
654 
905 
155 
403 
650 

895 
139 
382 

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437 
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(92) 


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953 
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145 

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207 
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599 
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634 
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939 
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00  000 

004 

022 

026 

030 

035 

N 

L  0 

1 

2 

3 

4 

5 

6 

7 

8 

9  |    P  p 

(93) 


w 


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L   0 

1 

2 

8 

9 

1000 

000  0000 

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100  1 

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5208 

5642 

6076 

6510 

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004  3214 

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1013 
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005  1805 
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007  3210 
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1023 
1024 
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012  4154 

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013  2587 
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5274 
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3105 
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3525 
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017  0333 

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1168 

1586 

2003 

2421 

2838 

3256 

3673 

4090 

1041 
1042 
1043 
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1045 
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4507 
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01  8  2843 
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020  3613 

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1994 
6147 

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9927 
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8253 
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4508 
8669 
2825 
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5270 
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6593 
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4925 
9084 
3240 
7392 

5684 
9824 

7010 
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5341 
9500 
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7427 
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5757 
9916 
4071 
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8260 
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4902 
9052 
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021  1893 

2307 

2720 

3134 

3547 

396i 

4374 

4787 

5201 

5614 

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L    0 

• 

2 

3 

4 

5 

6 

7 

8 

9 

'94) 


N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

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02  1  1893 

2307 

2720 

3134 

3547 

3961 

4374 

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1051 
1052 
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022  0157 
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023  2525 
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024  0750 
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9230 
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1078 
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030  1948 
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031  0043 
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032  2157 
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033  0214 

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9638 
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1080 

4238 

4640 

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5444 

5846 

6248 

6650 

7052 

7453 

7855 

1081 
1082 
1083 
1084 
1085 
1086 
1087 
1088 
1089 

8257 
034  2273 
6285 
035  0293 
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036  2295 
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037  0279 

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9060 
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3094 
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1076 

9462 
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7487 
1495 
5498 
9498 

3494 
7486 

1475 

9864 
3878 
7888 

1895 
5898 
9898 

3893 
7885 
1874 

4279 
8289 
2296 
6298 

4293 
8284 
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5482 
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3497 
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5491 
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5884 
9892 

3897 
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"1896 
5890 
9880 
3867 

1000 

4265 

4663 

5062 

5460 

5858 

6257 

6655 

7053 

7451 

7849 

1091 
1092 
1093 
1094 
1095 
1096 
1097 
1098 
1099 

8248 
038  2226 
6202 
039  0173 
4141 
8106 
040  2066 
6023 
9977 

8646 
2624 
6599 
0570 
4538 
8502 
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9044 
3022 
6996 
0967 
4934 
8898 
2858 
6814 
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9442 
3419 
7393 
1364 
5331 
9294 
3254 
7210 

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9839 
3817 
7791 
1761 
5727 
9690 
3650 
7605 
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4214 
8188 
2158 
6124 
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4045 
8001 
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4612 

8585 
2554 
6520 

4441 
8396 
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5009 
8982 

2951 
6917 
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4837 

5407 
9379 
3348 
7313 

5232 
9187 
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5804 
9776 

3745 
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5628 
9582 
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1100 

041  3927 

4322 

4716 

Sin 

5506 

5900 

6295 

6690 

7084 

7479 

N 

L   0 

1 

2 

3 

4 

5 

6 

7 

8 

9 

(95) 


96  RAILROAD  FIELD  MANUAL 


TABLE  XXV.  —  LOGARITHMS  OF  SINES,  TANGENTS,  COSINES, 
AND  COTANGENTS  FOR  EACH  0.01°  OF  THE  QUADRANT 

In  this  table  whenever  the  trigonometric  function  is  fractional,  as 
it  always  is  for  sines  and  cosines,  except  when  it  is  I,  the  logarithms 
have  been  increased  by  10  to  avoid  the  negative  characteristic.  But 
where  the  function  is  greater  than  I ,  as  are  cotangents  and  tangents  for 
certain  parts  of  the  circle,  the  logarithm  is  given  without  the  10.  Thus 
in  the  column  headed  cot  at  the  top  of  the  page  the  logarithms  are  un- 
augmented;  in  all  other  columns  they  are  augmented.  This  must  be 
remembered  in  working  with  them. 

To  find  the  square  root  of  the  sine  of  26.32°  we  find  on  page  151,  line 
33,  the  log  sin  to  be  9.64678,  which  must  be  divided  by  2  to  give  the 
logarithm  of  the  square  root;  the  operation  is  performed  thus: 

2)9.64678  -  10  = 
4-82339  -  5 

Whence  Vsin  26.32°  =  the  number  whose  log  is  1.82339  or  0.66587+. 
But  to  find  the  square  root  of  the  cotangent  of  26.32°,  page  151,  line  33, 
we  have  0.30569  -s-  2  =  0.152845,  which  corresponds  to  the  number 
1.4218+. 

The  numbering  of  the  pages.  —  On  each  page  there  will  be  found  four- 
degree  numbers  which  are  to  be  used  as  follows:  the  upper  left-hand 
figure  is  used  with  the  headings  at  the  tops  of  the  columns  and  the 
fractions  running  down  the  left  side  of  the  page.  The  lower  right-hand 
figure  is  used  with  the  headings  at  the  bottoms  of  the  columns,  and  frac- 
tions running  up  the  right-hand  side  of  the  page.  The  upper  right-hand 
figure  is  used  with  headings  at  the  tops  of  the  columns  and  fractions 
running  up  the  right-hand  side  of  the  page.  The  lower  left-hand  figure 
is  used  with  headings  at  the  bottom  of  the  page  and  fractions  running 
down  the  left-hand  side  of  the  page.  Generally  stated  the  figures  are 
used  with  the  headings  and  fractions  nearest  them. 

Example.  —  See  pages  163-164.  The  log  sin  of  32.4°  is  found  in  the 
2nd  column,  page  163,  4ist  line,  to  be  9.72902,  while  the  log  sin  of  122.4° 
is  found  in  the  7th  column  of  the  same  page  and  line  to  be  9.92651. 
The  log  sin  of  147.4°  is  found  in  the  2nd  column  on  page  164,  4ist  line 
from  the  bottom,  to  be  9.73140,  while  the  log  sin  57.4°  is  found  in  the 
7th  column  of  the  same  page  and  line  to  be  9.92555. 

When  the  function  or  angle  sought  is  not  in  the  table,  as  when  the  log 
sin  of  14.436°  or  the  angle  whose  sine  is  9.34220  is  wanted,  we  must 
interpolate  between  the  tabular  quantities.  Thus: 


LOGARITHMS  AND  TRIGONOMETRIC  FUNCTIONS       97 

(a)  Log  sin  14.43°  'ls  found  on  page  127,  line  44,  to  be  9.39654  with 
a  tabular  difference  of  30  for  a  change  of  o.oi  given  in  the  column  headed 
d.  Then  the  addition  for  6  tenths  of  0.01°  is  found  by  multiplying 
30  X  0.6  =  18,  and  adding  to  9.39654  giving  9.39672  as  the  required 
sine.  When  the  quantities  are  less  simple  the  proportional  part  given 
in  the  right-hand  column  of  the  page  may  be  used.  If  the  angle 
is  14.4362°  the  table  of  proportional  parts  is  convenient  even  for  the 
simple  difference  of  30.  Thus,  from  the  values  in  the  right-hand  column 
headed  "30"  we  find  18  opposite  6;  moving  the  decimal  point  one  place 
to  the  left,  we  find  0.6  opposite  2;  adding  we  get  ,000186,  or  .00019,  to 
be  added  to  the  log  sin  14.43°  to  give  log  sin  14.4362°.  The  figures  are 
uncertain  beyond  five  places  and  may  be  a  fraction  of  one  in  error  in 
the  fifth  place. 

(6)  For  the  angle  whose  log  sine  is  9.34220  we  find  on  page  124 
the  next  smaller  log  sin  =  9.34212  =  log  sin  12.70°;  the  difference  is 
9.34220  —  9.34212  =  8  in  the  last  place.  The  tabular  difference  is  34. 
Looking  in  the  column  of  proportional  parts  under  34  we  find  6.8  next 
smaller  number  than  8  corresponding  to  0.002  and  leaving  1.2  unused; 
moving  the  decimal  point  one  place  to  the  left  in  the  tabular  quanti- 
ties, the  next  smaller  and  nearest  number  is  1.02  opposite  3.  There- 
fore the  angle  is  12.7023°.  The  last  figure  is  uncertain. 

For  fractional  angles  near  o°  and  90°,  the  differences  are  changing  so 
rapidly  that  linear  interpolation  is  not  sufficiently  exact.     The  right- 
hand  columns  of  pages  99  to  104  show  what  to  do.      Thus  to  find 
the  log  sin  0.1246°  we  find  (pages  76  and  99) 
Log.  0.1246  =1.09552 
5    =  1.75812 
7-33740 

To  find  log  cos  and  log  cot  we  find  log  sin  and  tangents  of  comple- 
mentary angles.  Thus,  to  get  log  cos  89.367°,  we  get  log  sin  0.633°. 
Conversely,  to  find  the  angle  whose  log  sin  is  7.33740,  we  refer  to 
page  99,  and  find  that  the  angle  is  between  0.12°  and  0.13°  and  hence 

S  =  1.75812 
log  sin  =  7-3374Q  —  io 
(page  76)  log  0.1246°  =  9-09552  -  10  =  1.09552. 

TABLE  XXVI.  —  LOGARITHMIC  VERSED  SINES  AND  EXTERNAL 
SECANTS  FOR  EACH  0.02°  OF  THE  QUADRANT 

The  use  of  this  table  will  be  evident  except  the  interpolation  for  small 
angles  and  for  external  secants  for  angles  near  90°. 


98  RAILROAD   FIELD  MANUAL 

For  small  angles  use  the  quantity  V  for  versed  sines  and  E  for  external 
secants  as  follows: 

Log  vers  a    =  2  log  a°  +  V. 
Log  exsec  a.  =  2  log  a°  -f-  E. 

Interpolate  for  V  and  E  when  necessary. 
Example.  —  Required  log  vers  1.354°. 

Log  1.354  =  0.13162 
2 

0.26324 
Ffor  1.36°  =  6.18270 

Log  vers  1-354°  =  6.44594- 
0  _  log  vers  a  —  V  _  log  exsec  a  —  E 

For  external  secants  near  90°  the  interpolation  is  as  follows: 
Log  exsec  A  =  log  vers  A  —  log  sin  (90  —  A). 


179< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

00 

100 

5 

01 

6.24188 

6.24188 

3.75812 

o.ooooo 

99 

oa 
03 

6.54291 
6.71900 

30103 
17609 

6.54291 
6.71900 

30103 
17609 

3.45709 
3.28100 

o.ooooo 
o.ooooo 

98 
97 

J_    1.758 
.0         123 

04 
05 
06 

6.84394 
6.94085 
7.02003 

12494 
9691 
7918 
6695 

6.84394 
6.94085 
7.02003 

12494 

9691 
7918 
6695 

3-15606 
3.05915 
2.97997 

o.ooooo 
o  .  ooooo 

0.00000 

96 
95 
94 

.1         123 

.2           124 

.3         125 
4         126 

07 

7.08698 

7.08698 

2.91302 

o.ooooo 

93 

08 

7-14497 

5799 

7-14497 

5799 

2.85503 

o.ooooo 

92 

09 

7.19612 

5H5 
.-»£ 

7.19612 

5H5 

2.80388 

o.ooooo 

9i 

10 

7.24188 

7.24188 

2.75812 

o.ooooo 

90 

ii 

7-28327 

7.28327 

2.71673 

o.ooooo 

89 

12 
13 

7.32106 
7.35582 

3779 
3476 

7.32106 
7.35582 

3779 
3476 

2.67894 
2.64418 

o.ooooo 
o.ooooo 

88 
87 

14 

7.38800 

7.388oi 

2.61199 

o.ooooo 

86 

IS 
16 

7-41797 
7.44600 

2997 
2803 

7.41797 
7.44600 

2996 
2803 
2677 

2.58203 

2.55400 

o.ooooo 
o.ooooo 

85 
84 

£.    | 

17 
18 

7.47233 
7-49715 

2482 

7-47233 
7-49715 

2482 

2.52767 
2.50285 

o.ooooo 
o.ooooo 

83 
82 

£ 

0          '   "S 

ah.  g 

19 

7.52063 

2348 

7.52063 

2348 

2.47937 

o.ooooo 

81 

o+  8 

20 

7.54291 

7.54291 

2.45709 

o.ooooo 

80 

7  2*° 

21 

7.56410 

7.56410 

2.43590 

o  .  ooooo 

79 

8  -3   rt 

22 

7.58430 

2020 

7.58430 

2020 

2.41570 

o  .  ooooo 

78 

^  |  J3*« 

23 

7.60360 

1930 

1840 

7.60361 

1931 
1848 

2.39639 

o.ooooo 

77 

24 

7.62209 

7.62209 

2.37791 

o.ooooo 

76 

'  4)  "*  ^  .S 

25 

7-63982 

1773 

7.63982 

1773 

2.36018 

o.ooooo 

75 

S  ^  +  ^ 

26 

7.65685 

1703 
1630 

7-65685 

1703 
1639 

2.34315 

0.00000 

74 

J§0    «  % 

27 

7-67324 

7.67324 

2.32676 

o.ooooo 

73 

P?    8  'to  °Q 

28 

7-68903 

1579 

7.68904 

1580 

2.31096 

9.99999 

72 

c  -2.2  5s 

29 

7.70427 

1524 

7.70428 

1524 

2.29572 

9.99999 

71 

Jill 

30 

7.71900 

1473 

7.71900 

2.28100 

9.99999 

70 

u   S°«  "S 

3i 

7.73324 

7.73324 

2.26676 

9-99999 

69 

15  "in    o1^ 

32 

7.74703 

1379 

7.74703 

1379 

2.25297 

9-99999 

68 

f  t       1 

33 

7.76039 

1336 
1206 

7.76040 

1337 
1296 

2.23960 

9-99999 

67 

34 

7-77335 

7.77336 

2.22664 

9  99999 

66 

.S 

35 

7.78594 

1259 

7-78595 

1259 

2.21405 

9-99999 

65 

£      1 

36 

7.79818 

1224 

7.79819 

1224 

2.20181 

9-99999 

64 

37 

7.81008 

' 

7.81009 

2.18991 

9-99999 

63 

38 

7.82166 

1158 

7.82167 

1158 

2.17833 

9-99999 

62 

39 

7-83294 

1128 

7-83295 

2  .  16705 

9-99999 

61 

40 

7-84393 

1099 

7-84394 

1099 

2.15606 

9-99999 

60 

41 

42 

7.85466 
7.86512 

1046 

7-85467 
7.86513 

1046 

2.14533 
2.13487 

9-99999 
9-99999 

59 
58 

T 

43 

7-87534 

7-87535 

2.12465 

9-99999 

57 

44 

7-88533 

999 

7.88534 

2.11466 

9-99999 

56 

°     1.758 

45 

7.89509 

970 

7.89510 

970 

2.10490 

9-99999 

55 

.0        123 

46 

7.90463 

954 

7-90464 

954 

2.09536 

9-99999 

54 

.1            122 

47 

7.91397 

934 

7.91398 

934 

2.08602 

9-99999 

53 

.2           121 

48 
49 

7.923H 
7.93207 

914 
896 

877 

7.92313 
7.93208 

915 
895 
878 

2.07687 
2.06792 

9-99998 
9-99998 

52 

5i 

•  3           "9 

.4         "6 

50 

7.94084 

7.94086 

2.05914 

9.99998 

50 

.5         H2 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

90° 


(99) 


179< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

50 
51 

52 

53 

54 
55 
56 

57 
58 
59 
60 
6i 
62 
63 
64 
65 
66 

67 
68 
69 
70 

71 

72 

73 
74 
75 
76 

77 
78 
79 
80 
81 
82 
83 
84 
85 
86 

87 
88 
89 
90 

92 
93 
94 
95 
96 

97 
98 
99 
100 

7.94084 

860 
843 
828 

811 
797 
783 
769 
755 
742 

730 
7i8 
706 
695 
684 
673 
663 

653 

644 
634 
624 
616 
608 
599 
59i 
583 
575 
568 
56o 
553 
546 
540 
533 
526 

520 
514 
508 

502 
496 
491 
485 
480 
475 
469 
465 
459 
455 
450 
445 
441 
437 

7.94086 

860 
843 
828 

811 
797 
783 
769 
755 
742 
730 
7i8 
707 
695 
684 
673 
663 

653 
644 
634 
625 
616 
607 
599 
591 
583 
576 

567 
56i 
553 
547 
539 
533 
527 
520 
514 
508 

502 
496 
491 

486 
480 
474 
470 

464 
460 
455 
450 
446 
441 
436 

2.05914 

9.99998 

50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 

32 

31 
30 

29 

28 

27 

26 

24 
23 

22 
21 
20 
19 

18 
17 
16 
15 
14 
13 

12 
II 

10 

09 
08 
07 
06 
05 
04 

03 
02 

OI 

00 

b  o  oo  ^  b»  6,  1  „  To  interpolate  when  angles  are  small:  S  i  bo  C»  b>  6,  1  0 

!_  log  sin  n  =  log  n  —  .S;  Ing  tan  n  —  lr>g  n°  —  T-  1 

.M  loga°  =  logsina  +  S  =  logtana  +  r.  M  • 

<O^^M<!K>00  &  0  Xl  £  M  00  00 

» 

7-94944 
7.95787 
7.96615 
7.97426 
7-98223 
7.99006 

7-99775 
8.00530 
8.01272 

7.94946 
7.95789 
7.96617 
7.97428 
7.98225 
7.99008 

7-99777 
8.00532 
8.01274 

2.05054 
2.04211 
2.03383 
2.02572 
2.01775 
2.00992 

2.00223 
1.99468 
1.98726 

9-99998 
9.99998 
9-99998 
9-99998 
9-99998 
9-99998 
9-99998 
9-99998 
9-99998 

8.O2OO2 

8  .  02004 

1.97996 

9-99998 

8  .  02720 
8.03426 
8.04121 
8.04805 
8.05478 
8.06141 

8.06794 
8.07438 
8.08072 

8.02722 
8.03429 
8.04124 
8.04808 
8.05481 
8.06144 
8.06797 
8.07441 
8.08075 

1.97278 
1.96571 
1.95876 
I.95I92 
I.945I9 
1.93856 

1.93203 
1.92559 
1.91925 

9.99998 
9-99997 
9-99997 
9-99997 
9-99997 
9-99997 
9-99997 
9-99997 
9-99997 

8.08696 

8.08700 

1.91300 

9-99997 

8.09312 
8.09920 
8.10519 
S.iiiio 
8.11693 
8.12268 
8.12836 
8.13396 
8.13949 

8.09316 
8.09923 
8  .  10522 
8.11113 
8.11696 
8.12272 

8.12839 
8.13400 
8.13953 

1.90684 
1.90077 
1.89478 

1.88887 
1.88304 
1.87728 
1.87161 
1.86600 
1.86047 

9-99997 
9-99997 
9-99996 
9.99996 
9-99996 
9.99996 
9.99996 
9^9996 
9.99996 

8.14495 

8.14500 

1.85500 

9.99996 

8.15035 
8.15568 
8.16094 

8.16614 
8.17128 
8.17636 
8.18138 
8.18634 
8.19125 

8.IS039 
8.15572 
8.16099 

8.16619 
8.I7I33 
8.17641 
8.18143 
8.18639 
8.19130 

1.84961 
1.84428 
1.83901 

1-83381 
1.82867 
1.82359 
1.81857 
1.81361 
1.80870 

9.99996 
9.99996 
9-99995 
9-99995 
9-99995 
9-99995 
9-99995 
9-99995 
9-99995 

8.19610 

8.19616 

1.80384 

9-99995 

8.20090 
8.20565 
8.21034 

8.21499 
8.21958 
8.22413 

8.22863 
8.23308 
8.23749 

8.20096 
8.20570 
8.21040 
8.21504 
8.21964 
8.22419 
8.22869 
8.23315 
8.23756 

1.79904 
1-79430 
1.78960 

1.78496 
1.78036 
I.7758I 

I.77I3I 
1.76685 
1.76244 

9-99995 
9-99994 
9-99994 
9-99994 
9-99994 
9-99994 
9-99994 
9-99994 
9-99994 

8.24186 

8.24192 

i.758o8 

9-99993 

Cos 

d. 

Cot 

d.c. 

Tan            Sin 

90' 


(ioo) 


178' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

00 

8.24186 

8.24192 

I.75&CS 

9-90993 

100 

01 

8.24618 

8.24624 

.75376 

C-  99993 

99 

s 

02 

8.25045 

427 

8.25052 

•74948 

9-99993 

98 

°       i  758 

03 

8.25469 

424 
420 

8.25476 

424 
420 

•74524 

9-99993 

97 

i.o         145 

04 
05 

8.25889 
8.26304 

415 

8.25896 
8.26312 

416 

.74104 
.73688 

9-99993 
9-99993 

96 
95 

.1         149 

.2            154 

o6 

8.26716 

408 

8.26723 

408 

.73277 

9-99993 

94 

.3        160 

07 

8.27124 

8.27131 

.72869 

9-99992 

93 

.4         166 

08 

8.27528 

404 

8.27535 

404 

.72465 

9-99992 

92 

-5         172 

09 

8.27928 

400 

8.27936 

401 

.72064 

9.99992 

91 

10 

8.28324 

8.28332 

.71668 

9-99992 

90 

ii 

8.28717 

8.28725 

.71275 

9-99992 

89 

12 
13 

8.29107 
8.29493 

390 
386 
382 

8.29115 
8  .  29501 

39O 
386 
383 

.70885 
.70499 

9-99992 
9.99992 

88 
87 

14 

8.29875 

8.29884 

.70116 

9-99991 

86 

§ 

15 

8.30255 

380 

8.30263 

379 

.69737 

9-99991 

85 

s 

16 

8.30631 

376 
372 

8.30639 

37O 
373 

.69361 

9-99991 

84 

-a 

e 

17 

8.31003 

8.31012 

.68988 

9-99991 

83 

£ 

18 

8.31373 

37O 

8.31382 

37O 

.68618 

9.99991 

82 

i     £ 

19 

8.31739 

366 
34 

8.31749 

307 

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9.99991 

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8.32103 

8.32112 

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.67888 

9.99990 

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g+$ 

21 

8.32463 

3  o 

8.32473 

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9.99990 

79 

22 

8.32820 

357 

8.32830 

357 

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9.99990 

78 

«  §  * 

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8.33175 

355 
352 

8.33185 

355 

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9.99990 

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24 

8.33527 

8.33537 

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9.99990 

76 

•9   fc|  •    9 

25 

26 

8.33875 
8.34221 

348 
346' 

344 

8.33886 
8.34232 

349 
346' 
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9-99990 
9.99989 

75 

74 

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8.34565 

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9.99989 

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S  i  «| 

28 

29 

8.34905 
8.35243 

340 
338 

8.34916 
8.35254 

341 
338 

.65084 
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9.99989 
9.99989 

72 
71 

fill 

30 

8.35578 

8.35590 

33 

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9.99989 

70 

Sr7  * 

31 

8.359H 

8.35922 

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9.99989 

69 

*"  a 

32 
33 

8.36241 
8.36569 

330 
328 
325 

8.36253 
8.36581 

331 
328 
325 

.63747 
.63419 

9.99988 
9.99988 

68 
67 

m 

34 

8.36894 

8.36906 

.63094 

9-99988 

66 

35 

8.37217 

323 

8.37229 

323 

.62771 

9.99988 

65 

<u             w 

36 

8.37538 

321 
318 

8.37550 

321 
318 

.62450 

9.99988 

64 

G             8 

37 

8.37856 

8.37868 

.62132 

9-99988 

63 

o 
H          fe 

38 

8.38171 

315 

8.38184 

3!0 

.61816 

9.99987 

62 

39 

8.38485 

314 

8.38498 

314 

.61502 

9.99987 

61 

40 

8.38796 

8.38809 

.61191 

9.99987 

60 

4i 

8.39105 

8.39118 

.60882 

9.99987 

59 

42 

8.39412 

307 

8.39425 

307 

.60575 

9.99987 

58 

43 

8.39717 

3°5 
302 

8.39730 

305 
303 

.60270 

9.99986 

57 

r 

44 

8.40019 

8.40033 

.59967 

9-99986 

56 

0   1  758 

45 
46 

8.40320 
8.40618 

301 
298 
297 

8.40334 
8.40632 

301 

298 

297 

.59666 
.59368 

9.99986 
9.99986 

55 
54 

i.o         079 
.1         069 

47 

8.40915 

8.40929 

.59071 

9.99986 

53 

48 

8.41209 

294 

8.41224 

295 

.58776 

9.99986 

52 

3         048 

49 

8.41501 

292 

8.41516 

292 

.58484 

9-99985 

Si 

.4          036 

50 

8.41792 

8.41807 

I.58I93 

9.99985 

50 

•5         023 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

(101) 


178  < 


Sin" 

d. 

*  Tan  V 

'd.V  ' 

Cot 

Cos 

50 

8.41.792 

8.41807 

1.58193 

9.99985 

50 

Si  ' 

8.4vc3q 

8.42095 

.I-S7905 

9.99985 

49 

5 

52 

53 

8.42367 
8.42652 

285 
283 

8.42382 
8.42667 

285 
283 

1.57618 
1-57333 

9-99985 
9-99985 

48 
47 

_1_      1-758 
1-5            172 

54 
55 

8.42935 
8.43216 

281 

8.42950 
8.43232 

282 

1.57050 
1.56768 

9.99984 
9.99984 

46 
45 

.6           179 
7           186 

56 

8.43495 

279 
277 

8.435H 

279 
278 

1.56489 

9.99984 

44 

.8           194 

57 

8.43772 

8.43789 

1.56211 

9.99984 

43 

•  9              202 

58 

8.44048 

270 

8.44064 

275 

1-55936 

9.99983 

42 

2.O              211 

59 

8.44322 

274 

8.44339 

275 

i.5566i 

9.99983 

41 

60 

8.44594 

8.44611 

1.55389 

9-99983 

40 

6i 

8.44865 

8.44882 

I.55H8 

9.99983 

39 

62 

8.45133 

8.45I5I 

269 

1.54849 

9.99983 

38 

63 

8.45401 

268 
265 

8.45418 

267 
266 

1.54582 

9.99982 

37 

^ 

64 

8.45666 

8.45684 

I.543I6 

9.99982 

36 

(U 

65 
66 

8.45930 
8.46192 

264 
262 

261 

8.45948 
8.46211 

264 
263 
261 

1.54052 
1.53789 

9.99982 
9.99982 

35 
34 

67 

8.46453 

8.46472 

1.53528 

9.99982 

33 

"          0 

68 

8.46712 

259 

8.46731 

259 

1.53269 

9.99981 

32 

1      £ 

69 

8.46970 

258 
2rfi 

8.46989 

2^6 

I.  5301  I 

9.99981 

3i 

8  ^  a 

70 

8.47226 

8.47245 

1.52755 

9.99981 

30 

7i 

8.47481 

8.47500 

1.52500 

9.99981 

29 

Jjl 

72 

8.47734 

253 

8.47754 

254 

1.52246 

9.99980 

28 

73 

8.47986 

252 

8.48006 

252 

I.5I994 

9.99980 

27 

oS    o'aa 

74 

8.48236 

250 

8.48256 

250 

I.5I744 

9.99980 

26 

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75 

8.48485 

249 

8.48505 

249 

I-5I495 

9.99980 

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s  ~  ^  ° 

76 

8.48732 

247 

8.48753 

248 

I.5I247 

9.99980 

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£  C/3  -f-  8> 

77 

8.48978 

8.48999 

1.51001 

9-99979 

23 

78 

8.49223 

245 

8.49244 

245 

1.50756 

9-99979 

22 

3  "  "3  2 

79 

8.49466 

243 

8.49487 

243 

1.50513 

9-99979 

21 

C    0    0  ~ 

80 

8.49708 

8.49729 

1.50271 

9-99979 

20 

S-"  "  S 

81 

8.49948 

8.49970 

I  .  50030 

9.99978 

19 

|1  "^ 

82 

8.50188 

240 

8.50209 

239 

I-4979I 

9.99978 

18 

83 

8.50425 

237 

8.50448 

239 
236 

1-49552 

9.99978 

17 

~  3      -d 

84 

8.50662 

8.50684 

I.493I6 

9.99978 

16 

p<             rt 

8s 

8.50897 

235 

8.50920 

230 

1.49080 

9.99977 

IS 

O                    t/3 

86 

8.51131 

234 
233 

8.5"54 

234 
233 

1.48846 

9-99977 

14 

'o           o 

87 

8.51364 

8.51387 

1.48613 

9-99977 

13 

H          fa 

88 

8.51596 

232 

8.51619 

232 

1.48381 

9-99977 

12 

89 

8.51826 

230 

8.51850 

231 

1.48150 

9.99976 

II 

90 

8.52055 

228 

8.52079 

228 

I.4792I 

9.99976 

10 

9i 

8.52283 

8.52307 

1.47693 

9.99976 

09 

92 

8.52510 

227 

8-52534 

227 

1.47466 

9.99976 

08 

r 

93 

8.52735 

225 
225 

8.52760 

225 

1.47240 

9-99975 

07 

°           i-75 

94 
95 
96 

8.52960 
8.53183 
8.53405 

223 

222 

221 

8.52985 
8.53208 
8.53430 

223 
222 
221 

I.470I5 
1.46792 
1.46570 

9-99975 
9-99975 
9-99975 

06 

05 
04 

1.5         8023 
.6         8010 
•7         7995 

97 

8.53626 

8.53651 

1.46349 

9-99974 

03 

.8         7980 

98 

8.53846 

220 

8.53872 

1.46128 

9-99974 

02 

•9         7963 

99 

8.54064 

8.54091 

219 

1.45909 

9-99974 

01 

2.0         7946 

100 

8.54282 

8.54308 

1.45692 

9-99974 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

88 c 


(102) 


177' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

00 

8.54282 

216 

8.54308 

1.45692 

9-99974 

100 

01 
02 

03 
04 
05 
06 

07 
08 
09 

8.54498 
8.54714 
8.54928 
8.55142 
8.55354 
8.55565 
8.55775 
8.55985 
8.56193 

216 
214 
214 

212 
211 
210 

210 
208 

8.54525 
8.54741 
8.54956 

8.55169 
8.55382 
8.55593 
8.55804 
8.56013 
8.56222 

216 
215 
213 
213 

211 
211 
209 
209 

•45475 
•45259 
•45044 

•  44831 
.44618 
.44407 
.44196 
.43987 
.43778 

9-99973 
9-99973 
9-99973 
9.99972 
9.99972 
9.99972 
9.99972 
9-99971 
9.99971 

99 
98 
97 
96 
95 
94 

93 
93 

5 
°  1.758 

2.O     211 
.1     22O 
.2     229 

•  3    239 

•  4    250 
.5    260 

10 

8.56400 

8.56429 

•43571 

9-99971 

90 

II 

12 
13 

14 
IS 
16 

17 
18 
19 

8.56606 
8.56811 
8.57016 

8.57219 
8.57421 
8.57623 
8.57823 
8.58023 
8.58222 

205 

205 
203 
2O2 
202 
2OO 
200 

199 
197 

8.56636 
8.56841 
8.57046 

8.57249 
8-57452 
8.57654 
8.57854 
8.58054 
8.58253 

205 

205 
203 
203 
2O2 
200 
2OO 
199 
IQ8 

•43364 
•43159 
.42954 
.42751 
•42548 
.42346 
.42146 
.41946 
•41747 

9-99971 
9-99970 
9.99970 

9-99970 
9.99969 
9.99969 

9.99969 
9.99969 
9.99968 

89 
88 
87 
86 
85 
84 

83 
82 
81 

;a°-r; 

{•T. 
an  of  complement. 

20 

8.58419 

107 

8.58451 

1  08 

•41549 

9.99968 

80 

£«£ 

21 
22 
23 
24 
25 
26 

27 

28 

29 

8.58616 
8.58812 
8.59007 
8.59201 
8.59395 
8.59587 

8-59779 
8.59970 
8.60160 

I96 
195 
194 
194 
192 
192 

191 
190 
1  80 

8.58649 
8.58845 
8.59040 

8.59235 
8.59428 
8.59621 

8.59813 
8.60004 
8  .  60194 

196 

195 
195 
193 
193 
192 
191 
190 

•4I35I 
•4II55 
.40960 

•40765 
.40572 
.40379 
.40187 
.39996 
.39806 

9-99968 
9.99967 
9-99967 
9.99967 
9-99967 
9.99966 

9-99966 
9.99966 
9.99965 

79 
78 
77 
76 
75 
74 
73 

73 

angles  are  small: 
loga°  —  S;  log  tan  a  = 
log  sin  a  -f-  S  =  log  tan 
gles  near  90°  use  sin  an 

30 

8.60349 

188 

8.60384 

1  88 

.39616 

9.99965 

70 

go"  S 

31 
32 
33 
34 
35 
36 

37 
38 
39 

8.60537 
8.60725 
8.60911 
8.61097 
8.61282 
8.61467 
8.61650 
8.61833 
8.62015 

188 
186 
186 

185 
185 
183 

183 
182 
181 

8.60572 
8.60760 
8.60947 
8.61133 
8.61319 
8.61504 
8.61687 
8.61870 
8.62053 

188 
187 
186 
186 
185 
183 
183 
183 
181 

.39428 
.39240 
.39053 
.38867 
.38681 
.38496 
.38313 
.38130 
•37947 

9-99965 
9.99964 
9.99964 

9.99964 
9.99963 
9-99963 
9.99963 
9-99963 
9.99962 

69 
68 
67 
66 
65 
64 

63 
62 
6z 

To  interpolate  wh 
log  sin 
log  a 
For  cos  and  cot  o! 

40 

8.62196 

181 

8.62234 

181 

•37766 

9.99962 

60 

41 
42 
43 
44 
45 
46 

47 
48 
49 

8.62377 
8.62556 
8.62735 
8.62914 
8.63091 
8.63268 

8.63444 
8.63619 
8.63794 

179 
179 
179 
177 
177 
176 

175 
175 

8.62415 
8.62595 
8.62774 
8.62953 
8.63131 
8.63308 

8.63484 
8.63660 
8.63835 

180 
179 
179 
178 
177 
176 

176 
175 

.37585 
.37405 
.37226 

•37047 
.36869 
.36692 
.36516 
.36340 
.36165 

9.99962 
9.99961 
9.99961 
9.99961 
9.99960 
9.99960 
9.99960 
9-99959 
9-99959 

59 
58 
57 
56 
55 
54 
53 

52 

5i 

T 
_1  '-757 

2.0     946 
.1     928 
.2     909 

.3    889 
.4    869 
.5    847 

50 

8.63968 

8.64009 

I-3599I 

9-99959 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

92' 


87' 


(103) 


177  < 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos     ' 

50 

8.63968 

8.64009 

1.35991 

9-99959 

50 

51 

52 

53 
54 
55 
56 

57 
58 
59 

8.64141 
8.64314 
8.64486 

8.64657 
8.64827 
8.64997 
8.65166 
8.65335 
8.65503 

173 
172 
171 
170 
170 
169 
I69 
168 
167 

8.64183 
8.64356 
8.64528 
8.64700 
8.64870 
8.65041 
8.65210 
8.65379 
8.65547 

173 
172 
172 
170 
171 
169 
169 
168 
1  68 

.35817 
.35644 
•35472 
.35300 
.35130 

.34959 
•34790 
.34621 
•34453 

9-99958 
9-99958 
9-99958 
9-99957 
9-99957 
9-99957 
9-99956 
9-99956 
9.99956 

49 
48 
47 
46 
45 
44 
43 
42 
41 

2.5 

.6 
.7 
.8 
•  9 
3-0 

5 

1.758 
260 
27* 
283 

29<5 

308 

321 

60 

8.65670 

167 

8.65715 

167 

•34285 

9-99955 

40 

61 
62 
63 
64 
65 
66 

67 
68 
69 

8.65837 
8.66003 
8.66168 
8.66333 
8.66497 
8.66660 

8.66823 
8.66985 
8.67147 

166 
165 
165 
164 
163 
163 
162 
162 
161 

8.65882 
8.66048 
8.66214 

8.66379 
8.66543 
8.66707 

8.66870 
8.67033 
8.67195 

166 
166 

165 
164 
164 
163 

163 
162 
161 

.34118 
•33952 
•33786 
.33621 
•33457 
.33293 
•33130 
•32967 
.32805 

9-99955 
9-99955 
9-99954 
9-99954 
9-99954 
9-99953 
9-99953 
9-99952 
9-99952 

39 
38 
37 
36 
35 
34 
33 
32 
31 

E 

la-  —2, 

-T. 
m  of  complement. 

70 

8.67308 

ifin 

8.67356 

161 

.32644 

9-99952 

30 

5-  -1-43 

y    8  T) 

71 

72 

73 
74 
75 
76 

77 
78 
79 

8.67468 
8.67628 
8.67788 

8.67946 
8.68104 
8.68262 
8.68419 
8.68575 
8.68731 

160 
160 
158 
158 
158 
157 
156 
156 

8.67517 
8.67677 
8.67837 
8.67996 
8.68154 
8.68312 

8.68470 
8.68626 
8.68783 

160 
160 
159 
158 
158 
158 
156 
157 

•32483 
.32323 
.32163 
.32004 
.31846 
.31688 
.31530 
•31374 
•3I2I7 

9-99951 
9-99951 
9-99951 
9-99950 
9-99950 
9-99950 
9-99949 
9-99949 
9-99948 

29 

28 

27 

26 

25 

24 

23 

22 
21 

angles  are  small: 

log  a  —  o;  log  tan  a  — 
log  sin  a  +  5  =  log  tan 
gles  near  90°  use  sin  an 

80 

8.68886 

8.68938 

.31062 

9-99948 

20 

g 

'  "S 

81 
82 
83 
84 
85 
86 

87 
88 
89 

8.69041 
8.69195 
8.69349 
8.69502 
8.69654 
8.69806 

8.69958 
8.70109 
8.70259 

154 
154 
153 
152 
152 
152 

151 
ISO 

8.69093 
8.69248 
8.69402 

8.69555 
8.69708 
8.69860 
8.70012 
8.70164 
8.70314 

155 
154 
153 
153 
152 
152 
152 
ISO 

.30907 
.30752 
.30598 

.30445 
.30292 
.30140 
.29988 
.29836 
.29686 

9-99948 
9-99947 
9-99947 
9-99947 
9.99946 
9.99946 

9-99945 
9-99945 
9-99945 

19 
18 
17 
16 
15 
14 
13 

12 

II 

To  interpolate  wh 

log  sin  i 
log  a 
For  cos  and  cot  o 

90 

8.70409 

8.70465 

•29535 

9-99944 

10 

9i 
92 
93 
94 
95 
96 
97 
98 
99 

8.70558 
8.70707 
8.70856 
8.71003 
8.71151 
8.71298 

8.71444 
8.71590 
8.71735 

149 
149 
147 
148 
147 
146 
146 
145 

8.70614 
8.70764 
8.70912 
8.71061 
8.71208 
8.71356 
8.71502 
8.71649 
8.71794 

150 
148 
149 
147 
148 
146 

147 
145 
146 

.29386 
.29236 
.29088 

-28939 
.28792 
.28644 
.28498 
.28351 
.28206 

9-99944 
9-99944 
9-99943 
9-99943 
9-99942 
9-99942 
9-99942 
9-99941 
9-99941 

09 
08 
07 
06 
05 
04 

03 

02 
01 

0 

2.5 

.6 
.7 
.8 
•  9 
•      3-0 

T 

1-757 
847 
824 
801 
111 
752 
725 

100 

8.71880 

8.71940 

1.28060 

9-99940 

00 

Cos 

d. 

Cot 

d.c. 

Tan 

Sin 

92' 


87' 


(104) 


3° 


176< 


Sin 

d. 

Tan 

d.c. 

Cot 

Cos 

P.  P. 

145 

143 

00 

8.71880 

144 

8.71940 

144 

1.28060 

9-99940 

100 

i 

14-5 

14-3 

OI 
02 

8.72024 
8.72168 

144 

8.72084 
8.72229 

145 

1.27916 
i.  27771 

9-99940 
9.99940 

99 
98 

2 
3 

29.0 
43-5 
58.0 

28.6 
42.9 
57.2 

03 

8.72312 

144 

8.72373 

1.27627 

9-99939 

97 

5 

72.5 

71-5 

04 

05 

8.72455 
8.72597 

142 

8.72516 
8.72659 

143 

1.27484 
1-27341 

9-99939 
9-99938 

96 
95 

6 

7 
8 

87.0 
101.5 
116.0 

85.8 

IOO.I 

114.4 

06 

8.72739 

142 

8.72801 

1.27199 

9-99938 

94 

9 

130.5 

128.7 

07 

8.72881 

8.72943 

1.27057 

9-99938 

93 

141 

139 

08 

09 

8.73022 
8.73163 

141 
141 

8.73085 
8.73226 

142 

141 

1.26915 
1.26774 

9-99937 
9-99937 

92 
91 

2 

3 

14.1 

28.2 
42.3 

13-9 
27.8 
41-7 

10 

8.73303 

139 

8.73366 

140 

1.26634 

9.99936 

90 

4 
5 

56-4 
7o  5 

55-6 
69-5 

iz 

8.73442 

8.73506 

1.26494 

9-99936 

89 

6 

84-6 

83-4 

12 

8.73582 

140 

8.73646 

140 

1-26354 

9-99936 

88 

7 

98.7 

97-3 

13 

8.73721 

139 
138 

8.73785 

139 
139 

1.26215 

9-99935 

87 

8 
Q 

112.  8 

126.9 

III.  2 
I25.I 

14 

8.73859 

8.73924 

1.26076 

9-99935 

86 

138 

137 

15 

8-73997 

138 

8.74063 

139 

1-25937 

9-99934 

85 

I 

13-8 

13-7 

16 

8.74134 

137 

8.74201 

138 

1.25799 

9-99934 

84 

2 

27.6 

27.4 

138 

137 

3 

41.4 

41.1 

17 

8.74272 

8.74338 

1.25662 

9-99933 

83 

4 

54-8 

18 

8.74408 

130 

8.74475 

137 

1.25525 

9-99933 

82 

5 

69.0 

68.5 

19 

8-74544 

136 
iifi 

8.74612 

137 

Tlfi 

1.25388 

9-99933 

81 

6 

82.8 

82.2 

20 

8.74680 

136 

8.74748 

136 

1.25252 

9-99932 

80 

7 
8 

110.4 

95-9 
109.6 

21 
22 
23 

8.74816 
8-74950 
8.75085 

134 
135 
134 

8.74884 
8.75019 
8.75154 

135 
135 
135 

1.25116 
1.24981 
1.24846 

9-99932 
9-99931 
9-99931 

79 
78 

77 

9 
2 

124.2 
135 
13-5 
27.0 

123-3 
133 

13-3 
26.6 

24 

8.75219 

8.75289 

1.24711 

9-99931 

76 

3 

40-5 

39-9 

25 

8.75353 

134 

8.75423 

134 

1.24577 

9-99930 

75 

4 

54-0 
fi?  <c 

66  * 

26 

8.75486 

133 
133 

8.75556 

133 
134 

1.24444 

9-99930 

74 

i 

8l.o 

79-8 

27 

28 

29 

8.75619 
8.75751 
8.75883 

132 
132 

8.75690 
8.75823 
8.75955 

133 
132 

1.24310 
1.24177 

1.24045 

9.99929 
9.99929 
9.99928 

73 

72 

71 

7 
8 
9 

94.5 
108.0 
121.  5 

131 

93.1 
106.4 
119.7 
129 

30 

8.76015 

131 

8.76087 

132 

1.23913 

9-99928 

70 

i 

I3-I 

26  2 

12.9 
25  8 

31 

8.76146 

8.76219 

1.23781 

9-99927 

69 

3 

39-3 

38.7 

32 

8.76277 

131 

8.76350 

131 

1.23650 

9.99927 

68 

4 

51.6 

33 

8.76408 

131 
130 

8.76481 

131 
131 

I.235I9 

9-99927 

67 

78^6 

64-5 

77-4 

34 

8.76538 

8.76612 

1.23388 

9-99926 

66 

7 

91.7 

90.3 

35 

8.76667 

129 

8.76742 

130 

1.23258 

9.99926 

65 

8 

104.8 

103.2 

36 

8.76797 

130 

8.76871 

129 

1.23129 

9-99925 

64 

9 

II7-9 

116.1 

129 

130 

128 

127 

37 

8.76926 

8.77001 

1.22999 

9-99925 

63 

i 

12.8 

12.7 

38 

8-77054 

8.77130 

129 

1.22870 

9.99924 

62 

2 

25.6 

25.4 

39 

8.77182 

128 

8.77258 

1.22742 

9.99924 

61 

3 

38-4 

g-J 

40 

8.77310 

128 

8.77387 

127 

i  .  22613 

9.99923 

60 

4 

51-2 
64.0 

50.8 
63.5 

41 
42 
43 

8.77438 
8.77565 
8.77691 

127 
126 
126 

8-77514 
8.77642 
8.77769 

128 

127 
127 

1.22486 
1.22358 
i  .  22231 

9.99923 
9.99922 

59 
58 
57 

7 
8 
9 

76.8 
89.6 
102.4 
II5-2 

76.2 
88.9 
101.6 
II4-3 

44 
45 
46 

8.77817 
8.77943 
8.78069 

126 
126 
125 

8.77896 
8.78022 
8.78148 

126 
126 
126 

i  .  22104 
1.21978 
1.21852 

9-99922 
9.99921 
9-99921 

56 
55 
54 

i 

2 

3 

125 

12.5 
25.0 
37-5 

124 

12.4 
24.8 
37-2 

47 

8.78194 

8.78274 

1.21726 

9.99920 

53 

4 

50.0 

49-6 

48 
49 

8.78319 
8.78443 

124 

8.78399 
8.78524 

125 
125 

i.  21601 
1.21476 

9.99920 
9-99919 

52 

51 

5 
6 

7 

62.5 
75-0 
87  5 

62.0 
74-4 
86.8 

50 

8.78568 

8.78649 

1.21351 

9-99919 

50 

8 
9 

IOO.O 
112.  5 

99-2 
in.  6 

Cos 

d. 

Cot 

d.c. 

Tan 

Sin 

P.P. 

'105) 


86< 


176< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.P. 

60 

8.78568 

123 

8.78649 

1.21351 

9.99919 

50 

i 

123 

12.3 

122 

12.2 

Si 

53 

8.78691 
8.78815 

124 

8.78773 
8.78897 

124 

1.21227 
1.21103 

9.99918 
9.99918 

49 
48 

2 
3 

24.6 
36.9 
4Q  2 

24-4 
36.6 
48  8 

53 

8.78938 

123 

122 

8.79020 

123 
123 

I  .  20980 

9.99918 

47 

5 

61.5 

61.0 

54 

8  .  79060 

8.79143 

1.20857 

9.99917 

46 

73-8 

73-2 

55 

8.79183 

123 

8.79266 

123 

1.20734 

9.99917 

45 

8 

08  4 

85-4 
97  6 

56 

8.79305 

8.79389 

123 

I.  20611 

9.99916 

44 

9 

110.7 

109.8 

57 

8.79426 

8-795H 

1.20489 

9.99916 

43 

121 

119 

58 

8.79548 

8.79633 

I  .  20367 

9-99915 

42 

ii-9 

21   8 

59 

8.79669 

8.79754 

I  .  20246 

9-99915 

41 

3 

24.2 
36.3 

35-7 

60 

8.79789 

121 

8.79875 

121 

I.  20125 

9.99914 

40 

4 
5 

48.4 
60  5 

47-6 
59  5 

6i 

8.79910 

8.79996 

I  .  20004 

9.999U 

39 

6 

72.6 

71.4 

62 

8.80030 

8.  80116 

1.19884 

9.999I3 

7 

84-7 

83-3 

J>3 

8.80149 

I2O 

8.80237 

119 

1.19763 

9-99913 

37 

8 
9 

96.8 
108.9 

95-2 
107.1 

64 

8.80269 

8.80356 

1.19644 

9-99912 

36 

118 

117 

65 

8.80388 

119 

8.80476 

I2O 

1.19524 

9.99912 

35 

i 

II.  8 

ii.  7 

66 

8.80506 

118 

8.80595 

119 

I  .  19405 

9.99911 

34 

2 

23.6 

23-4 

119 

H9 

3 

35.4 

35-1 

67 

8.80625 

8.80714 

I  .  19286 

9-999" 

33 

4 

47-2 

46.8 

68 

8.80743 

8.80832 

I  .  19168 

9.99910 

32 

5 

59-0 

58.5 

69 

8.80860 

117 
118 

8.80950 

118 

1.19050 

9.99910 

31 

6 

70.8 

70.2 

70 

8.80978 

117 

8.81068 

118 

1.18932 

9.99909 

30 

7 
8 

94.4 

81.  Q 

93-6 

71 

73 
73 

8.81095 
8.81212 
8.81328 

ii? 
116 
116 

8.81186 
8.81303 
8.81420 

117 
117 
117 

1.18814 

1.18697 
I  .  18580 

9.99909 
9-99908 
9.99908 

29 

28 

27 

9 

i 

2 

106.2 
116 
ii.  6 
23.2 

105-3 
115 

n.  5 
23.0 

74 
75 
76 

8.81444 
8.81560 
8.81675 

116 

us 

116 

8.81537 
8.81653 
8.81769 

116 
116 
116 

I  .  18463 
1.18347 

I  .  18231 

9.99907 
9.99907 
9.99906 

26 

25 

24 

3 
4 
5 
6 

34-8 

46.4 
58.0 
69.6 

34-5 
46.0 
57-5 
69.0 

77 
78 
79 

8.81791 
8.81905 
8.82020 

H4 
US 

8.81885 
8.82000 
8.82115 

US 
US 

1.18115 
1.18000 

1.17885 

9.99906 
0.99905 
9.99905 

23 
22 
21 

7 
8 
9 

81.2 
92.8 
104.4 
114 

80.5 
92.0 
103.5 
113 

80 

8.82134 

114 

8.82230 

114 

I  .  17770 

9.99904 

20 

i 

ii.  4 

22  8 

11.3 

22  6 

81 

8.82248 

8.82344 

I  .  17656 

9.99904 

19 

3 

34.2 

33-9 

82 

8.82362 

114 

8.82458 

114 

I  .  17542 

9.99903 

18 

4 

45-6 

45.2 

83 

8.82475 

in 

8.82572 

114 
114 

I  .  17428 

9.99903 

17 

5 
6 

6M 

56-5 
67.8 

84 

8.82588 

8.82686 

1.17314 

9-99902 

16 

7 

79-8 

79.1 

85 

8.82701 

113 

8.82799 

113 

I  .  17201 

9-99902 

IS 

8 

91.2 

90-4 

86 

8.82814 

H3 

8.82912 

113 

I  .  17088 

9-99901 

14 

9 

102.6 

101.7 

112 

113 

112 

111 

87 

8.82926 

8.83025 

I  .  16975 

9-99901 

13 

i 

II.  2 

II.  I 

88 

8.83038 

8.83137 

I  .  16863 

9.99900 

12 

2 

22.4 

22.2 

89 

8.83149 

8.83249 

1.16751 

9-99900 

II 

3 

33.6 

33-3 

90 

8.83261 

III 

8.83361 

112 

I  .  16639 

9.99899 

10 

4 
5 

44-8 
56.0 

44-4 
55-5 

91 

93 

8.83372 
8.83482 

no 

8.83473 
8.83584 

III 

1.16527 

1.16416 

9.99899 
9.99898 

09 
08 

6 
7 
8 

67.2 
78-4 
89  6 

66.6 
77-7 
88.8 

93 

8.83593 

8.83695 

I  .  16305 

9.99898 

07 

9 

100.8 

99-9 

94 
95 

8.83703 
8.83813 

IIO 

8.83806 
8.83916 

IIO 

1.16194 
I  .  16084 

9.99897 
9.99897 

06 
05 

I 

109 

10.9 

21  8 

108 

10.8 

21  6 

96 

8.83923 

109 

8  .  84026 

IIO 

i.  15974 

9.99896 

04 

3 

32-7 

32-4 

97 

8.84032 

8.84136 

1.15864 

9.99896 

03 

4 

43-6 

43-2 

98 
99 

8.84141 
8.84250 

109 
109 
1  08 

8.84246 
8.84355 

IIO 
109 

i.  15754 
1.15645 

9.99895 
9.99895 

02 
01 

5 
6 
7 

1! 

54  -° 
64.8 
75-6 

100 

8.84358 

8.84464 

i  .  15536 

9.99894 

00 

8 
9 

87.2 
98.1 

86.4 
97-2 

Cos 

d. 

Cot        d.  c. 

Tan 

Sin 

P.  P. 

93' 


(106) 


86 c 


175  < 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

109 

108 

00 

8.84358 

IOQ 

8.84464 

109 

I.I5536 

9.99894 

100 

i 

10.9 

10.8 

OI 

02 
03 

8.84467 
8.84575 
8.84682 

108 
107 
108 

8.84573 
8.84682 
8.84790 

109 
108 
1  08 

i  •  15427 
1.15318 
1.15210 

9.99894 
9-99893 
9.99892 

99 
98 
97 

2 

3 
4 
5 

21.8 

32.7 
43-6 
54-5 

21.6 

32.4 
43-2 
SJ-° 

04 
OS 

8.84790 
8.84897 

107 

8.84898 
8.85006 

108 

I  .  15102 
I.  14994 

9.99892 
9.99891 

96 
95 

7 
8 

65.4 
76.3 
87.2 

75-6 
86.4 

06 

8.85004 

107 

8.85113 

107 

1.14887 

9.99891 

94 

9 

98.1 

97-2 

07 
08 
09 

8.85111 
8.85217 
8.85323 

107 

106 
106 

Tnfi 

8.85220 
8.85327 
8.85434 

107 

107 
107 

Tflfi 

I  .  14780 
1.14673 
I  .  14566 

9.99890 
9.99890 
9.99889 

93 
92 
9i 

i 

2 
3 

107 

10.7 
21.4 
32.1 

106 

10.6 

21.2 

31-8 

10 

8.85429 

106 

8.85540 

106 

I  .  14460 

9.99889 

90 

4 
5 

42.8 
53-5 

42.4 
53-0 

ii 

8.85535 

8.85646 

I  •  14354 

9.99888 

8q 

6 

64.2 

63.6 

12 

8.85640 

105 

8.85752 

106 

I  .  14248 

9-99888 

88 

7 

I4'?- 

74-2 

13 

8.85745 

105 
105 

8.85858 

106 
105 

1.14142 

9.99887 

87 

8 
9 

85.6 
96.3 

84.8 
95-4 

14 

8.85850 

8.85963 

I.I4037 

9.99887 

86 

105 

104 

15 

8.85955 

105 

8.86069 

I.I393I 

9.99886 

85 

i 

10.  s 

10.4 

16 

8.86059 

104 

8.86173 

104 

1.13827 

9.99885 

84 

2 

21.0 

20.8 

104 

105 

3 

31.5 

31.2 

17 

8.86163 

8.86278 

I.I3722 

9.99885 

83 

4 

42.0 

41.6 

18 

8.86267 

104 

8.86383 

105 

1.13617 

9.99884 

82 

s 

52.0 

19 

8.86370 

103 

8.86487 

104 

I.I35I3 

9.99884 

81 

6 

63.0 

62.4 

20 

8.86474 

103 

8.86591 

103 

I.I3409 

9.99883 

80 

8 

73-5 
84.0 

83.2 

21 
22 

8.86577 
8.86680 

103 

8.86694 
8.86798 

104 

I  •  13306 
1.13202 

9.99883 
9.99882 

79 
78 

9 

94-5 
103 

93-6 
102 

23 

8.86782 

102 

8.86901 

103 

I.I3099 

9.99882 

77 

2 

1U.J 
20.6 

2O.4 

24 
25 

8.86885 
8.86987 

103 
102 

8.87004 
8.87106 

103 

102 

1.12996 
1.12894 

9.99881 
9.99880 

76 
75 

3 

4 

30.9 

41.2 

30.6 
40.8 

26 

8.87089 

IO2 
101 

8.87209 

103 
I  O2 

1.12791 

9.99880 

74 

6 

61.8 

61.2 

27 

28 

29 

8.87190 
8.87292 
8.87393 

IO2 
101 

8.87311 
8.87413 
8.87515 

102 
102 

i  .  12689 
1.12587 
i  .  12485 

9.99879 
9.99879 
9.99878 

73 

72 

71 

7 
8 
9 

B:J 

92.7 
101 

71.4 
81.0 
91-8 
100 

30 

8.87494 

IOO 

8.87616 

IOI 

1.12384 

9.99878 

70 

i 

2 

10.  1 
2O  2 

10.  0 

20  o 

31 

8.87594 

8.87717 

i  .  12283 

9.99877 

69 

3 

30-3 

30.0 

32 

8.87695 

8.87819 

i.  12181 

9.99876 

68 

4 

40.4 

40.0 

33 

8.87795 

IOO 
IOO 

8.87919 

IOO 
IOI 

i.  12081 

9.99876 

67 

5 
6 

50.5 
60.6 

50.0 
60.0 

34 

8.87895 

8.88020 

1.11980 

9.99875 

66 

7 

70.7 

70.0 

35 

8.87995 

8.88120 

i.  11880 

9.99875 

65 

8 

80.8 

80.0 

36 

8.88094 

99 

8.88220 

IOO 

i  .  11780 

9-99874 

64 

9 

90.9 

90.0 

IOO 

IOO 

99 

98 

37 

8.88194 

8.88320 

i.  11680 

9.99874 

63 

i 

9.9 

9.8 

18 

8.88293 

99 

8.88420 

1.11580 

9.99873 

62 

2 

IQ.8 

19.6 

39 

8.88392 

99 

oo 

8.88519 

99 

1.11481 

9.99872 

61 

3 

29-7 

29.4 

40 

8.88490 

99 

8.88618 

99 
99 

1.11382 

9.99872 

60 

4 

s 

39-6 
49-5 

39-2 
49-0 

41 

8.88589 

8.88717 

1.11283 

9.99871 

59 

0 

59-4 
60  "* 

58.8 
68  6 

42 

8.88687 

9» 

8.88816 

99 

1.11184 

9.99871 

58 

8 

79-2 

78.4 

43 

8.88785 

9» 

QQ 

8.88915 

99 

QO 

1.11085 

9.99870 

57 

9 

89.1 

88.2 

44 

8.88883 

8.89013 

1.10987 

9.99869 

56 

97 

96 

45 

8.88980 

97 

8.89111 

98 

1.10889 

9.99869 

55 

i 

9-7 

9.6 

46 

8.89077 

97 
97 

8.89209 

98 
98 

i  .  10791 

9-99868 

54 

3 

29.1 

28.8 

47 
48 

8.89174 
8.89271 

97 

8.89307 
8.89404 

97 

1.10693 
i  .  10596 

9-99868 
9.99867 

53 

52 

4 

i 

38.8 
48.5 

rg  2 

38.4 
48.0 

r?  g 

49 

8.89368 

97 
06 

8.89501 

97 

i  .  10499 

9.99867 

5i 

7 

67-9 

67.2 

50 

8.89464 

8.89598 

I  .  10402 

9-99866 

60 

8 
9 

77-6 
87-3 

76.8 

86.4 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

(107) 


86< 


176' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P 

50 

8.89464 

8.89598 

i  .  10402 

9.99866 

50 

Si 

52 

53 
54 
55 
56 

57 
58 
59 

8.89561 
8.89657 
8.89752 
8.89848 
8.89943 
8.90038 

8.90133 
8.90228 
8.90323 

96 
95 
96 
95 
95 
95 
95 
95 

8.89695 
8.89792 
8.89888 

8.89984 
8.90080 
8.90176 
8.90272 
8.90367 
8.90462 

97 
96 
96 

96 
96 
96 
95 
95 

QC 

•10305 
.10208 

.10112 
.10016 
.09920 
.09824 
.09728 
.09633 
.09538 

9.99865 
9.99865 
9.99864 
9.99864 
9.99863 
9.99862 

9.99862 
9.99861 
9.99860 

49 
48 
47 
46 
45 
44 

43 

42 
41 

i 

2 
3 
4 
5 
6 
7 
8 
9 

97 

9-7 
19-4 
29.1 
38.8 
48-5 
58.2 

77:8 
87.3 

95 

96 

9-6 
19.2 
28.8 
38.4 
48.0 

|S 

76.8 

86.4 
94 

60 

8.90417 

QA 

8.90557 

Qtr 

.09443 

9.99860 

40 

i 

9-5 

9-4 

18  8 

61 
62 
63 
64 
65 
66 

67 
68 
69 

8.90511 
8.90605 
8.90699 
8.90792 
8.90885 
8.90978 
8.91071 
8.91164 
8.91257 

94 
94 
93 
93 
93 
93 
93 
93 

8.90652 
8.90746 
8.90841 

8.90935 
8.91029 
8.91122 
8.91216 
8.91309 
8.91402 

94 
95 
94 
94 
93 
94 
93 
93 
93 

.09348 
.09254 
•09159 
.09065 
.08971 
.08878 

.08784 
.08691 
.08598 

9.99859 
9.99859 
9.99858 

9-99857 
9-99857 
9.99856 
9-99856 
9.99855 
9.99854 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

3 
4 
5 
6 
7 
8 
9 

i 

2 

28.5 
38.0 
47-5 
57-0 
66.5 
76.0 
85-5 

93 

9-3 
18.6 

28.2 
37-6 
47-0 

65.8 
75-2 
84.6 

92 

9-2 

18.4 

70 

8.91349 

8.91495 

q-i 

.08505 

9-99854 

30 

3 

4 

27.9 
37  2 

27.6 
36.8 

71 

72 

73 
74 
75 
76 

77 
78 
79 

8.91441 
8.91533 
8.91625 

8.91716 
8.91807 
8.91898 

8.91989 
8.92080 
8.92171 

92 
92 
91 
91 
91 
91 
91 
91 

8.91588 
8.91680 
8.91773 
8.91865 
8.91957 
8.92049 

8.92140 
8.92231 
8.92323 

92 
93 
92 
92 
92 
91 
91 
92 
91 

.08412 
.08320 
.08227 

.08135 
.08043 
.07951 
.07860 
.07769 
.07677 

9-99853 
9.99852 
9.99852 

9.99851 
9.99851 
9.99850 

9.99849 
9.99849 
9.99848 

29 

28 
27 

26 

25 

24 
23 

22 
21 

7 
8 
9 

i 

2 
3 

4 

46.5 
55-8 
65.1 
74-4 
83-7 

91 

9-1 
18.2 

3:J 

46.0 
55-2 
64.4 
73-6 
82.8 

90 

9.0 
18.0 
27.0 
36.0 

80 

8.92261 

8.92414 

90 

.07586 

9.99847 

20 

i 

45-5 
54-6 

54-0 

81 
82 
83 
84 
85 
86 

87 
88 
89 

8.92351 
8.92441 
8.92531 
8.92621 
8.92710 
8.92799 
8.92888 
8.92977 
8.93066 

90 
90 
90 
89 
89 
89 
89 
89 
88 

8.92504 
8-92595 
8.92685 

8.92776 
8.92866 
8.92956 
8.93045 
8.93135 
8.93224 

91 
90 
91 
90 
90 
89 
90 
89 
89 

.07496 
•07405 
.07315 
.07224 
.07134 
.07044 

.06955 
.06865 
.06776 

9.99847 
9.99846 
9.99846 
9.99845 
9.99844 
9.99844 
9.99843 
9.99842 
9.99842 

19 
18 
17 
16 
15 
14 
13 

12 
II 

7 
8 
9 

63.7 
72.8 
81.9 

89 

i  * 

2       I' 
3       2( 

4  3. 

5  4^ 

6  s; 

7  6: 

63.0 
72.0 
8l.o 

*.9 

i.i 

u 

1-5 
J-4 
>  3 

90 

8.93154 

8q 

8.93313 

89 

.06687 

9.99841 

10 

8  71 

.2 

91 
9» 
93 
94 
95 
96 
97 
98 
99 

8,93243 
8.93331 
8.93419 
8.93507 
8.93594 
8.93682 

8.93769 
8.93856 
8.93943 

88 
88 
88 

87 
88 
87 
87 
87 
87 

8.93402 
8-93491 
8.93580 

8.93668 
8.93756 
8.93845 
8.93932 
8.94020 
8.94108 

89 
89 
88 

88 
89 
87 
88 
88 
87 

.06598 
.06509 
.06420 
.06332 
.06244 
.06155 
.06068 
.05980 
.05892 

9.99840 
9.99840 
9.99839 
9.99838 
9.99838 
9.99837 
9.99836 
9.99836 
9.99835 

09 
08 
07 
06 
05 
04 
03 

02 
01 

i 

2 

3 

4 
5 
6 
7 
8 
9 

9  & 

88 

8.8 
17.6 
26.4 
35-2 
44-0 
52.8 
61.6 
70.4 
79.2 

).I 

87 

8.7 
17-4 
26.1 
34-8 
43-5 
52.2 
60.9 
69.6 
78.3 

100 

8.94030 

8.94195 

1.05805 

9.99834 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.  P 

94' 


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8.94030 

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8.94282 
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1.05198 
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9.99833 

9.99832 
9.99831 
9.99830 

9.99830 
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9.99828 

99 
98 
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13 
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8.95226 
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8.95562 
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84 

85 
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8.95145 
8.95231 
8.95316 

8.95401 
8.95486 
8-95570 
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8.95739 
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9.99827 
9.99826 
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9.99825 
9.99824 
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9.99823 
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88 
87 
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8.96143 
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8.96308 
8.96390 
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83 
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8.95991 
8.96075 
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84 
84 
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1.03925 
1.03841 
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9.99820 
9.99820 
9.99819 
9.99818 
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9.99817 
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8.96635 
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8.97231 
8.97313 
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9.99813 
9.99813 
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9.998io 
9.99810 

9.99809 
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42 
43 
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45 
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47 
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8.97443 
8.97523 
8.97603 

8.97682 
8.97762 
8.97841 
8.97920 
8.98000 
8.98078 

80 
80 
79 
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8.97637 
8.97717 
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8.97878 
8.97959 
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8.98119 
8.98199 
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80 
81 
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1.02363 
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1.02202 
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9.998o6 
9.99805 
9-99805 
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9-99803 
9.99803 
9.99802 
9.998oi 
9-99800 

59 
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8.98157 

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8.98358 

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95' 


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p.p. 

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8.98157 

8.98358 

1.01642 

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8.98236 

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8.98471 
8.98549 
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78 
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8.98674 
8.98753 
8.98832 

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79 
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1.01326 
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9-99797 
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1.01090 

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8.99067 

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1.00933 

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8.98937 

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8.99145 

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1.00855 

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1.00777 

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8.99456 

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65 

8.99322 

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8-99534 

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i  .  00466 

9.99788 

35 

7 
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53-9 
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8-99399 

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8.99611 

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1.00389 

9.99788 

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8.99688 

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9.99787 

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8.99765 

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70 

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36.5 

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9.01123 

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9-01353 

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0.98647 

9-99770 

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9.01196 

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9.01427 

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0.98573 

9.99769 

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9.01269 

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9.01501 

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0.98499 

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9-01343 

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P.  P. 

95° 


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d. 

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d.  c. 

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9-01923 

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0.97692 

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9-02139 

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0.97620 

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9.99756 

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0.97258 

9-99755 

92 

9 

65.7 

09 

9.02568 

71 

9.02813 

71 

0.97187 

9-99754 

72 

71 

10 

9-02639 

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9.02885 

72 

0.97115 

9-99753 

90 

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7-1 

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12 

9.02710 
9  .  02780 

1  *• 

70 

9.02957 
9.03028 

72 
71 

0.97043 
0.96972 

9-99753 
9-99752 

89 

88 

2       14.4 

3     21.6 
4      28.8 

14.2 
21.3 
28.4 

13 

9.02851 

71 

9  .  03100 

72 

o  .  96900 

9-99751 

87 

5      36.0 

35-5 

14 

9.02921 

70 

9.03171 

71 

0.96829 

9-99750 

86 

6      43-2 

42.6 

15 

9-02992 

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9-03242 

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0.96758 

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49-7 

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9-03132 

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9-03455 

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0.96545 

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9-04171 
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0.95564 
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9-99735 
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9.04308 

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0.95426 

9-99734 

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9-04376 

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9.04643 

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0.95357 

9-99733 

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9.04444 

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0.95150 

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9.04648 

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0.95082 

9.99729 

61 

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40.2 

40 

9.04715 

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68 

9.04987 

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0.95013 

9.99728 

60 

7 
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46.9 
53.6 

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9.04783 

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9-05055 

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0.94945 

9-99728 

59 

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60.3 

42 

9.04850 

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66 

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0.94808 

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9-05328 

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50 

9-05386 

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9.05666 

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d.           Cot        d.  c.        Tan 

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9-05733 
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9.06068 

9-06135 
9.06202 
9.06268 

68 
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66 
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0.94267 
0.94199 
0.94132 
0.94065 
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0-93932 
0.93865 
0-93798 
0.93732 

9-99719 
9-99718 
9.99717 
9.99716 
9.99716 
9-99715 
9.99714 
9-99713 
9.99712 

49 
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*>4 

e-2 

0.83705 

9-99545 

72 

8 

42.4 

29 

9-15892 

52 
52 

9-16348 

55 
53 

0.83652 

9-99544 

7i 

9 

47-7 

30 

9-!5944 

51 

9.16401 

53 

0.83599 

9-99543 

70 

31 

9-15995 

e*j 

9.16454 

C.7 

0.83546 

9-99542 

69 

52 

32 

9-16047 

D" 

9-16507 

oo 

Cl 

0.83493 

9-99540 

68 

I 

SO 

33 

9.16099 

S2 
52 

9.16560 

5o 

53 

0.83440 

9-99539 

6? 

2 

•  • 

10.4 

34 
35 

9.16151 
9  .  16203 

52 

9.16613 
9.16665 

52 

C"2 

0.83387 
0.83335 

9-99538 
9-99537 

66 

6s 

3 

4 

15-6 

20.8 

oA  o 

36 

9-16254 

51 

52 

9.16718 

5o 

53 

0.83282 

9-99536 

64 

56 

20.  0 

31.2 

37 

9.16306 

9.16771 

C-7 

0.83229 

9-99535 

63 

7 

36.4 

38 

9-16357 

51 

9.16823 

5^ 

0.83177 

9-99534 

62 

8 

41.6 

39 

9.16409 

52 
51 

9.16876 

53 
52 

0.83124 

9-99533 

61 

9 

46.8 

40 

9.16460 

51 

9.16928 

53 

0.83072 

9-99532 

60 

4i 

9.16511 

CO 

9.16981 

CO 

0.83019 

9-99530 

59 

51 

42 

9-16563 

O-* 

51 

9-I7033 

O-* 

52 

0.82967 

9.99529 

58 

I 

5.1 

43 

9.16614 

51 

9.17085 

53 

0.82915 

9-99528 

57 

2 

10.2 

44 

9-16665 

9-I7I38 

0.82862 

9-99527 

56 

3 

15-3 

45 

9.16716 

51 

CT 

9.17190 

52 

CO 

0.82810 

9-99526 

55 

4 

20.4 

46 

9.16767 

51 
51 

9.17242 

o^ 

52 

0.82758 

9-99525 

54 

5 
6 

25.5 

30.6 

47 

9.16818 

CT 

9.17294 

co 

0.82706 

9-99524 

53 

7 

35-7 

48 

9.16869 

OA 

9-I7346 

D-* 

0.82654 

9-99523 

52 

8 

40.8 

49 

9.16919 

SO 
51 

9-17398 

52 
52 

0.82602 

9-99521 

51 

9 

45-9 

50 

9.16970 

9-17450 

0.82550 

9.99520 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

98C 


81' 


171' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

50 

9.16970 

51 

9-17450 

S2 

o  .  82550 

9.99520 

50 

51 

9.17021 

CT 

9-17502 

51 

0.82498 

9.99519 

49 

52 

52 

9.17072 

O1- 

9-17553 

o  82447 

9.99518 

48 

53 

9.17122 

5O 
51 

9-17605 

52 

52 

0.82395 

9.99517 

47 

I 

2 

:>••* 

10.4 

54 

9.I7I73 

Cn 

9.17657 

51 

0.82343 

9.99516 

46 

3 

I5« 

55 

9.17223 

Ou 

9.17708 

co 

0.82292 

9-99515 

45 

4 

20.  8 

56 

9.17273 

5° 
51 

9.17760 

O^ 

51 

0.82240 

9-99514 

44 

5 
6 

26.0 
31.2 

57 

9-17324 

cn 

9.17811 

CO 

0.82189 

9-99512 

43 

7 

36.4 

58 

9-17374 

5O 

9-17863 

5* 

CT 

0.82137 

9-995II 

42 

8 

41.6 

59 

9.17424 

SO 
50 

9-I79I4 

5* 
51 

0.82086 

9.99510 

41 

9 

46.8 

60 

9-17474 

50 

9-I7965 

52 

0.82035 

9-99509 

40 

6i 

9-I7524 

CT 

9.18017 

CT 

0.81983 

9-99508 

39 

fil 

62 

9-17575 

OA 

9.18068 

OA 

0.81932 

9-99507 

38 

63 

9.17624 

49 

50 

9.18119 

51 
51 

o.  81881 

9.99505 

37 

I 

2 

5-1 

10.2 

64 

9-I7674 

9.18170 

0.81830 

9-99504 

36 

3 

15-3 

65 

9.17724 

50 

en 

9.18221 

51 

CT 

0.81779 

9-99503 

35 

4 

20.4 

66 

9-17774 

O(J 

50 

9.18272 

o1 

51 

0.81728 

9-99502 

34 

5 
6 

25-5 
30.6 

67 

9.17824 

9-18323 

0.81677 

9-99501 

33 

7 

35-7 

68 

9.17873 

49 

9-18374 

51 

0.81626 

9-99500 

32 

8 

40.8 

69 

9.17923 

5° 
5° 

9.18425 

51 

50 

0.81575 

9-99499 

31 

9 

45-9 

70 

9-17973 

49 

9-18475 

51 

0.81525 

9-99497 

30 

71 

9.18022 

*ry 

Cft 

9.18526 

CT 

0.81474 

9.99496 

29 

so 

73 

9.18072 

5° 

9.18577 

D* 

cn 

0.81423 

9-99495 

28 

73 

9.18121 

49 

49 

9.18627 

ou 
51 

0.81373 

9-99494 

27 

2 

5-O 

10.  0 

74 

9.18170 

rn 

9.18678 

cn 

0.81322 

9-99493 

26 

3 

iS-o 

75 

9.18220 

5° 

9.18728 

oy 

0.81272 

9.99492 

25 

4 

20.  o 

76 

9.18269 

49 
49 

9.18778 

SO 
51 

0.81222 

9.99490 

24 

5 
6 

25.0 
30.0 

77 

9.18318 

9.18829 

0.81171 

9.99489 

23 

7 

35-0 

78 

9-18367 

49 

9.18879 

SO 

0.81121 

9.99488 

22 

8 

40.0 

79 

9.18416 

49 

AQ 

9-18929 

SO 
5° 

0.81071 

9.99487 

21 

9 

45-0 

80 

9.18465 

*ty 

4Q 

9.18979 

SO 

0.81021 

9.99486 

20 

8z 

9-18514 

ly 

9.19029 

CT 

0.80971 

9.99485 

19 

49 

82 

9-18563 

49 

9.19080 

J* 

o  .  80920 

9-99483 

18 

j 

4O 

83 

9.18612 

49 
49 

9.I9I30 

SO 

49 

0.80870 

9.99482 

17 

2 

•  y 
9-8 

84 
85 

9.18661 
9-18709 

48 

9.19179 
9-19229 

50 

cn 

0.80821 
0.80771 

9.99481 
9-99480 

16 
IS 

3 

4 

14-7 
19.6 

86 

9-18758 

49 
48 

9.19279 

ou 

so 

0.80721 

9-99479 

14 

g 

24.5 
29-4 

87 

9.18806 

9.19329 

0.80671 

9-99477 

13 

7 

34  3 

88 

9-18855 

49 

9-19379 

5° 

AQ 

0.80621 

9.99476 

12 

8 

39-2 

89 

9.18904 

49 
d8 

9.19428 

VJ 
50 

0.80572 

9-99475 

II 

9 

44.1 

90 

9.18952 

40 
48 

9.19478 

SO 

0.80522 

9-99474 

10 

9i 

9.19000 

9.19528 

Af\ 

0.80472 

9-99473 

09 

48 

92 

9.19049 

49 

4.8 

9-19577 

4y 
So 

0.80423 

9-99472 

08 

I 

4-8 

93 

9.19097 

4° 
48 

9.19627 

49 

0.80373 

9.99470 

07 

2 

96 

94 

9.I9I45 

.0 

9.19676 

Af\ 

0.80324 

9.99469 

06 

3 

A 

14.4 

IQ  2 

95 

9.I9I93 

40 

Ao 

9.19725 

4y 

cn 

0.80275 

9.99468 

05 

5 

j.y  .  * 
24.O 

96 

9.19241 

40 

48 

9-19775 

5U 

49 

0.80225 

9-99467 

04 

6 

28.8 

97 

9.19289 

48 

9.19824 

AQ 

0.80176 

9.99466 

03 

7 
g 

33-6 

,0        A 

98 

9-19337 

40 

.0 

9.19873 

Hy 

AQ 

0.80127 

9.99464 

02 

g 

3O.4 

43-2 

99 

9.19385 

40 

48 

9.19922 

4y 
49 

0.80078 

9.99463 

01 

100 

9-19433 

9.19971 

o  .  80029 

9.99462 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

81' 


(116) 


170' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

00 

9  15433 

48 

9.I997I 

49    • 

0.80029 

9.99462 

100 

01 

.9.19481 

9.20020 

0.79980 

9.99461 

99 

O2 

9.19529 

48 

9.20069 

49 

0.79931 

9.99460 

98 

49 

03 

9-19577 

40 
47 

9.20118 

49 

0.79882 

9-99458 

97 

i 

Si 

04 
05 

9.19624 
9.19672 

48 

47 

9.20167 
9.20216 

49 
49 

0.79833 
0.79784 

9-99457 
9-99456 

96 
95 

2 

3 
4 

98 
14.7 
19.6 

06 

9.19719 

48 

9.20265 

48 

0.79735 

9-99455 

94 

5 

24.5 

07 

9.19767 

9  20313 

0.79687 

9-99454 

93 

6 

29.4 

08 

9.19814 

48 

9.20362 

49 

0.79638 

9-99452 

92 

7 
g 

34-3 
39  2 

09 

9.19862 

47 

9.20411 

48 

0.79589 

9-99451 

91 

9 

44.1 

10 

9.19909 

47 

9.20459 

49 

0.79541 

9-99450 

90 

II 

9-19956 

Ao 

9.20508 

48 

0.79492 

9-99449 

89 

12 

9.20004 

40 

9-20556 

40 

0.79444 

9-99447 

88 

48 

13 

9.20051 

47 

9.20605 

48 

0.79395 

9.99446 

87 

i 

2 

4-8 
9.6 

14 

9.20098 

47 

9-20653 

48 

0.79347 

9-99445 

86 

3 

14-4 

15 

9-20145 

9.20701 

0.79299 

9.99444 

85 

4 

19.2 

16 

9  .  20192 

47 

9-20750 

48 

0.79250 

9-99443 

84 

i 

24-0 
28  8 

17 

9-20239 

9.20798 

48 

0.79202 

9.99441 

83 

7 

33  6 

a 

9.20286 

•  47 

9.20846 

48 

0.79154 

9-99440 

82 

8 

38.4 

19 

9-20333 

47 

9.20894 

48 

0.79106 

9-99439 

81 

9 

43-2 

20 

9.20380 

47 

9.20942 

48 

0.79058 

9-99438 

80 

21 

9.20427 

46 

9.20990 

48 

0.79010 

9.99436 

79 

47 

22 

9-20473 

/17 

9.21038 

48 

0.78962 

9-99435 

78 

4»y 

23 

9.20520 

4/ 

47 

9.21086 

48 

0.78914 

9-99434 

77 

2 

•  7 

9.4 

24 

9.20567 

46 

9-2II34 

48 

0.78866 

9-99433 

76 

3 

14  1 

25 

9.20613 

9.21182 

0.78818 

9-99432 

75 

4 

18.8 

26 

9.20660 

46 

9.21229 

48 

0.78771 

9-99430 

74 

5 
6 

23-5 
28.2 

27 

9.20706 

46 

9.21277 

48 

0.78723 

9.99429 

73 

7 

32-9 

28 

9.20752 

9-21325 

4° 

0.78675 

9-99428 

72 

8 

37.6 

29 

9-20799 

46 

9-21372 

48 

0.78628 

9-99427 

7i 

9 

42.3 

30 

9.20845 

46 

9.21420 

47 

0.78580 

9.99425 

70 

31 

9.20891 

47 

9.21467 

48 

0.78533 

9.99424 

69 

46 

32 

9-20938 

46 

9-2I5I5 

47 

0.78485 

9-99423 

68 

i 

4.6 

33 

9.20984 

46 

9.21562 

48 

0.78438 

9-99422 

67 

2 

9   o 

34 

9  .  21030 

46 

9.21610 

47 

0.78390 

9.99420 

66 

3 

4 

13  8 
18.4 

35 

9.21076 

46 

9-21657 

47 

0.78343 

9.99419 

65 

5 

23.0 

36 

9.21122 

46 

9.21704 

47 

0.78296 

9.99418 

64 

6 

27.6 

37 

9.21168 

46 

9-2I75I 

47 

0.78249 

9.99417 

63 

7 
8 

32.2 

38 

9.21214 

46 

9.21798 

48 

0.78202 

9-99415 

62 

41  .4 

39 

9.21260 

46 

9.21846 

47 

0.78154 

9-99414 

61 

40 

9.21306 

45 

9-21893 

47 

0.78107 

9-99413 

60 

41 

9.21351 

46 

9.21940 

47 

0.78060 

9.99412 

59 

45 

42 

9-21397 

46 

9-21987 

47 

0.78013 

9.99410 

58 

i 

4-5 

43 

9-21443 

45 

9.22034 

46 

0.77966 

9.99409 

57 

2 
3 

9-0 
13.5 

44 

9.21488 

46 

9.22080 

47 

0.77920 

9.99408 

56 

4 

18.0 

45 

9.21534 

45 

9.22127 

47 

0.77873 

9.99407 

55 

5 

22.5 

46 

9-21579 

46 

9.22174 

47 

0.77826 

9.99405 

54 

6 

7 

27.0 
31.5 

47 

9.21625 

45 

9.22221 

46 

0.77779 

9-99404 

53 

8 

36.0 

48 

9.21670 

46 

9.22267 

47 

0.77733 

9-99403 

52 

9 

40.5 

49 

9.21716 

45 

9.22314 

47 

0.77686 

9.99402 

Si 

50 

9.21761 

9.22361 

0.77639 

9.99400 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

99° 


80° 


170' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

50 

9.21761 

45 

9.22361 

46 

0.77639 

9.99460 

50 

51 

9.21806 

9.22407 

0-77593 

9-99399 

49 

52 

9.21851 

45 

A6 

9.22454 

47 
46 

0.77546 

9-99398 

48 

47 

53 

9.21897 

4" 
45 

9.22500 

47 

0.77500 

9-99396 

47 

2 

4-7 

9    a 

54 

9.21942 

45 

9.22547 

46 

0-77453 

9-99395 

46 

3 

•  4 
14  I 

55 

9.21987 

AC 

9-22593 

46 

0.77407 

9-99394 

45 

4 

18.8 

56 

9.22032 

4o 

45 

9-22639 

46 

o.7736i 

9-99393 

44 

5 

23-5 

57 

9.  22077 

9.22685 

0.77315 

9-99391 

43 

6 

28.2 

58 

9.22122 

45 

AC 

9.22732 

47 
46 

0.77268 

9-99390 

42 

7 
8 

32-9 
37-6 

59 

9.22167 

4o 

44 

9.22778 

46 

0.77222 

9-99389 

41 

9 

42.3 

60 

9.22211 

45 

9.22824 

46 

0.77176 

9-99388 

40 

6i 

9.22256 

45 

9.22870 

46 

0.77130 

9-99386 

39 

A.K. 

62 

9  .  22301 

9.22916 

46 

0.77084 

9.99385 

38 

63 

9-22346 

45 
44 

9  .  22962 

4" 
46 

0.77038 

9.99384 

37 

I 

2 

4.6 

9-2 

64 

9.22390 

45 

9.23008 

46 

0.76992 

9.99382 

36 

3 

13-8 

65 

9-22435 

AC 

9-23054 

d6 

0.76946 

9.99381 

35 

4 

18.4 

66 

9.22480 

4o 

44 

9.23100 

4*J 
46 

0.76900 

9.99380 

34 

5 
g 

23.0 

27   ft 

67 

9.22524 

44 

9-23146 

45 

0.76854 

9-99379 

33 

7 

27.O 
32-2 

68 

9.22568 

45 

9.23191 

46 

0.76809 

9-99377 

32 

8 

36-8 

69 

9-22613 

44 

9.23237 

46 

0.76763 

9-99376 

31 

9 

41.4 

70 

9.22657 

45 

9-23283 

45 

0.76717 

9-99375 

30 

71 

9.22702 

44 

9-23328 

46 

0.76672 

9-99373 

29 

45 

72 

9.22746 

44 

9  23374 

45 

0.76626 

9-99372 

28 

! 

4-5 

73 

9.22790 

44 

9.234I9 

46 

0.76581 

9-99371 

27 

2 

9.0 

74 

9-22834 

44 

9-23465 

45 

0.76535 

9.99369 

26 

3 

13  5 

TQ      -. 

75 

9.22878 

44 

9.23510 

46 

0.76490 

9.99368 

25 

4 

lo.  O 
oo    c 

76 

9.22922 

45 

9-23556 

45 

0.76444 

9-99367 

24 

6 

6Z,  .  $ 

27.0 

77 

9-22967 

44 

9.23601 

45 

0.76399 

9.99366 

23 

7 

31.5 

78 

9-23011 

A*l 

9-23646 

46 

0.76354 

9.99364 

22 

8 

36.0 

79 

9.23054 

4o 

44 

9.23692 

45 

0.76308 

9.99363 

21 

9      1^.3 

80 

9-23098 

44 

9-23737 

45 

0.76263 

9.99362 

20 

81 

9-23142 

AA 

9-23782 

45 

0.76218 

9.9936o 

19 

44 

82 

9.23186 

44 

44 

9.23827 

45 

0.76173 

9-99359 

18 

I 

4.4 

83 

9-23230 

44 

9-23872 

45 

0.76128 

9-99358 

17 

2 
3 

8.8 

13   2 

84 

9.23274 

A"t 

9.23917 

45 

0.76083 

9  99356 

16 

4 

17^6 

85 

9.23317 

4o 

44 

9.23962 

45 

0.76038 

9-99355 

15 

5 

22.  0 

86 

9.23361 

43 

9.24007 

45 

0.75993 

9-99354 

14 

6 

26.4 

10  8 

87 

9.23404 

44 

9-24052 

45 

0.75948 

9-99352 

13 

7 
8 

o°  •  " 
35-2 

88 

9.23448 

43 

9.24097 

45 

0.75903 

9-99351 

12 

9 

39-6 

89 

9-23491 

44 

9.24142 

44 

0.75858 

9.99350 

II 

90 

9-23535 

43 

9.24186 

45 

0.75814 

9-99348 

10 

91 

9-23578 

44 

9-24231 

45 

0.75769 

9-99347 

09 

so 

9a 

9.23622 

43 

9.24276 

45 

0.75724 

9.99346 

08 

i 

2 

4-3 
8.6 

93 

9-23665 

43 

9-24321 

44 

0.75679 

9-99344 

07 

3 

12^9 

94 

9-23708 

44 

9.24365 

45 

0.75635 

9-99343 

06 

4 

17.2 

95 

9  23752 

43 

9.24410 

44 

0.75590 

9-99342 

05 

I 

21  .5 

96 

9-23795 

43 

9-24454 

45 

0.75546 

9-99340 

04 

o 

7 

25.8 
30.1 

97 

9.23838 

43 

9.24499 

44 

0-75501 

9-99339 

03 

8 

34-4 

98 

9.23881 

43 

9.24543 

45 

0-75457 

9-99338 

02 

9 

38-7 

99 

9.23924 

43 

9.24588 

44 

0.75412 

9-99336 

OI 

100 

9.23967 

9.24632 

0.75368 

9-99335 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.  P. 

99 


80' 


(118) 


169< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

00 

9.23967 

43 

9.24632 

44 

0.75368 

9-99335 

100 

OI 

9  .  24010 

A1 

9.24676 

AA 

0.75324 

9-99334 

99 

02 

9-24053 

4o 

A1 

9.24720 

44 

0.75280 

9-99332 

98 

03 

9.24096 

4o 

43 

9.24765 

45 
44 

0.75235 

9-99331 

97 

44 

04 

9.24139 

A1? 

9.24809 

A  A 

0.75I9I 

9-99330 

96 

I 

4-4 

05 

9.24181 

4* 
43 

9-24853 

44 
44 

0-75147 

9.99328 

95 

2 

8.8 

06 

9.24224 

43 

9.24897 

44 

0.75103 

9-99327 

94 

3 

13-2 

07 

9.24267 

A1 

9.24941 

0.75059 

9.99326 

93 

4 

17.6 

08 

9-24310 

4o 

9-24985 

44 

0.75015 

9-99324 

92 

5 

22.  0 

09 

9.24352 

42 

43 

9.25029 

44 
44 

0.74971 

9-99323 

91 

6 

26.4 

10 

9-24395 

42 

9.25073 

44 

0.74927 

9.99322 

90 

7 
8 

3O.8 
35-2 

II 

9-24437 

43 

9.25117 

44 

0.74883 

9-99320 

89 

9 

39.6 

12 

9.24480 

A1} 

9-25161 

0.74839 

9-99319 

88 

13 

9.24522 

{\& 

43 

9.25205 

44 
43 

0.74795 

9-99318 

87 

14 

9.2456s 

A? 

9.25248 

0.74752 

9-99316 

86 

15 

9.24607 

l\4 

A? 

9.25292 

44 

0.74708 

9-99315 

85 

43 

16 

9.24649 

4* 

43 

9-25336 

44 
43 

0.74664 

9-99314 

84 

i 

4-3 

17 

9.24692 

42 

9-25379 

AA 

0.74621 

9-99312 

83 

2 

8.6 

18 

9.24734 

42 

9-25423 

44 

A1 

0.74577 

9-993II 

82 

3 

12.9 

19 

9.24776 

42 

9-25466 

4o 
44 

0.74534 

9-99310 

81 

4 

17.2 

20 

9.24818 

42 

9.255io 

43 

0.74490 

9.99308 

80 

5 

21.5 
?c  8 

21 

9.24860 

42 

9-25553 

44 

0.74447 

9-9930? 

79 

7 

25.  o 
30.1 

22 

9.24902 

42 

9-25597 

A1 

0.74403 

9-99305 

78 

g 

1A   A. 

23 

9-24944 

42 

9-25640 

4o 
44 

0.74360 

9.99304 

77 

9 

o4-  4 

38.7 

24 

9.24986 

42 

9-25684 

A1 

0.74316 

9.99303 

76 

25 

9.25028 

42 

9-25727 

4o 
43 

0.74273 

9-99301 

75 

26 

9.25070 

42 

9.25770 

43 

0.74230 

9-99300 

74 

27 

9.25112 

42 

9-25813 

A  A 

0.74187 

9-99299 

73 

42 

28 

9.25I54 

42 

9.25857 

44 

A"2 

0.74143 

9.99297 

72 

I 

4.2 

29 

9.25196 

41 

9.25900 

4o 
43 

0.74100 

9.99296 

71 

2 

8.4 

30 

9.25237 

42 

9-25943 

AT. 

0-74057 

9.99294 

70 

3 

12.6 

31 

9-25279 

42 

9-25986 

*K3 

A1 

0.74014 

9-99293 

69 

4 

16.8 

32 

9-25321 

41 

9.26029 

4o 

A1 

0.73971 

9.99292 

68 

5 

21  -O 

33 

9-25362 

42 

9.26072 

4o 

43 

0.73928 

9-99290 

67 

7 

25.2 
29.4 

34 

9.25404 

41 

9.26115 

A1 

0.73885 

9.99289 

66 

8 

33-6 

35 

9-25445 

42 

9.26158 

4o 

0.73842 

9.99288 

65 

g 

37-8 

36 

9.25487 

41 

9  .  26201 

43 

42 

0.73799 

9.99286 

64 

37 

9.25528 

42 

9-26243 

A1 

0.73757 

9.99285 

63 

38 

9-25570 

41 

9.26286 

4o 

0.73714 

9.99283 

62 

39 

9.25611 

41 

9-26329 

43 
43 

0.73671 

9.99282 

61 

41 

40 

9-25652 

42 

9-26372 

42 

0.73628 

9.99281 

60 

i 

4-1 

41 

9.25694 

41 

9.26414 

0.73586 

9-99279 

59 

2 

8.2 

42 

9-25735 

41 

9.26457 

43 

0-73543 

9.99278 

58 

3 

12.3 

43 

9.25776 

41 

9.26500 

43 

0.73500 

9.99276 

57 

4 

16.4 

44 

9.25817 

4A 
41 

9-26542 

42 
43 

0.73458 

9-99275 

56 

5 

6 

20.5 

24  6 

45 

9-25858 

41 

9.26585 

42 

0.73415 

9-99274 

55 

&i\.\j 
28  7 

46 

9-25899 

41 

9.26627 

43 

0.73373 

9.99272 

54 

8 

zo.  / 
32.8 

47 

9.25940 

41 

9.26670 

0.73330 

9.99271 

53 

9 

36.  Q 

48 

9-25981 

41 

9.26712 

42 

y«2 

0.73288 

9.99269 

52 

49 

9  .  26022 

41 

9-26754 

4~ 

43 

0.73246 

9.99268 

Si 

50 

9.26063 

9.26797 

0.73203 

9.99267 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

100C 


79 ' 


(119) 


10' 


169' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.P. 

50 

9.26063 

41 

9.26797 

42 

0.73203 

9.99267 

50 

51 

9.26104 

41 

9-26839 

42 

0.73161 

9-99265 

49 

52 

9-26145 

41 

9.26881 

0.73119 

9.99264 

48 

53 

9.26186 

41 

9-26923 

43 

0.73077 

9-99262 

47 

43 

54 

9.26227 

40 

9.26966 

0.73034 

9.99261 

46 

I 

4-3 

55 

9.26267 

9.27008 

0.72992 

9.99260 

45 

2 

8.6 

56 

9.26308 

41 

9-27050 

42 

0.72950 

9.99258 

44 

3 

12.9 

57 

9-26349 

9-27092 

0.72908 

9.99257 

43 

4 

17.2 

58 

9.26389 

40 

9.27I34 

42 

0.72866 

9.99255 

42 

5 

21.5 

OF*   & 

59 

9.26430 

4O 

9.27176 

42 

0.72824 

9.99254 

41 

25.8 

60 

9.26470 

41 

9.27218 

42 

0.72782 

9.99252 

40 

8 

34-4 

6i 

9.26511 

9.27260 

0.72740 

9-99251 

39 

9 

38.7 

62 

9-26551 

40 

9.27302 

42 

0.72698 

9.99250 

38 

63 

9.26592 

4^ 
40 

9-27343 

41 
42 

0.72657 

9.99248 

37 

64 

9.26632 

?9-  27385 

0.72615 

9.99247 

36 

65 

9.26672 

4O 

9.27427 

0-72573 

9.99245 

35 

42 

66 

9-26713 

41 

4O 

9-27469 

42 
41 

0.72531 

9.99244 

34 

i 

4-2 

67 

9-26753 

9-27510 

o.  724*90 

9-99243 

33 

2 

8.2 

68 

9-26793 

9.27552 

0.72448 

9.99241 

32 

3 

12.6 

69 

9-26833 

4O 

40 

9-27594 

42 
41 

0.72406 

9.99240 

31 

4 

16.8 

70 

9-26873 

4O 

9-27635 

42 

0.72365 

9.99238 

30 

5 
6 

21  .0 
25.2 

71 

9-26913 

9.27677 

0.72323 

.9.99237 

29 

7 

29.4 

72 

9-26954 

ACt 

9.27718 

0.72282 

9-99236 

28 

8 

33-6 

73 

9-26994 

4U 

40 

9-27760 

41 

0.72240 

9-99234 

27 

9 

37-8 

74 

9.27034 

9.27801 

41 

0.72199 

9-99233 

26 

75 

9.27073 

39 

9.27842 

0.72158 

9.99231 

25 

76 

9.27II3 

40 
40 

9.27884 

42 
41 

0.72116 

9.99230 

24 

41 

77 

9.27153 

9.27925 

0.72075 

9.99228 

23 

•A 

78 

9.27193 

40 

9.27966 

41 

0.72034 

9.99227 

22 

I 

4.1 

79 

9-27233 

40 
40 

9.28008 

42 
41 

0.71992 

9.99225 

21 

2 

8.2 

80 

9-27273 

39 

9-28049 

41 

0.71951 

9.99224 

20 

3 

12.3 

81 

9.27312 

9.28090 

0.71910 

9-99222 

19 

20.5 

82 

9-27352 

40 

9.28131 

41 

0.71869 

9-99221 

18 

6 

24.6 

83 

9.27392 

40 
39 

9.28172 

4i 

0.71828 

9-99220 

17 

7 

28.7 

84 

9-27431 

9.28213 

0.71787 

9.99218 

16 

8 

32.8 

85 

9.27471 

40 

9.28254 

41 

0.71746 

9.99217 

IS 

9 

36.9 

86 

9-27510 

39 
40 

9.28295 

41 
41 

0.71705 

9.992I5 

14 

87 

9.27550 

9.28336 

0.71664 

9.99214 

13 

88 

9-27589 

39 

9-28377 

41 

0.71623 

9.99212 

12 

89 

9.27629 

40 

9.28418 

41 
41 

0.71582 

9.99211 

II 

40 

90 

9.27668 

39 

9-28459 

41 

0.71541 

9.99209 

10 

I 

4-0 

8.^ 

92 

9.27707 
9.27747 

40 

9.28500 
9-28540 

40 

0.71500' 
0.71460 

9.99208 
9.99206 

09 
08 

2 

3 

.0 

12.0 

16  o 

93 

9-27786 

39 

9.28581 

41 

0.71419 

9-99205 

07 

5 

20.  0 

94 

9-27825 

9  .  28622 

0.71378 

9.99203 

06 

6 

24.0 

95 

9.27864 

39 

9.28662 

40 

0.71338 

9-99202 

05 

7 

28.0 

96 

9.27904 

40 
39 

9-28703 

41 
41 

0.71297 

9.99201 

04 

8 

32.0 

97 

9-27943 

9-28744 

0.71256 

9-99199 

03 

9 

36.0 

98 

9-27982 

39 

9.28784 

40 

0.71216 

9.99198 

02 

99 

9.28021 

39 
39 

9.28825 

41 

40 

0.71175 

9.99196 

01 

100 

9.28060 

9.28865 

0.71135 

9.99195 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

100° 


79' 


(120) 


ir 


168< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.P. 

00 

9.28060 

39 

9.28865 

41 

o.7"35 

9.99195 

100 

01 

9-28099 

Of\ 

9.28906 

/in 

0.71094 

9.99193 

99 

02 

9.28138 

oy 
"3O 

9.28946 

4U 
Art 

0.71054 

9.99192 

9» 

03 

9.28177 

oy 
39 

9.28986 

4u 
41 

0.71014 

9.99190 

97 

41 

04 

9.28216 

og 

9.29027 

An 

0.70973 

9.99189 

96 

i 

4-1 

OS 

9.28254 

o° 

•3Q 

9.29067 

4U 
40 

0.70933 

9.99187 

95 

2 

8.2 

06 

9-28293 

oy 
39 

9.29107 

41 

0.70893 

9.99186 

94 

3 

12.3 

07 

9-28332 

OfJ 

9.29148 

0.70852 

9.99184 

93 

4 

16.4 

08 

9-28371 

oy 

•*8 

9.29188 

4O 

0.70812 

9.99183 

92 

5 

20.5 

09 

9.28409 

o» 
3Q 

9.29228 

4O 

4O 

0.70772 

9.99i8i 

9i 

6 

24.6 

10 

9.28448 

oy 

39 

9.29268 

40 

0.70732 

9.99180 

90 

7 
g 

28.7 
32.8 

II 

9.28487 

38 

9-29308 

40 

0.70692 

9.99178 

89 

9 

36.Q 

12 

9.28525 

•7Q 

9.29348 

/in 

0.70652 

9.99177 

88 

13 

9.28564 

oy 
38 

9-29388 

4u 

40 

0.70612 

9-99175 

87 

14 

9.28602 

OQ 

9.29428 

0.70572 

9.99174 

86 

IS 

9.28641 

oy 

-,o 

9.29468 

40 

0.70532 

9.99172 

85 

40 

16 

9.28679 

JO 

39 

9.29508 

40 
40 

0.70492 

9.99171 

84 

i 

4-0 

17 

9.28718 

38 

9.29548 

Af\ 

0.70452 

9.99169 

83 

2 

8.0 

18 

9.28756 

^8 

9.29588 

£\\J 

0.70412 

9.99168 

82 

3 

12.0 

19 

9.28794 

o° 

39 

9.29628 

40 

40 

0.70372 

9.99166 

81 

4 

16.0 

20 

9-28833 

38 

9.29668 

TO 

0.70332 

9.99165 

80 

5 

20.0 

21 

9.28871 

?8 

9.29707 

oy 

ACt 

0.70293 

9.99163 

79 

7 

24.O 
28.0 

22 

9.28909 

O° 

og 

9.29747 

4vJ 

0.70253 

9.99162 

78 

8 

32.O 

23 

9.28947 

O° 

38 

9.29787 

40 

40 

0.70213 

9.99160 

77 

9 

36.0 

24 

9.28985 

7Q 

9.29827 

•7ft 

0.70173 

9-99159 

76 

25 

9.29024 

oy 

•3g 

9.29866 

M 

0.70134 

9.99157 

75 

26 

9.29062 

o° 

38 

9.29906 

40 

7O 

0.70094 

9.99I56 

74 

27 

9.29100 

Og 

9-29945 

oy 

0.70055 

9-99154 

73 

39 

28 

9.29138 

o° 

T« 

9.29985 

40 

0.70015 

9.99153 

72 

i 

3-9 

29 

9.29176 

o° 

38 

9-30024 

39 
40 

0.69976 

9.99I5I 

71 

2 

7-8 

30 

9.29214 

38 

9-30064 

TO 

0.69936 

9.99150 

70 

3 

II.  7 
_-  /? 

3i 
32 

9.29252 
9-29289 

37 

T« 

9-30103 
9-30143 

Oy 

40 

0.69897 
0.69857 

9.99148 
9.99147 

69 
68 

4 

5 
g 

IS-O 
19-5 

33 

9-29327 

o° 

38 

9.30182 

39 
39 

0.69818 

9.99I45 

67 

7 

23.4 
27-3 

34 

9.29365 

•jR 

9.30221 

0.69779 

9-99144 

66 

8 

31-2 

35 

9.29403 

o° 

38 

9.30261 

40 

OQ 

0.69739 

9.99142 

65 

9 

35-1 

36 

9.2944I 

37 

9-30300 

oy 
39 

o  .  69700 

9.99141 

64 

37 

9.29478 

og 

9-30339 

0.69661 

9.99139 

63 

38 

9-29516 

o° 

og 

9.30378 

39 

0.69622 

9.99138 

62 

39 

9-29554 

o° 
37 

9.30418 

40 
-jq 

0.69582 

9.99136 

61 

38 

40 

9.29591 

38 

9-30457 

oy 
39 

0.69543 

9-99135 

60 

i 

3.8 

41 

9.29629 

77 

9.30496 

7Q 

0.69504 

9.99133 

59 

2 

7-6 

42 

9.29666 

O/ 
og 

9.30535 

oy 

"JO 

0.69465 

9.99132 

58 

3 

K  .4 

43 

9.29704 

o° 
37 

9-30574 

oy 
39 

0.69426 

9.99130 

57 

4 
5 

15-2 
19.0 

44 

9.29741 

og 

9-30613 

7Q 

0.69387 

9.99128 

56 

6 

22.8 

45 

9-29779 

O° 
77 

9-30652 

oy 

7O 

0.69348 

9.99127 

55 

7 

26.6 

46 

9.29816 

O/ 

38 

9-30691 

oy 
39 

0.69309 

9.99125 

54 

8 

30.4 

47 

9.29854 

-3<7 

9.30730 

on 

0.69270 

9.99124 

53 

9 

34-2 

48 

9.29891 

O/ 

77 

9-30769 

»3y 

18 

0.69231 

9.99122 

52 

49 

9.29928 

O/ 

38 

9-30807 

o° 
39 

0.69193 

9.99121 

5i 

50 

9.29966 

9-30846 

0.69154 

9.99H9 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

101 ( 


78 c 


(121) 


11' 


168< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

p 

.P. 

50 

9.29966 

37 

9.30846 

39 

0.69154 

9.99119 

50 

Si 

52 

53 

54 
55 
56 

57 
58 
59 

9.30003 
9.30040 
9.30077 

9-30II4 
9-30ISI 
9.30188 
9.30226 
9.30263 
9-30299 

37 
37 
37 
37 
37 
38 

37 
36 
37 

9-30885 
9.30924 
9-30963 
9.31001 
9.31040 
9.31078 

9-3III7 
9.3II56 
9-3II94 

39 
39 
38 

39 
38 
39 

39 
38 
39 

0.69115 
0.69076 
0.69037 
0.68999 
0.68960 
0.68922 
0.68883 
0.68844 
0.68806 

9.99H8 
9.99116 
9-99II5 

9-99II3 
9-99II2 
9.99110 
9.99108 
9.99107 
9.99105 

49 
48 
47 
46 
45 
44 
43 
42 
41 

I 

2 

3 

4 
5 
6 

38 

3.8 
7-6 
II.  4 
15-2 
19.0 
22.8 

60 

9.30336 

37 

9-31233 

38 

0.68767 

9.99104 

40 

7 
8 

30.4 

6z 
62 
63 
64 
65 
66 

67 
68 
69 

9-30373 
9.30410 
9.30447 

9-30484 
9.30521 
9-30557 
9-30594 
9-30631 
9.30667 

37 
37 
37 
37 
36 
37 
37 
36 
37 

9-31271 
9.3i3io 
9.31348 
9.31386 
9.31425 
9-3I463 
9-3I50I 
9-3I540 
9.31578 

39 
38 

38 

39 
38 
38 

39 
38 
38 

0.68729 
0.68690 
0.68652 
0.68614 
0.68575 
0.68537 

0.68499 
0.68463 
0.68422 

9.99102 
9-99IOI 
9.99099 

9.99098 
9.99096 
9.99094 

9.99093 
9.99091 
9.99090 

39 
38 
37 
36 
35 
34 
33 
32 
31 

9 

I 

2 

3 

4 

34-2 

37 

3-7 
7-4 
ii.  i 
14.8 

70 

9-30704 

37 

9.31616 

38 

0.68384 

9.99088 

30 

5 
6 

18.5 

22  2 

71 

72 

73 

74 
75 
76 

77 
78 
79 

9.30741 
9.30777 
9-30814 
9-30850 
9.30887 
9-30923 
9-30960 
9.30996 
9-31032 

36 
37 
36 

37 
36 
37 
36 
36 
36 

9.31654 
9.31692 
9-3I730 
9.31768 
9.31806 
9-3I844 
9.31882 
9-31920 
9.31958 

38 
38 
38 
38 
38 
38 
38 
38 

og 

0.68346 
0.68308 
0.68270 
0.68232 
0.68194 
0.68156 
o.  68118 
0.68080 
0.68042 

9.99087 
9.99085 
9.99083 
9-99082 
9.99080 
9.99079 
9-99077 
9.99076 
9.99074 

29 

28 

27 

26 

25 

24 

23 
22 
21 

7 
8 
9 

I 

2 

25-9 
29.6 
33-3 

36 

3.6 

7-2 

80 

9.31068 

37 

9.31996 

38 

0.68004 

9.99072 

20 

3 

10.8 

8z 

83 

83 
84 

85 
86 

87 
88 
89 

9-3II05 
9.3II4I 
9-3II77 
9.31213 
9-31250 
9.31286 
9.31322 
9.31358 
9-31394 

36 
36 
36 

37 
36 
36 
36 
36 
36 

9-32034 
9.32072 
9.32110 

9-32147 
9-32185 
9.32223 
9.32260 
9.32298 
9-32336 

38 
38 

37 
38 
38 
37 
38 
38 

0.67966 
0.67928 
0.67890 

0.67853 
0.67815 
0.67777 
0.67740 
0.67702 
0.67664 

9.99071 
9-99069 
9.99068 
9.99066 
9.99064 
9-99063 
9.99o6i 
9.99060 
9.99058 

19 
18 
17 
16 
15 
14 
13 

12 
XX 

5 
6 
7 
8 
9 

18.0 

21.6 

25.2 
28.8 
32.4 

35 

90 

9.3I430 

36 

9-32373 

38 

0.67627 

9.99056 

10 

I 

3-5 

91 
92 
93 
94 
95 
96 
97 
98 
99 

9.31466 
9.3I502 
9.31538 

9.31573 
9-31609 
9.3I645 
9.31681 
9.3I7I7 
9-31752 

36 
36 
35 
36 
36 
36 
36 
35 
36 

9-324II 
9-32448 
9.32486 

9.32523 
9-32561 
9.32598 
9.32636 
9-32673 
9.32710 

37 
38 

37 
38 
37 
38 
37 
37 
37 

0.67589 
0.67552 
0.67514 
0.67477 
0.67439 
0.67402 

0.67364 
0.67327 
0.67290 

9.99055 
9.99053 
9-99052 
9.99050 
9.99048 
9-99047 

9.99045 
9.99044 
9.99042 

09 
08 
07 
06 
05 
04 

03 
02 
OX 

3 

4 
5 
6 
7 
8 
9 

7.0 
10.5 
14.0 
17-5 

21.0 
24-5 
28.0 
31-5 

100 

9.31788 

9.32747 

0.67253 

9.99040 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

I 

>.  P. 

ior 


178° 


(122) 


167* 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.P. 

00 

9-31788 

36 

9-32747 

38 

0.67253 

9.99040 

100 

01 

9-31824 

-3C 

9.32785 

o° 
77 

0.67215 

9.99039 

99 

02 

9.3I8S9 

OJ 
•jg 

9.32822 

J/ 

0*7 

0.67178 

9.99037 

98 

03 

9-31895 

Ou 

35 

9-32859 

J/ 

37 

0.67141 

9.99036 

97 

38 

04 

9.31930 

16 

9.32896 

77 

0.67104 

9-99034 

96 

I 

3-8 

05 

9.31966 

Ow 

7tr 

9-32933 

O/ 

og 

0.67067 

9.99032 

95 

2 

7-6 

06 

9.32001 

oo 

36 

9-3297I 

o° 

37 

0.67029 

9.99031 

94 

3 

II.  4 

07 

9-32037 

9.33008 

0.66992 

9.99029 

93 

4 

15.2 

08 

9.32072 

35 
^6 

9-33045 

37 

77 

0.66955 

9.99028 

92 

5 

19.0 

09 

9.32108 

Jw 

35 

9.33082 

O/ 

"V7 

0.66918 

9.99026 

91 

6 

22.8 

10 

9  32143 

35 

9-33II9 

O/ 

37 

0.66881 

9-99024 

90 

7 
3 

26.6 

7O  A 

II 

9.32178 

36 

9  33156 

37 

0.66844 

9.99023 

89 

9 

Ju«*l 

34-2 

12 

9.32214 

-2C 

9-33193 

0*7 

0.66807 

9.99021 

88 

13 

9-32249 

O%> 

35 

9-33230 

O/ 

36 

0.66770 

9.99019 

87 

14 

9.32284 

1C 

9-33266 

0.66734 

9.99018 

86 

IS 

9-32319 

65 
•*6 

9.33303 

37 

0.66697 

9.99016 

85 

37 

16 

9-32355 

JO 
35 

9-33340 

37 
37 

0.66660 

9.99014 

84 

I 

3-7 

17 

9.32390 

9-33377 

0.66623 

9.99013 

83 

2 

7-4 

18 

9-32425 

35 

7C 

9-33414 

37 

16 

0.66586 

9-990II 

82 

3 

II.  I 

19 

9.32460 

Jj 

35 

9-33450 

JO 

37 

0.66550 

9.99010 

81 

4 

14.8 

20 

9-32495 

35 

9.33487 

37 

0.66513 

9.99008 

80 

5 

18.5 

21 
22 

9.32530 
9-32565 

35 

'JC 

9-33524 
9-3356o 

36 

77 

0.66476 
0.66440 

9.99006 
9.99005 

79 
78 

7 
8 

22.2 

25.9 
29.6 

23 

9.32600 

oa 

35 

9-33597 

Ol 

37 

0.66403 

9-99003 

77 

9 

33.3 

24 

9-32635 

9  33634 

ifi 

0.66366 

9.99001 

76 

25 

9-32670 

35 

•JC 

9-33670 

O" 
0*7 

0.66330 

9.99000 

75 

26 

9-32705 

OJ 

35 

9.33707 

J/ 
36 

0.66293 

9.98998 

74 

27 

9.32740 

9-33743 

0.66257 

9.98996 

73 

36 

28 

9.32775 

35 

•JA 

9.3378o 

37 
76 

o  .  66220 

9.98995 

72 

i 

3-6 

29 

9.32809 

J4 

35 

9.33816 

ou 

77 

0.66184 

9.98993 

71 

2 

7-2 

30 

9-32844 

35 

9.33853 

O/ 

36 

0.66147 

9.98991 

70 

3 

10.8 

31 

9-32879 

35 

9-33889 

76 

0.66111 

9.98990 

69 

4 

14.4 
18  o 

32 

9-329I4 

1A 

9-33925 

O'J 

77 

0.66075 

9-98988 

68 

5 

g 

21  6 

33 

9.32948 

J4 

35 

9.33962 

O/ 
36 

0.66038 

9.98987 

67 

7 

25.2 

34 

9-32983 

•21- 

9.33998 

76 

0.66002 

9.98985 

66 

8 

28.8 

35 

9-330x8 

00 

7/1 

9.34034 

Ou 
77 

0.65966 

9-98983 

65 

9 

32.4 

36 

9.33052 

OH- 

35 

9-3407I 

O/ 

36 

0.65929 

9.98982 

64 

37 

9-33087 

9-34107 

•jfi 

0.65893 

9.98980 

63 

38 

9-33I2I 

34 

•jC 

9-34143 

30 

^6 

0.65857 

9.98978 

62 

39 

9.33156 

OJ 

34 

9.34179 

JO 

36 

0.65821 

9.98977 

61 

35 

40 

9.33190 

35 

9-34215 

"V7 

0.65785 

9.98975 

60 

I 

3-5 

41 

9-33225 

7/1 

9.34252 

o/ 
•76 

0.65748 

9.98973 

59 

2 

7-0 

42 

9.33259 

«54 
35 

9.34288 

3O 

05 

0.65712 

9.98972 

58 

3 

10.5 

43 

9.33294 

34 

9.34324 

o^ 
36 

0.65676 

9.98970 

57 

4 
5 

14.0 
17.5 

44 

9-33328 

Oyf 

9.34360 

7fi 

0.65640 

9.98968 

56 

6 

21.0 

45 

9-33362 

o4 

35 

9.34396 

JO 
06 

0.65604 

9.98967 

55 

7 

24.5 

46 

9-33397 

34 

9-34432 

ou 
36 

0.65568 

9-98965 

54 

8 

28.O 

47 

9-33431 

1A 

9.34468 

7fi 

0.65532 

9.98963 

53 

9 

31-5 

48 

9.33465 

o4 

34 

9.34504 

JO 

?6 

0.65496 

9.98962 

52 

49 

9-33499 

35 

9-34540 

O1-1 

36 

o  .  65460 

9.98960 

51 

60 

9-33534 

9.34576 

0.65424 

9.98958 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

102' 


77° 


(123) 


167' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.P. 

50 

5i 

52 

53 

54 
55 
56 

57 
58 
59 
60 
61 
62 
63 
64 
65 
66 

67 
68 
69 
70 
71 

72 
73 
74 
75 
76 

77 
78 
79 
80 
81 
82 
83 
84 
85 
86 

87 
88 
89 
90 
91 

92 

93 
94 
95 
96 
97 
98 
99 
100 

9-33534 

34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
34 
33 
34 
34 
34 
33 
34 
34 
33 
34 
33 
34 
33 
34 
33 
34 
33 
33 
34 
33 
33 
33 
34 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 

9-34576 

35 
36 
36 
36 
36 
35 
36 
36 
35 
36 
35 
36 
36 
35 
36 
35 
35 
36 
35 
36 

35 
35 
36 
35 
35 
35 
35 
36 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
35 
34 
35 
35 
35 
34 
35 
35 
35 
34 
35 
34 

0.65424 

9.98958 

50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 

28 

27 

26 

25 
24 

23 
22 
21 

20 

19 
18 
17 
16 
IS 
14 
13 

12 

ii 
10 

09 
08 
07 
06 
05 
04 

03 

oa 

01 

00 

2 
3 
4 
S 
6 
7 
8 
9 

i 

2 

3 
4 
5 
6 
7 
8 
9 

I 

2 
3 
4 
5 
6 
7 
8 
9 

i 

2 

3 
4 
5 
6 
7 
8 
9 

36 

3-6 

7-2 

10.8 

14-4 
18.0 

21.6 

25.2 
28.8 
32.4 

35 

3-5 

7-0 
10.5 
14.0 
17-5 

21.0 

24.5 
28.0 
31.5 

34 

3-4 
6.8 

10.2 

13-6 
17.0 
20.4 
23.8 
27.2 
30.6 

33 

3-3 
6.6 
9-9 
13-2 
16.5 
19-8 
23.1 
26.4 
29.7 

9-33568 
9.33602 
9-33636 
9.33670 
9.33704 
9-33738 
9-33772 
9.338o6 
9-33840 

9.346II 
9-34647 
9.34683 

9.34719 
9-34755 
9-3479° 
9.34826 
9.34862 
9.34897 

0.65389 
0.65353 
0.65317 
0.65281 
0.65245 
0.65210 

0.65174 
0.65138 
0.65103 

9.98956 
9-98955 
9-98953 
9.98951 
9.98950 
9.98948 

9.98946 
9.98945 
9.98943 

9-33874 

9-34933 

0.65067 

9.98941 

9.33908 
9-33942 
9-33976 
9-34010 
9-34043 
9-34077 
9-34IH 
9.34145 
9-34I78 

9.34968 
9-35004 
9-35040 
9.35075 
9-35III 
9-35I46 
9.35i8i 
9.35217 
9.35252 

0.65032 
0.64996 
0.64960 

0.64925 
0.64889 
0.64854 
0.64819 
0.64783 
0.64748 

9.98940 
9.98938 
9.98936 
9.98934 
9.98933 
•9-9893I 
9.98929 
9.98928 
9.98926 

9-34212 

9-35288 

0.64712 

9.98924 

9.34246 
9.34279 
9-34313 
9.34346 
9-34380 
9.344I3 

9-34447 
9.34480 
9-34514 

9-35323 
9-35358 
9-35394 
9-35429 
9.35464 
9-35499 
9-35534 
9-35570 
9.35605 

0.64677 
o  .  64642 
0.64606 

0.64571 
0.64536 
o  .  64501 
0.64466 
0.64430 
0.64395 

9.98923 
9.98921 
9.989I9 
9.98917 
9.98916 
9.98914 

9.98912 
9.98911 
9.98909 

9-34547 

9.35640 

0.64360 

9.98907 

9.34580 
9.34614 
9-34647 
9.34680 
9.34713 
9-34747 
9.34780 
9.34813 
9.34846 

9-35675 
9-35710 
9-35745 
9.3578o 
9.35815 
9.35850 
9-35885 
9-35920 
9-35955 

0.64325 
o  .  64290 
0.64255 
0.64220 
0.64185 
0.64150 

0.64115 
0.64080 
0.64045 

9.98905 
9.98904 
9.98902 
9-98900 
9.98898 
9.98897 
9-98895 
9.98893 
9.98892 

9-34879 

9-35989 

0.64011 

9.98890 

9-34912 
9-34945 
9-34978 
9-350II 
9.35044 
9-35077 
9  -351  10 
9-35143 
9-35I76 

9.36024 
9-36059 
9-36094 
9.36128 
9-36163 
9.36198 
9-36233 
9-36267 
9-36302 

0.63976 

0.63941 
0.63906 
0.63872 
0.63837 
0.63802 

0.63767 
0.63733 
0.63698 

9.98888 
9.98886 
9-98885 
9-98883 
9.98881 
9.98879 
9.98878 
9.98876 
9.98874 

9-35209 

9.36336 

o  .  63664 

9.98872 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

102 


77c 


(124) 


13' 


166' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

I 

'.P. 

00 

9.35209 

33 

9.36336 

35 

0.63664 

9.98872 

100 

ox 
02 
03 
04 

OS 
06 

07 
08 
09 

9.35242 
9-35274 
9.35307 
9-35340 
9-35373 
9-35405 
9-35438 
9-35471 
9-35503 

32 
33 
33 
33 

33 
33 
32 
33 

9-3637I 
9-36406 
9.36440 
9.36475 
9-36509 
9.36543 
9.36578 
9.36612 
9-36647 

35 
34 
35 

35 

34 
35 
34 

0.63629 
0.63594 
0.63560 

0.63525 
0.63491 
0.63457 
0.63422 
0.63388 
0.63353 

9.98871 
9-98869 
9-98867 
9-98865 
9.98864 
9.98862 
9.98860 
9.98816 
9-98857 

99 
98 
97 
96 
95 
94 
93 
92 

I 

2 
3 
4 
5 
6 

3S 

35 

7-0 
10.5 
14.0 
17-5 

21.0 

10 

9.35536 

32 

9.36681 

34 

0.63319 

9-98855 

90 

7 
8 

24-5 
28.0 

ii 

12 
13 
14 

15 
16 

17 
18 
19 

9-35568 
9.356oi 
9-35633 
9-35666 
9.35698 
9-35731 
9.35763 
9.35796 
9.35828 

33 

33 

32 

32 

33 
32 
32 

9-36715 
9-36750 
9-36784 
9.36818 
9-36852 
9-36887 
9-36921 
9.36955 
9-36989 

35 

34 
34 
35 
34 

34 

0.63285 
0.63250 
0.63216 
o  .  63182 
0.63148 
0.63113 

0.63079 
0.63045 
0.63011 

9.98853 
9.98851 
9-98850 
9-98848 
9-98846 
9.98844 
9.98842 
9.98841 
9-98839 

89 
88 
87 
86 
85 
84 

83 

82 
81 

9 

I 

2 
3 
4 

31-5 

34 

3-4 
6.8 

IO.2 
13-6 

20 

9.3586o 

33 

9.37023 

34 

0.62977 

9.98837 

80 

5 

17.0 

21 
22 
23 
24 
25 
26 

27 

28 

29 

9.35893 
9.35925 
9-35957 

9.35989 
9.36022 
9-36054 
9.36086 
9.36118 
9-36I50 

32 
33 
32 
32 
32 
32 
32 

9.37057 
9.37091 
9.37125 

9.37159 
9.37193 
9-37227 
9.37261 
9.37295 
9.37329 

34 
34 
34 
34 
34 
34 
34 

0.62943 
0.62909 
0.62875 
0.62841 
0.62807 
0.62773 
0.62739 
0.62705 
0.62671 

9-98835 
9.98834 
9-98832 

9-98830 
9.98828 
9.98826 

9.98825 
9.98823 
9.98821 

79 
78 
77 
76 
75 
74 
73 

72 

71 

7 
8 
9 

I 

2 

23.8 
27.2 
30.6 

33 

3-3 
6.6 

30 

9.36182 

32 

9.37363 

0.62637 

9.98819 

70 

3 

9-9 

31 

32 

33 
34 
35 
36 

37 
38 
39 

9-36214 
9-36246 
9-36278 
9-36310 
9.36342 
9-36374 
9-36406 
9.36438 
9.36470 

32 
32 
32 
32 

32 

32 
32 

9-37397 
9-37431 
9-37464 
9-37498 
9-37532 
9-37566 

9-37599 
9.37633 
9.37667 

34 
33 
34 
34 

33 

34 

o  .  62603 
0.62569 
0.62536 
o  .  62502 
o  .  62468 

0.62434 

o  .  62401 
0.62367 
0.62333 

9.98817 
9.98816 
9.98814 
9.98812 
9.98810 
9.98808 
9.98807 
9-98805 
9-98803 

69 
68 
67 
66 
65 
64 

63 
62 
61 

4 
5 
6 
7 
8 
9 

13-2 
16.5 
19.8 
23.1 
26.4 
29-7 

32 

40 

9.36502 

31 

9-37700 

34 

o  .  62300 

9.08801 

60 

I 

3-2 

41 
42 
43 
44 
45 
46 

47 
48 
49 

9.36533 
9-36565 
9-36597 
9-36629 
9-36660 
9-36692 

9.36755 
9-36787 

32 
31 

32 
32 

9-37734 
9-37768 
9.37801 

9.37835 
9.37868 
9-37902 
9-37935 
9.37969 
9.38002 

34 
33 
34 
33 
34 
33 

33 
33 

0.62266 
0.62232 
0.62199 
0.62165 
0.62132 
o  .  62098 
0.62065 
0.62031 
0.61998 

9.98799 
9.98798 
9-98796 

9.98794 
9.98792 
9.98790 
9.98789 
9.98787 
9-98785 

59 
58 
57 
56 
55 
54 
53 
52 
5i 

2 
3 
4 
5 
6 
7 
8 
9 

6.4 
9-6 

12.8 

16.0 
19.2 
22.4 
25.6 
28.8 

60 

9-36819 

9-38035 

0.61965 

9.98783 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P 

P. 

103* 


76C 


(125) 


166' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos    , 

P.  P. 

50 
Si 

53 

53 
54 
55 
56 

57 
58 
59 
60 
61 
fa 
63 
64 
65 
66 

67 
68 
69 
70 
71 

72 

73 
74 
75 
76 

77 
78 
79 
80 
81 
82 
83 
84 
85 
86 

87 
88 
89 
90 
91 

93 

93 
94 
95 
96 
97 
98 
99 
100 

9-36819 

31 

32 

31 
32 

31 
32 
31 
31 
32 
31 
31 
32 
3i 
31 
31 
32 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
31 
30 
31 
31 
31 
30 
31 
31 
30 

31 
31 
30 
31 
30 
31 
30 

31 

30 
31 

9-38035 

34 
33 
33 
34 
33 
33 
34 
33 
33 
33 
33 
33 
34 
33 
33 
33 
33 
33 
33 
33 
33 
33 

32 

33 
33 
33 
33 
33 
32 
33 
33 
32 
33 
33 
32 
33 
33 
32 
33 
32 

33 
32 
33 
32 
32 
33 
32 
32 
33 
32 

0.61965 

9.98783 

50 

49 
48 
47 
46 
45 
44 
43 
43 
41 
40 

39 
38 
37 
36 
35 
34 
33 
33 
31 
30 

39 

28 
37 

26 

35 

34 
33 

22 
21 
20 

19 
18 
17 
16 
IS 
14 
13 

13 
XI 

10 

09 
08 

07 
06 
05 
04 
03 

02 
01 

00 

i 

2 

3 

4 
5 
6 
7 
8 
9 

I 

2 
3 

4 
5 
6 
7 
8 
9 

I 

2 
3 

4 
5 
6 
7 
8 
9 

I 

2 

3 

4 
5 
6 
7 
8 
9 

33 

3-3 
6.6 
9-9 
13-2 
16.5 
19.8 
23.1 
26.4 
29-7 

32 

3-2 

6-4 
9-6 

12.8 

16.0 
19.2 
22.4 
25.6 
28.8 

31 

3-1 
6.2 

9-3 
12.4 
I5-S 
18.6 
21.7 
24.8 
27-9 

30 

3-0 
6.0 
9-0 

12.0 

15-0 
18.0 

21.0 

24.0 
27.0 

9-36850 
9.36882 
9-369I3 
9.36945 
9.36976 
9.37008 

9-37039 
9.37070 
9-37102 

9.38069 
9.38102 
9.38I35 
9.38169 
9.38202 
9-38235 
9.38269 
9-38302 
9.38335 

0.61931 
0.61898 
0.61865 
0.61831 
0.61798 
0.61765 
0.61731 
0.61698 
o  .  61665 

9.98781 
9.98780 
9.98778 
9.98776 
9.98774 
9.98772 
9.98770 
9.98769 
9.98767 

9-37133 

9.38368 

0.61632 

9.98765 

9.37I64 
9.37196 
9-37227 

9.37258 
9-37289 
9-37321 
9-37352 
9.37383 
9-37414 

9.38401 
9-38434 
9-38468 

9-38501 
9.38534 
9.38567 
9.38600 
9-38633 
9.38666 

0.61599 
0.61566 
0.61532 

0.61499 
0.61466 
0.61433 
0.61400 
0.61367 
0.61334 

9-98763 
9.98761 
9-98759 
9.98758 
9.98756 
9.98754 
9.98752 
9.98750 
9.98748 

9-37445 

9-38699 

0.61301 

9.98746 

9.37476 
9-37507 
9-37538 

9.37569 
9.376oo 
9.37631 
9.37662 
9-37693 
9.37724 

9.38732 
9-38765 
9.38797* 
9-38830 
9-38863 
9-38896 

9-38929 
9-38962 
9.38994 

0.61268 
0.61235 
0.61203 
0.61170 
0.61137 
0.61104 
0.61071 
0.61038 
0.61006 

9.98745 
9.98743 
9.98741 

9.98739 
9-98737 
9.98735 
9.98734 
9.98732 
9.98730 

9-37755 

9.39027 

0.60973 

9.98728 

9-37786 
9-37817 
9.37847 
9.37878 
9-37909 
9-37940 
9-37970 
9.38001 
9-38032 

9.39o6o 
9.39092 
9.39125 
9.39158 
9.39190 
9-39223 
9.39256 
9.39288 
9-39321 

0.60940 
0.60908 
0.60875 
0.60842 
0.60810 
0.60777 

0.60744 
0.60712 
0.60679 

9.98726 
9.98724 
9.98722 
9-98720 
9.98719 
9.98717 

9.98715 
9.98713 
9.98711 

9-38062 

9-39353 

0.60647 

9.98709 

9-38093 
9.38124 
9.38154 
9-38185 
9-38215 
9-38246 
9-38276 
9-38307 
9-38337 

9-39386 
9-39418 
9-39451 
9.39483 
9-39515 
9-39548 
9.39580 
9-39612 
9.39645 

0.60614 
0.60582 
0.60549 
0.60517 
0.60485 
0.60452 
0.60420 
0.60388 
0.60355 

9.98707 
9.98705 
9.98704 
9.98702 
9.98700 
9.98698 
9-98696 
9.98694 
9.98692 

9.38368 

9.39677 

0.60323 

9.98690 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

103* 


76' 


(126) 


166< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.P. 

00 

9.38368 

3° 

9.39677 

32 

0.60323 

9-98690 

100 

01 

9-38398 

or* 

9.39709 

T* 

0.60291 

9.98689 

99 

02 

9-38428 

ou 

OT 

9-39742 

oo 
12 

0.60258 

9.98687 

98 

03 

9-38459 

o* 
30 

9-39744 

o-*2 
32 

0.60226 

9-98685 

97 

S3 

04 

9.38489 

30 

9.398o6 

32 

0.60194 

9.98683 

96 

i 

3-3 

05 

9.38519 

9.39838 

0.60162 

9.98681 

95 

2 

6.6 

06 

9-38550 

31 
30 

9-39870 

32 

33 

0.60130 

9-98679 

94 

3 

9-9 

07 

9.38580 

9  39903 

•JO 

0.60097 

9.98677 

93 

4 

13-2 

08 

9.38610 

30 

9-39935 

o~ 

0.60065 

9-98675 

92 

5 

16.5 

09 

9.38640 

3° 
3o 

9.39967 

32 
32 

0.60033 

9.98673 

9i 

6 

19.8 

10 

9-38670 

31 

9-39999 

32 

0.60001 

9.98671 

90 

7 
g 

23.1 
26.4 

it 

9-38701 

30 

9-40031 

32 

0.59969 

9.98670 

89 

9 

29-7 

12 

9.38731 

30 

9.40063 

32 

0.59937 

9.98668 

88 

13 

9-3876I 

30 

9.40095 

32 

0.59905 

9.98666 

87 

14 

9.38791 

3° 

9.40127 

32 

0.59873 

9-98664 

86 

15 

9-38821 

-in 

9.40159 

32 

0.59841 

9.98662 

85 

32 

16 

9-3885I 

Ou 

30 

9.40191 

32 

0.59809 

9.98660 

84 

i 

3-2 

17 

9.38881 

Ort 

9.40223 

7-7 

0.59777 

9.98658 

83 

2 

6-4 

18 

9.38911 

•yJ 

•5O 

9  -40255 

o* 
32 

0.59745 

9.98656 

82 

3 

9-6 

19 

9.38941 

Ou 
3O 

9.40287 

32 

0.59713 

9.98654 

81 

4 

12.8 

20 

9-38971 

30 

9.40319 

32 

0.59681 

9-98652 

80 

5 
g 

16.0 

21 

9-39001 

3O 

9.40351 

31 

0.59649 

9.98650 

79 

7 

19-2 

22.4 

22 

9.39031 

30 

9-40382 

32 

0.59618 

9.98648 

78 

8 

25.6 

23 

9-39061 

30 

9.40414 

32 

0.59586 

9.98647 

77 

9 

28.8 

24 

9.39091 

30 

9.40446 

32 

0.59554 

9.98645 

76 

25 

9-39I2I 

20 

9.40478 

32 

0.59522 

9.98643 

75 

26 

9-39I50 

~y 
30 

9-40510 

31 

0.59490 

9.98641 

74 

27 

9-39180 

30 

9.40541 

32 

0.59459 

9.98639 

73 

31 

28 

9-39210 

30 

9.40573 

32 

0.59427 

9.98637 

72 

i 

3-1 

29 

9-39240 

30 

9-40605 

31 

0.59395 

9.98635 

71 

2 

6.2 

30 

9.39270 

29 

9-40636 

32 

0.59364 

9.98633 

70 

3 

9-3 

31 

9.39299 

30 

9.40668 

32 

0-59332 

9.98631 

69 

4 
5 

12.4 
15.5 

32 

9.39329 

30 

9.40700 

31 

0.59300 

9.98629 

68 

g 

18  6 

33 

9-39359 

29 

9.4073I 

32 

0.59269 

9.98627 

67 

7 

21.7 

34 

9.39388 

30 

9-40763 

32 

0.59237 

9.98625 

66 

8 

24.8 

35 

9.39418 

30 

9.40795 

31 

0.59205 

9-98623 

65 

9 

27-9 

36 

9-39448 

29 

9.40826 

32 

0.59174 

9.98621 

64 

37 

9-39477 

30 

9.40858 

31 

0.59142 

9  .  98620 

63 

38 

9-39507 

29 

9.40889 

32 

0.59111 

9.98618 

62 

39 

9-39536 

30 

9.40921 

31 

0.59079 

9.98616 

61 

30 

40 

9-39566 

29 

9.40952 

32 

0.59048 

9-98614 

60 

i 

3-0 

4i 

9-39595 

3° 

9.40984 

31 

0.59016 

9.98612 

59 

2 

6.0 

42 

9.39625 

29 

9-4IOI5 

31 

0.58985 

9.98610 

58 

3 

9-o 

43 

9.39654 

30 

9.41046 

32 

0.58954 

9.98608 

57 

4 
5 

12  .  0 
I5-O 

44 

9.39684 

29 

9.41078 

31 

0.58922 

9.98606 

56 

6 

18.0 

45 

9-39713 

30 

9.41109 

32 

0.58891 

9.98604 

55 

7 

21  .0 

46 

9-39743 

29 

9.41141 

31 

0.58859 

9.98602 

54 

8 

24.0 

47 

9-39772 

29 

9.41172 

31 

0.58828 

9.98600 

53 

9 

27.0 

48 

9.398oi 

30 

9.41203 

32 

0.58797 

9.98598 

52 

49 

9.39831 

29 

9-41235 

31 

0.58765 

9.98596 

Si 

50 

9.3986o 

9.41266 

0.58734 

9.98594 

60 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

104' 


76° 


(127) 


165' 


Sin 

d. 

Tan 

d.c. 

Cot 

Cos  , 

P.P. 

60 

9.39860 

29 

9.41266 

31 

0.58734 

9.98594 

50 

Si 

9-39889 

in 

9.41297 

TT 

0.58703 

9.98592 

49 

52 

9.39919 

o*J 
20 

9-41328 

O* 
-72 

0.58672 

9.98590 

48 

53 

9-39948 

•5P 
29 

9.4i36o 

O^ 

3i 

0.58640 

9.98588 

47 

31 

54 

9-39977 

on 

9.4I39I 

or 

0.58609 

9.98586 

46 

i 

31 

55 

9.40006 

*g 
on 

9.41422 

OA 

0.58578 

9.98584 

45 

2 

6.2 

56 

9.40035 

*9 

30 

9.4I453 

31 

31 

0.58547 

9.98582 

44 

3 

9-3 

57 

9.40065 

9.41484 

0.58516 

9.98580 

43 

4 

12.4 

58 

9.40094 

29 
on 

9.4T5I5 

31 

0.58485 

9.98578 

42 

5 

15.5 

59 

9.40123 

•» 

29 

9.41546 

31 
32 

0.58454 

9.98576 

41 

6 

18.6 

60 

9.40I52 

29 

9.41578 

31 

0.58422 

9.98574 

40 

7 
8 

21.7 
24.8 

61 

9.40181 

20 

9.41609 

OT 

0.58391 

9.98573 

39 

9 

27.9 

62 

9.40210 

~y 
on 

9.41640 

OA 
OT 

0.58360 

9.9857I 

38 

63 

9-40239 

•*y 
29 

9.41671 

OA 

31 

0.58329 

9-98569 

37 

64 

9.40268 

on 

9.41702 

0.58298 

9-98567 

36 

65 

9.40297 

*y 

OQ 

9.4I733 

31 
•7T 

0.58267 

9.98565 

35 

30 

66 

9-40326 

*y 

29 

9-41764 

o* 

3i 

0.58236 

9-98563 

34 

i 

3-0 

67 

9.40355 

20 

9.4I79S 

on 

0.58205 

9.98561 

33 

2 

6.0 

68 

9.40384 

^y 

on 

9-41825 

0*"* 

OT 

0.58175 

9-98559 

32 

3 

9-o 

69 

9.40413 

•*y 
29 

9.41856 

O*- 
31 

0.58144 

9.98557 

31 

4 

12.0 

70 

9.40442 

29 

9-41887 

31 

0.58113 

9.98555 

30 

5 
6 

iS-o 
18.0 

7i 

9.40471 

20 

9.41918 

•3T 

0.58082 

9.98553 

29 

7 

21.  0 

72 

9-40500 

~y 

20 

9.41949 

O-1- 
-2T 

0.58051 

9.98551 

28 

8 

24.0 

73 

9-40529 

*y 

28 

9.41980 

O-1- 
31 

0.58020 

9-98549 

27 

9 

27.0 

74 

9-40557 

20 

9.42011 

3O 

0.57989 

9.98547 

26 

75 

9.40586 

~y 

9.42041 

0.57959 

9.98545 

25 

76 

9.40615 

29 
29 

9.42072 

31 
31 

0.57928 

9-98543 

24 

OA 

77 

9.40644 

28 

9-42103 

31 

0.57897 

9.98S4I 

23 

29 

78 

9.40672 

20 

9-42134 

30 

0.57866 

9-98539 

22 

I 

2-9 

79 

9.40701 

^y 
29 

9.42164 

31 

0.57836 

9-98537 

21 

2 

5.8 

80 

9-40730 

29 

9.42I95 

31 

0.57805 

9-98535 

20 

3 

8.7 

TT    6 

81 

9.40759 

28 

9.42226 

30 

0.57774 

9.98533 

19 

4 
5 

II  .O 

14.5 

82 

9.40787 

29 

9.42256 

31 

0-57744 

9-98531 

18 

6 

17.4 

83 

9.40816 

28 

9.42287 

31 

0.57713 

9-98529 

17 

7 

20.3 

84 

9.40844 

20 

9.42318 

3° 

0.57682 

9-98527 

16 

8 

23.2 

85 

9-40873 

*y 
29 

9.42348 

31 

0.57652 

9-98525 

IS 

9 

26.1 

86 

9-40902 

28 

9.42379 

31 

0.57621 

9-98523 

14 

87 

9.40930 

20 

9.42410 

3° 

0.57590 

9.98521 

13 

88 

9.40959 

~y 

28 

9.42440 

31 

0.57560 

9-98519 

12 

89 

9.40987 

29 

9.42471 

30 

0.57529 

9.985I7 

II 

28 

90 

9.41016 

28 

9.42501 

31 

0-57499 

9.98SI5 

10 

i 

2.8 

^    r 

91 

9.41044 

29 

9.42532 

3O 

0.57468 

9-985I3 

09 

2 

5-O 

8.4 

92 

9.4I073 

28 

9.42562 

31 

0.57438 

9-985H 

08 

II  .2 

93 

9.41101 

29 

9-42593 

30 

0.57407 

9-98509 

07 

5 

14.0 

94 

9.4II30 

28 

9.42623 

3O 

0.57377 

9.98507 

06 

6 

16.8 

95 

9.4H58 

28 

9-42653 

31 

0.57347 

9.98505 

05 

7 

19.6 

96 

9.41186 

29 

9.42684 

30 

0.57316 

9.98502 

04 

8 

22.4 

97 

9-4I2I5 

28 

9.42714 

31 

0.57286 

9.98500 

03 

9 

25.2 

98 

9-41243 

28 

9.42745 

30 

0.57255 

9.98498 

02 

99 

9.41271 

29 

9.42775 

30 

0.57225 

9.98496 

OX 

100 

9.41300 

9  .  42805 

0.57195 

9  .  98494 

00 

Cos 

d 

Cot 

d.  c. 

Tan 

Sin 

P.  P. 

104' 


75 ( 


(128) 


164  < 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P. 

P. 

00 

9.41300 

28 

9.42805 

31 

0.57195 

9.98494 

100 

01 
02 

03 
04 
05 
06 

07 
08 
09 

9-41328 
9.4I356 
9-41384 

9.4I4I3 
9.41441 
9.41469 
9.41497 
9.41525 
9-41553 

28 
28 
29 
28 
28 
28 
28 
28 
29 

9.42836 
9.42866 
9.42896 
9.42926 
9-42957 
9.42987 

9.43017 

9.43047 
9.43077 

30 
30 
30 

31 

30 
30 
30 
30 
31 

0.57164 
0.57134 
0.57104 

0.57074 
0.57043 
0.57013 
0.56983 
0.56953 
0.56923 

49.98492 
9.98490 
9-98488 
9.98486 
9.98484 
9.98482 
9.98480 
9.98478 
9.98476 

99 
98 
97 
96 

95 
94 

93 
92 
91 

I 

2 

3 

4 
5 
6 

31 

3-1 

6.2 

9-3 

12-4 
15-5 
18.6 

10 

9.41582 

28 

9-43108 

3O 

0.56892 

9.98474 

90 

7 
8 

21.7 
24  8 

ii 

12 

13 

14 
15 
16 

17 
18 
19 

9.41610 
9.41638 
9.41666 

9.41694 
9.41722 
9.41750 
9.4I778 
9.41806 
9-4I834 

28 
28 
28 
28 
28 
28 
28 
28 
27 

9.43138 
9.43I68 
9.43I98 
9.43228 
9.43258 
9.43288 

9.43318 
9-43348 
9.43378 

30 
30 
30 
30 
30 
30 
30 
30 
3° 

0.56862 
0.56832 
0.56802 
0.56772 
0.56742 
0.56712 
0.56682 
0.56652 
0.56622 

9.98472 
9.98470 
9.98468 
9.98466 
9.98464 
9.98462 

9.98460 
9.98458 
9.98456 

89 
88 
87 
86 
85 
84 

83 
82 
81 

9 

I 

2 
3 
4 

27.9 

30 

3-0 
6.0 
9-0 

12.  0 

20 

9.41861 

28 

9.43408 

3° 

0.56592 

9.98453 

80 

5 
g 

15-0 
To  o 

21 
22 
23 
24 
25 
26 

27 

28 

29 

9-41889 
9.41917 
9.4I945 

9.4I973 
9.42001 
9.42029 
9.42056 
9.42084 
9.42112 

28 
28 
28 
28 
28 
27 
28 
28 
28 

9-43438 
9-43468 
9-43498 
9.43528 
9-43558 
9.43587 
9-43617 
9.43647 
9.43677 

30 
30 
30 
30 
29 
30 
30 
30 
3° 

o  .  56562 

0.56532 
0.56502 

0.56472 
0.56442 
0.56413 
0.56383 
0.56353 
0.56323 

9.98451 
9.98449 
9.98447 
9.98445 
9.98443 
9.98441 
9.98439 
9.98437 
9-98435 

79 
78 
77 
76 
75 
74 
73 

73 

71 

7 
8 
9 

I 

2 

21.0 
24.0 
27.0 

29 

2-9 

5-8 

30 

9.42140 

27 

9.43707 

29 

0.56293 

9.98433 

70 

3 

8-7 

3i 
32 
33 
34 
35 
36 

37 
38 
39 

9.42167 
9.42195 
9-42223 

9-42250 
9.42278 
9-42305 

9-42333 
9.42361 
9-42388 

28 
28 
27 
28 
27 
28 
28 
27 
28 

9.43736 
9-43766 
9.43796 
9.43826 
9»43855 
9-43885 

9-43915 
9-43944 
9-43974 

30 
30 
30 
29 
30 
30 
29 
30 
3° 

0.56264 
0.56234 
0.56204 

0.56174 
0.56145 
0.56115 

0.56085 
o  .  56056 
o  .  56026 

9.98431 
9.98429 
9.98427 

9-98425 
9.98422 
9.98420 
9.98418 
9.98416 
9-98414 

69 
68 
67 
66 
65 
64 

63 
62 
61 

4 
5 
6 
7 
8 
9 

I4-S 
17-4 
20.3 

23.2 
26.1 

28 

40 

9-42416 

27 

9.44004 

29 

0.55996 

9.98412 

60 

I 

2.8 

41 

42 
43 
44 
45 
46 

47 
48 
49 

9.42443 
9.42471 
9.42498 
9.42526 
9-42553 
9.42580 

9.42608 
9-42635 
9-42663 

28 
27 
28 
27 
27 
28 

27 
28 
27 

9-44033 
9.44063 
9.44092 
9.44122 
9.44I5I 
9.44181 
9.44210 
9.44240 
9.44269 

30 
29 
30 

29 
30 
29 

30 
29 
30 

0.55967 

0.55937 
0.55908 

0.55878 
0.55849 
0.55819 
0-55790 
0.55760 
0-55731 

9.98410 
9.98408 
9.98406 

9.98404 
9.98402 
9.98399 
9-98397 
9.98395 
9.98393 

59 
58 
57 
56 
55 
54 
53 

52 

Si 

2 

3 

4 
5 
6 
7 
8 
9 

5-6 
8.4 

II.  2 
14.0 

16.8 
19.6 
22.4 
25.2 

50 

9.42690 

9.44299 

0.55701 

9.98391 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P 

P. 

105* 


(129) 


16 


164 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.P. 

50 

9.42690 

27 

9-44299 

2Q 

o.557oi 

9.98391 

50 

51 

9.42717 

28 

9-44328 

~y 

0.55672 

9.98389 

49 

52 

9-42745 

27 

9-44358 

3° 
20 

0.55642 

9-98387 

48 

53 

9.42772 

*? 
27 

9.44387 

~y 
29 

0.55613 

9.98385 

47 

29 

54 

9.42799 

9.44416 

in 

0.55584 

9-98383 

46 

I 

2.9 

55 

9.42826 

27 
28 

9.44446 

ou 

0.55554 

9-98381 

45 

2 

5-8 

56 

9.42854 

27 

9-44475 

29 
29 

0.55525 

9.98378 

44 

3 

8.7 

57 

9.42881 

•7*7 

9-44504 

in 

0.55496 

9.98376 

43 

4 

ii.  6 

58 

9-42908 

<=7 

9-44534 

o*-' 

0.55466 

9.98374 

42 

5 

14-5 

59 

9-42935 

27 
27 

9-44563 

29 
29 

0.55437 

9.98372 

41 

6 

17-4 

60 

9-42962 

27 

9-44592 

30 

0.55408 

9.98370 

40 

7 
8 

20.3 
23.2 

6i 

9.42989 

2R 

9-44622 

0.55378 

9.98368 

39 

9 

26.1 

62 

9-43017 

2o 

9.4465I 

29 

0-55349 

9.98366 

38 

63 

9-43044 

27 
27 

9.44680 

29 
29 

0.55320 

9-98364 

37 

64 

9.4307I 

9.44709 

0.55291 

9.98361 

36 

65 

9.43098 

27 

9.44738 

29 

0.55262 

9.98359 

35 

28 

66 

9-43125 

27 
27 

9-44768 

3° 
29 

0.55232 

9.98357 

34 

i 

2.8 

6? 

9.43I52 

9-44797 

0.55203 

9.98355 

33 

2 

5.6 

68 

9.43179 

27 

9-44826 

29 

0.55174 

9.98353 

32 

3 

8.4 

69 

9-43206 

27 
27 

9.44855 

29 
2Q 

0.55145 

9.98351 

31 

4 

II.  2 

70 

9-43233 

27 

9.44884 

*y 
29 

0.55116 

9-98349 

30 

5 
5 

14.0 

16.8 

71 

9.43260 

•7*7 

9-44913 

on 

0.55087 

9-98347 

29 

7 

19.6 

72 

9.43287 

•* 

•9*7 

9.44942 

~y 

•7O 

0.55058 

9-98344 

28 

8 

22.4 

73 

9.433I4 

*7 

27 

9-44971 

*SP 

29 

0.55029 

9.98342 

27 

9 

25.2 

74 

9-43341 

26 

9-45000 

20 

0.55000 

9.98340 

26 

75 

9.43367 

•jn 

9.45029 

4y 

OQ 

0.54971 

9.98338 

25 

76 

9-43394 

•f 

27 

9-45058 

*y 

29 

0.54942 

9-98336 

24 

77 

9-43421 

9.45087 

0.54913 

9.y8334 

23 

27 

78 

9-43448 

27 

0*7 

9-45ii6 

29 
20 

0.54884 

9.98332 

22 

I 

2.7 

79 

9-43475 

1 
27 

9.45145 

~y 

29 

0.54855 

9-98329 

21 

2 

5-4 

80 

9-43502 

26 

9-45174 

*y 
29 

0.54826 

9-98327 

20 

3 

8.1 

T.      Q 

81 

9-43528 

07 

9-45203 

20 

0.54797 

9-98325 

19 

4 

IO  .  o 
TO    r 

82 

9-43555 

*7 

9-45232 

•*y 
20 

0.54768 

9-98323 

18 

5 

AO  •  O 

16.2 

83 

9.43582 

27 

27 

9-4526I 

vy 

29 

0.54739 

9.98321 

17 

7 

I8.'9 

84 

9-43609 

96 

9-45290 

0.54710 

9.98319 

16 

8 

21.6 

85 

9.43635 

20 

9.45319 

29 

0.54681 

9.98317 

»*5 

9 

24.3 

86 

9.43662 

27 

27 

9-45348 

29 
28 

0.54652 

9.983I4 

14 

87 

9.43689 

26 

9.45376 

20 

0.54624 

9-98312 

13 

' 

88 

9-43715 

9-45405 

~y 

0.54595 

9-98310 

12 

89 

9-43742 

27 
27 

9-45434 

29 

20 

0.54566 

9-98308 

II 

26 

90 

9.43769 

26 

9-45463 

~y 

29 

0.54537 

9.98306 

10 

i 

2.6 

9i 

9-43795 

O*T 

9-45492 

28 

0.54508 

9.98304 

09 

2 

5-2 

7Q 

92 

9.43822 

*7 
?fi 

9-45520 

0.54480 

9-98302 

08 

3 

.8 

93 

9-43848 

20 

27 

9-45549 

29 

29 

0.54451 

9.98299 

07 

4 
5 

IO.4 
I3.O 

94 

9.43875 

26 

9-45578 

28 

0.54422 

9-98297 

06 

6 

15.6 

95 

9-43901 

2*7 

9.456o6 

2O 

0.54394 

9-98295 

05 

7 

18.2 

96 

9.43928 

*/ 

26 

9.45635 

~y 
29 

0.54365 

9.98293 

04 

8 

20.8 

97 

9-43954 

27 

9.45664 

28 

0.54336 

9.98291 

03 

9 

23  4 

98 

9.43981 

26 

9.45692 

29 

0.54308 

9-98289 

02 

99 

9-44007 

27 

9-45721 

29 

0-54279 

9.98286 

01 

100 

9.44034 

9-45750 

0.54250 

9-98284 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.  P. 

(130) 


16' 


163' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

00 

OI 

02 
03 

04 
05 
06 

07 
08 
09 
10 
ii 

12 
13 

U 
IS 
16 

17 
18 
19 
20 

21 
22 
23 

24 
25 
26 

27 

28 

29 

30 

31 
32 
33 
34 
35 
36 

37 
38 
39 
40 

4i 
42 
43 
44 
45 
46 
47 
48 
49 
50 

9-44034 

26 

27 
26 
26 

2? 
26 
26 

27 

26 
26 

27 
26 
26 
26 
26 

27 

26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 

25 

26 
26 
26 
26 

25 

26 
26 
26 

25 

26 
26 

25 

26 
26 

25 

9-45750 

28 

29 
28 
29 
28 
29 
29 
28 
28 
29 
28 

29 
28 
29 
28 
28 
29 
28 
28 

29 

28 
28 
28 
29 
28 
28 
28 
28 
29 
28 

28 
28 
28 
28 
28 
28 
28 
28 
28 

28 

28 
28 
28 
28 
28 
28 
28 
28 
28 
27 

0.54250 

9.98284 

100 

99 
98 
97 
96 
95 
94 

93 
92 
91 
90 

89 
88 
87 
86 
85 
84 

83 

82 
81 
80 

79 
78 
77 
76 
75 
74 
73 

72 

71 
70 

69 
68 
67 

'S 

64 

63 
62 
61 
60 

59 
58 
57 
56 
55 
54 
53 
52 
Si 
50 

I 

2 

3 

4 
5 
6 
7 
8 
9 

i 

2 
3 
4 
5 
6 
7 
8 
9 

I 

2 

3 

4 
5 
6 
7 
8 
9 

I 
2 
3 
4 
5 
6 
7 
8 
9 

29 

2.9 
5-8 
8.7 
11.  6 
14-5 
17-4 
20.3 
23.2 
26.1 

28 

2.8 

5-6 
8.4 
II.  2 

14-0 

16.8 
19.6 
22.4 
25.2 

27 

2.7 

5-4 
8.1 
10.8 
13-5 
16.2 
18.9 

21.6 

24-3 
26 

2.6 
5-2 

7-8 
10.4 
13-0 
15.6 
18.2 

20.8 

23-4 

9.44o6o 
9.44087 
9-44II3 

9.44139 
9.44166 
9.44192 
9.44218 
9-44245 
9.44271 

9-45778 
9-45807 
9.45835 
9.45864 
9-45892 
9-45921 
9-45950 
9-45978 
9.46006 

0.54222 
0.54193 
0.54165 
0.54136 
0.54108 
0.54079 
0.54050 
0.54022 
0.53994 

9.98282 
9.98280 
9.98278 
9-98275 
9-98273 
9.98271 

9-98269 
9.98267 
9-98265 

9.44297 

9-46035 

0.53965 

9.98262 

9-44324 
9-44350 
9-44376 
9.44402 
9.44428 
9-44455 
9.44481 
9.44507 
9-44533 

9-46063 
9-46092 
9.46120 

9.46149 
9.46177 
9-46205 

9-46234 
9.46262 
9.46290 

0.53937 
0.53908 
0.53880 

0.53851 
0.53823 
0.53795 
0.53766 
0.53738 
0.53710 

9.98260 
9.98258 
9.98256 

9-98254 
9.98251 
9.98249 
9.98247 
9-98245 
9-98243 

9-44559 

9-46319 

0.53681 

9.98240 

9-44585 
9.44611 
9-44637 
9.44663 
9.44689 
9-44715 
9.44741 
9.44767 
9-44793 

9.46347 
9-46375 
9-46403 
9-46432 
9.46460 
9.46488 
9.46516 
9-46544 
9.46573 

0.53653 
0.53625 
0.53597 
0.53568 
0.53540 
0.53512 

0.53484 
0.53456 
0.53427 

9-98238 
9.98236 
9-98234 
9.98232 
9.98229 
9.98227 
9.98225 
9.98223 
9.98221 

9.44819 

9.46601 

0.53399 

9.98218 

9-44845 
9.44871 
9-44897 
9-44923 
9.44948 
9-44974 
9.  45000 
9.45026 
9.45052 

9-46629 
9.46657 
9.46685 

9-467I3 
9.46741 
9.46769 
9.46797 
9.46825 
9.46853 

0.53371 
0.53343 
0.53315 
0.53287 
0.53259 
0.53231 
0.53203 
0.53175 
0.53147 

9.98216 
9-98214 
9.98212 

9-98209 
9.98207 
9-98205 
9.98203 
9.98201 
9.98198 

9-45077 

9.46881 

0.53H9 

9-98196 

9-45103 
9-45129 
9-45155 
9.45i8o 
9.45206 
9-45232 

9-45257 
9.45283 
9.45309 

9.46909 
9.46937 
9-46965 

9.46993 
9.47021 
9.47049 

9.47077 
9-47105 
9-47133 

0.53091 
0.53063 
0.53035 
0.53007 
0.52979 
0.52951 
0.52923 
0.52895 
0.52867 

9.98194 
9-98192 
9.98189 
9.98187 
9-98185 
9.98183 
9.98180 
9.98178 
9.98176 

9-45334 

9.47160 

0.52840 

9.98174 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.  P. 

106< 


73 


163' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos     , 

P.  P. 

50 

9-45334 

26 

9.47160 

28 

0.52840 

9.98174 

50 

5i 

9.4536o 

9.47188 

28 

0.52812 

9.98171 

49 

52 

9-45385 

26 

9.47216 

28 

0.52784 

9.98169 

48 

53 

9-454II 

25 

9.47244 

28 

0.52756 

9-98167 

47 

28 

54 

9-45436 

26 

9.47272 

0.52728 

9.98165 

46 

i 

2.8 

55 

9.45462 

9-47299 

27 

0.52701 

9.98162 

45 

2 

5-6 

56 

9-45487 

25 
26 

9.47327 

28 

0.52673 

9.98160 

44 

3 

8.4 

57 

9-45513 

9-47355 

28 

0.52645 

9-98158 

43 

4 

II.  2 

58 

9.45538 

26 

9.47383 

07 

0.52617 

9.98156 

42 

5 
g 

I4.O 

16.8 

59 

9-45564 

25 

9.47410 

•*/ 

28 

0.52590 

9.98153 

41 

7 

19.6 

60 

9.45589 

26 

9-47438 

28 

o  .  52562 

9.98151 

40 

8 

22.4 

6i 

9.45615 

9.47466 

0.52534 

9.98149 

39 

9 

25.2 

62 

9.45640 

25 

or 

9-47493 

27 
28 

0.52507 

9.98147 

38 

63 

9.45665 

*O 
26 

9-47521 

28 

0.52479 

9.98144 

37 

64 

9.45691 

9-47549 

0.52451 

9.98142 

36 

27 

65 

9.45716 

25 
26 

9-47576 

27 
28 

0.52424 

9.98140 

35 

I 

2.7 

66 

9-45742 

25 

9.47604 

28 

0.52396 

9.98138 

34 

2 

5-4 

67 

9.45767 

9.47632 

0*7 

0.52368 

9.98135 

33 

3 

8.1 

68 

9-45792 

9.47659 

•*  / 
28 

0.52341 

9.98I33 

32 

4 

10.8 

69 

9-458I7 

26 

9.47687 

27 

0.52313 

9-98131 

31 

5 

13-5 

70 

9.45843 

25 

9.47714 

28 

0.52286 

9-98129 

30 

6 

16.2 
18  o 

71 

9-45868 

9.47742 

0.52258 

9.98126 

29 

7 
8 

10.  y 
21.6 

72 

9-45893 

9.47769 

27 
28 

0.52231 

9.98124 

28 

24.3 

73 

9.459I8 

26 

9-47797 

27 

0.52203 

9.98122 

27 

74 

9-45944 

9.47824 

28 

0.52176 

9.98H9 

26 

75 

9.45969 

' 

9.47852 

0.52148 

9.98117 

25 

76 

9-45994 

25 

9.47879 

27 
28 

0.52121 

9.98II5 

24 

77 

9-46019 

9-47907 

0.52093 

9-98113 

23 

78 

9.46044 

' 

9-47934 

2? 

0.52066 

9.98110 

22 

25 

79 

9.46069 

26 

9.47961 

27 
28 

0.52039 

9.98108 

21 

i 

2-5 

80 

9-46095 

25 

9.47989 

27 

0.52011 

9.98106 

20 

2 

5-0 

81 

9.46120 

9  .  48016 

0.51984 

9-98103 

19 

3 

7-5 

82 

9.46145 

25 

9.48044 

2 

0.51956 

9.98101 

18 

4 

' 

83 

9.46170 

25 
25 

9.48071 

27 
27 

0.51929 

9.98099 

17 

5 
6 

12.5 

15-0 

84 

9.46195 

9-48098 

28 

0.51902 

9.98097 

16 

7 

17-5 

85 

9.46220 

25 

9.48126 

0.51874 

9.98094 

IS 

8 

20.  o 

86 

9.46245 

25 

25 

9.48I53 

27 
2? 

0.51847 

9-98092 

14 

9 

22.5 

87 

9.46270 

9.48180 

28 

0.51820 

9.98090 

13 

88 

9-46295 

' 

9.48208 

0.51792 

9.98087 

12 

89 

9-46320 

25 
25 

9-48235 

27 
27 

0.51765 

9-98085 

II 

24 

90 

9.46345 

25 

9.48262 

27 

0.51738 

9-98083 

10 

i 

2.4 

91 

9-46370 

9.48289 

0.51711 

9.98080 

09 

2 

4-8 

92 

9.46395 

25 

9-483I7 

2 

0.51683 

9.98078 

08 

3 

7-2 

93 

9.46420 

25 

9.48344 

27 

0.51656 

9-98076 

07 

4 

9-6 

94 

9.46444 

24 

9-48371 

27 

0.51629 

9.98074 

06 

5 

12.0 

95 
96 

9-46469 
9.46494 

25 

25 

25 

9.48398 
9-48425 

27 
27 

28 

0.51602 

0.51575 

9.98071 
9-98069 

05 
04 

7 
8 

14.4 

16.8 

19.2 

97 

9-46519 

9.48453 

0.51547 

9.98067 

03 

9 

21.6 

98 

9.46544 

25 

9.48480 

27 

0.51520 

9.98064 

02 

99 

9-46569 

25 

25 

9-48507 

27 
27 

0.51493 

9.98062 

OI 

100 

9.46594 

9.48534 

0.51466 

9.98060 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.  P. 

106° 


73° 


(132) 


162  < 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

00 

9-46594 

24 

9.48534 

27 

0.51466 

9.98060 

100 

01 

9.46618 

9-48561 

0.51439 

9.98057 

99 

02 

9-46643 

25 

9.48588 

2? 

0.51412 

9.98055 

98 

03 

9.46668 

25 
25 

9-48615 

27 
27 

0.51385 

9.98053 

97 

27 

04 

9-46693 

9.48642 

0.51358 

9.98050 

96 

i 

2-7 

05 

9.46717 

24 

9.48669 

27 

0.51331 

9-98048 

95 

2 

5-4 

06 

9-46742 

25 
25 

9.48696 

27 
27 

0.51304 

9.98046 

94 

3 

A 

8.1 
10.8 

07 
08 

9.46767 
9.46791 

24 

2S 

9.48723 

9.48750 

27 

07 

0.51277 
0.51250 

9.98043 
9.98041 

93 
92 

5 
g 

13  5 
16.2 

09 

9.46816 

25 

9.48777 

f 

27 

0.51223 

9.98039 

9i 

7 

18.9 

10 

9.46841 

24 

9.48804 

27 

0.51196 

9-98036 

90 

8 

21.6 

ii 

9-46865 

or 

9.48831 

27 

0.51169 

9.98034 

89 

9 

24.3 

12 

9.46890 

•*o 
or 

9-48858 

*/ 

07 

0.51142 

9.98032 

88 

13 

9-469I5 

-so 
24 

9-48885 

•*  / 

27 

0.51115 

9.98029 

87 

14 

9-46939 

9.48912 

0.51088 

9.98027 

86 

26 

IS 

9-46964 

25 

0/1 

9.48939 

27 

07 

0.51061 

9-98025 

85 

I 

2.6 

16 

9-46988 

•d 

25 

9.48966 

•? 

27 

0.51034 

9.98022 

84 

2 

52 

17 

9-47013 

OA 

9.48993 

27 

0.51007 

9  .  98020 

83 

3 

7-8 

18 

9-47037 

£t\ 

or 

9.49020 

26 

0.50980 

9.98018 

82 

4 

10.4 

19 

9.47062 

•^O 
24 

9.49046 

27 

0.50954 

9-98015 

Si 

5 

13-0 

20 

9.47086 

25 

9-49073 

27 

0.50927 

9.98013 

80 

6 

15-6 
18  2 

21 

9-47III 

2/1 

9.49ioo 

27 

0.50900 

9.98011 

79 

7 
8 

20.8 

22 

9.47I35 

^4 

or 

9.49127 

•f 

07 

0.50873 

9.98008 

78 

9 

23.  ,1 

23 

9-47i6o 

•^j 

24 

9.49154 

*? 

27 

0.50846 

9.98006 

77 

24 

9.47184 

oe 

9.49I81 

26 

0.50819 

9-98004 

76 

25 

9.47209 

•^o 

*?A 

9.49207 

07 

0.50793 

9.98001 

75 

26 

9-47233 

•^4 

24 

9-49234 

*? 

27 

0.50766 

9-97999 

74 

27 

9-47257 

9.49261 

0.50739 

9-97997 

73 

28 

9.47282 

25 

9.49288 

27 
26 

0.50712 

9-97994 

72 

25 

29 

9.47306 

24 
24 

9-49314 

27 

0.50686 

9.97992 

71 

i 

2.5 

30 

9-47330 

25 

9-49341 

27 

0.50659 

9.97989 

70 

2 

S.o 

31 

9-47355 

*?A 

9-49368 

26 

o  .  50632 

9.97987 

69 

3 

7.5 

IO  O 

32 

9-47379 

XQ 
24 

9-49394 

27 

0.50606 

9.97985 

68 

4 
5 

12.5 

33 

9-47403 

25 

9-49421 

27 

0.50579 

9.97982 

67 

6 

15.0 

34 

9-47428 

0,4 

9-49448 

26 

0.50552 

9.97980 

66 

7 

17.5 

35 

9-47452 

•n 

0,4 

9-49474 

97 

0.50526 

9.97978 

65 

8 

20.  o 

36 

9.47476 

^4 

24 

9-49501 

*f 

27 

0.50499 

9-97975 

64 

9 

22.5 

37 

9.47500 

oe 

9-49528 

26 

0.50472 

9-97973 

63 

38 

9-47525 

•*o 

24 

9-49554 

27 

0.50446 

9-97971 

62 

39 

9-47549 

24 

9-49581 

26 

0.50419 

9.97968 

6x 

24 

40 

9-47573 

24 

9.49607 

27 

0.50393 

9.97966 

60 

i 

2.4 

41 

9-47597 

9.49634 

26 

0.50366 

9.97963 

59 

2 

4-8 

42 

9.47621 

24 

9.49660 

0.50340 

9.97961 

58 

3 

7.2 

43 

9.47646 

25 

24 

9.49687 

27 

26 

0.50313 

9-97959 

57 

4 

9-6 

44 

9.47670 

•7/1 

9-49713 

o  .  50287 

9.97956 

56 

5 

12.  0 

45 

9.47694 

^4 
24 

9-49740 

27 

26 

o  .  50260 

9-97954 

55 

6 

14.4 

Tr    o 

46 

9-47718 

24 

9.49766 

27 

0.50234 

9-97951 

54 

7 
8 

10.  o 

19.2 

47 

9-47742 

24 

9-49793 

26 

o  .  50207 

9-97949 

53 

9 

21.6 

48 

9.47766 

24 

9-49819 

27 

0.50181 

9-97947 

52 

49 

9.47790 

24 

9.49846 

26 

0.50154 

9-97944 

Si 

50 

9.47814 

9.49872 

0.50128 

9.97942 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

107' 


72 


(133) 


162 ! 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

50 

9.47814 

24 

9.49872 

27 

0.50128 

9-97942 

50 

Si 

9.47838 

2A 

9.49899 

26 

0.50101 

9-97940 

49 

52 

9.47862 

"Q 
•2\ 

9.49925 

26 

0.50075 

9-97937 

48 

53 

9.47886 

44 
24 

9-49951 

27 

0.50049 

9-97935 

47 

27 

54 

9-47910 

2A 

9-49978 

26 

o  .  50022 

9-97932 

46 

I 

2.7 

55 

9-47934 

A(\ 

OA 

9.50004 

2*7 

0.49996 

9-97930 

45 

2 

5-4 

56 

9-47958 

•*4 
24 

9-50031 

•*/ 

26 

0.49969 

9.97928 

44 

3 

8.1 

57 

9.47982 

9.50057 

26 

0.49943 

9.97925 

43 

4 

10.8 

58 

9.48006 

24 

2A 

9-50083 

27 

0.49917 

9.97923 

42 

5 

13-5 

fC     ~ 

59 

9-48030 

AI\ 
24 

9.50110 

26 

0.49890 

9-97920 

41 

10.2 
T8   Q 

60 

9.48054 

24 

9.50136 

26 

0.49864 

9.97918 

40 

7 
8 

io.y 
21.6 

61 

9.48078 

°/t 

9.50162 

26 

0.49838 

9.97916 

39 

9 

24-3 

62 

9.48102 

^4 

0-2 

9.50188 

0*7 

0.49812 

9.97913 

38 

63 

9-48125 

^O 
24 

9-50215 

^7 
26 

0.49785 

9.97911 

37 

64 

9.48149 

0,1 

9-50241 

26 

0.49759 

9.97908 

36 

26 

65 

9.48173 

^4 
24 

9-50267 

26 

0.49733 

9.97906 

35 

I 

2.6 

66 

9.48197 

24 

9-50293 

27 

0.49707 

9.97904 

34 

2 

5-2 

67 

9.48221 

?A 

9-50320 

26 

0.49680 

9.97901 

33 

3 

7.8 

68 

9.48245 

4t\ 

00 

9.50346 

26 

0.49654 

9.97899 

32 

4 

10.4 

69 

9.48268 

•^O 
24 

9.50372 

26 

0.49628 

9.97896 

31 

5 

13-0 

70 

9-48292 

24 

9.50398 

26 

0.49602 

9.97894 

30 

6 

15-6 

,Q     r> 

7i 

9-48316 

24 

9-50424 

27 

0.49576 

9.97891 

29 

7 
8 

lo  .  2 
20.8 

72 

9.48340 

27. 

9.50451 

26 

0.49549 

9-97889 

28 

9 

27    A 

73 

9-48363 

•*O 

24 

9.50477 

26 

0.49523 

9.97887 

27 

74 

9-48387 

24 

9.50503 

26 

0.49497 

9.97884 

26 

75 

9.48411 

9.50529 

26 

0.49471 

9-97882 

25 

76 

9.48434 

23 
24 

9-50555 

26 

0.49445 

9-97879 

24 

77 

9.48458 

9-50581 

26 

0.49419 

9.97877 

23 

78 

9.48482 

24 
o-? 

9-50607 

26 

0.49393 

9.97874 

22 

24 

79 

9.48505 

*J 

24 

9-50633 

26 

0.49367 

9.97872 

21 

i 

2.4 

80 

9.48529 

23 

9-50659 

26 

0.49341 

9.97870 

20 

2 

4-8 

81 

9.48552 

9A 

9.50685 

26 

0.49315 

9.97867 

19 

3 

7.2 
o  6 

82 

9.48576 

*4 

tJA 

9.507H 

26 

0.49289 

9-97865 

18 

4 

y.o 

83 

9.48600 

•*4 

23 

9-50737 

26 

0.49263 

9.97862 

17 

5 
6 

14.4 

84 

9.48623 

OA 

9-50763 

26 

0.49237 

9.97860 

16 

7 

16.8 

85 

9.48647 

•*4 

0-5 

9-50789 

26 

0.49211 

9.97857 

15 

8 

19.2 

86 

9.48670 

A3 

24 

9-50815 

26 

0.49185 

9-97855 

14 

9 

21.6 

87 

9.48694 

00 

9.50841 

26 

0.49159 

9.97853 

13 

88 

9.48717 

A5 

9.50867 

26 

0.49133 

9.97850 

12 

89 

9.48741 

24 

23- 

9-50893 

26 

0.49107 

9.97848 

II 

23 

90 

9-48764 

24 

9.50919 

26 

0.49081 

9-97845 

10 

I 

2.3 

9i 

9.48788 

O-J 

9.50945 

26 

0.49055 

9-97843 

09 

2 

4-6 

92 

9.48811 

A3 

9.5097I 

26 

0.49029 

9.97840 

08 

3 

6-9 

93 

9.48835 

24 
23 

9-50997 

26 

0.49003 

9.97838 

07 

4 

9-2 

94 

9.48858 

9.51023 

0.48977 

9-97835 

06 

5 

II.  5 

95 

9.48881 

23 

9.51048 

25 
•?fi 

0.48952 

9-97833 

05 

13-8 

96 

9.48905 

24 
23 

9.51074 

2O 
26 

o  .  48926 

9.97830 

04 

7 
8 

16.  i 
18.4 

97 

9.48928 

OA 

9.51100 

26 

0.48900 

9-97828 

03 

9 

20.7 

98 

9.48952 

]M| 
07 

9-51126 

26 

0.48874 

9.97826 

02 

.  99 

9.48975 

A3 
23 

9-5II52 

26 

0.48848 

9.97823 

01 

100 

9.48998 

9.5H78 

0.48822 

9.97821 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.P. 

107( 


72° 


d34) 


18' 


161' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

P.  P. 

00 

9.48998 

24 

9-5H78 

25 

o  .  48822 

9.97821 

100 

OI 

9.49022 

01 

9-51203 

26 

0.48797 

9.97818 

99 

02 

9.49045 

*6 

9-51229 

26 

0.48771 

9.97816 

98 

03 

9.49068 

23 
23 

9-51255 

26 

0.48745 

9-978I3 

97 

26 

04 

9.49091 

9.51281 

9C 

0.48719 

9.978H 

96 

I 

2.0 

05 

9-49IIS 

24 

9-51306 

*i> 

26 

0.48694 

9.97808 

95 

2 

5-2 

06 

9-49I38 

23 
23 

9-5I332 

26 

0.48668 

9.978o6 

94 

3 

7-8 
10  4 

07 

9.49161 

27 

9.51358 

26 

0.48642 

9.97803 

93 

4 
5 

13.0 

08 

9.49184 

*o 

?A 

9.51384 

2C 

0.48616 

9.97801 

92 

6 

15.6 

09 

9.49208 

•Nt 

21 

9.51409 

^o 

26 

0.48591 

9-97798 

9i 

7 

18.2 

10 

9.49231 

*o 
23 

9-51435 

26 

0.48565 

9.97796 

90 

g 

20.8 

ii 

9-49254 

o-i 

9.51461 

25 

0.48539 

9-97793 

89 

9 

23.4 

12 

9-49277 

^O 

07. 

9.51486 

26 

0.48514 

9-97791 

88 

13 

9.49300 

•^o 

23 

9.5I5I2 

25 

0.48488 

9.97788 

87 

14 

9-49323 

2A 

9-51537 

26 

0.48463 

9.97786 

86 

15 

9-49347 

iBQ 
07 

9.5I563 

26 

0.48437 

9-97784 

85 

I 

2.5 

16 

9-49370 

•*O 
23 

9.5I589 

25 

0.48411 

9.97781 

84 

2 

5-0 

17 

9-49393 

9.5i6i4 

26 

0.48386 

9-97779 

83 

3 

7-5 

18 

9.49416 

23 

9-51640 

0.48360 

9.97776 

82 

4 

IO.O 

19 

9-49439 

23 
23 

9-51665 

25 

26 

0.48335 

9-97774 

81 

5 
g 

12.5 

1C.    O 

20 

9.49462 

23 

9.51691 

26 

0.48309 

9-97771 

80 

7 

*O-  w 

17.5 

21 

9.49485 

07 

9.5I7I7 

or 

0.48283 

9.97769 

79 

8 

20.0 

22 

9-49508 

*o 

07 

9.51742 

*O 
26 

0.48258 

9.97766 

78 

9 

22.5 

23 

9-49531 

•*O 

23 

9.51768 

25 

0.48232 

9-97764 

77 

24 

9-49554 

07 

9-51793 

26 

0.48207 

9.97761 

76 

25 

9-49577 

AS 

9.51819 

or 

0.48181 

9-97759 

75 

26 

9.49600 

23 

23 

9.51844 

•^5 

26 

0.48156 

9-97756 

74 

27 

9-49623 

07 

9.51870 

Or 

0.48130 

9-97754 

73 

24 

28 

9-49646 

•^0 

9.51895 

*O 

or 

0.48105 

9-97751 

72 

29 

9.49669 

23 
23 

9.51920 

*5 

26 

0.48080 

9-97749 

71 

i 

2.4 

.       Q 

30 

9-49692 

23 

9.51946 

25 

0.48054 

9-97746 

70 

2 
3 

4.0 

7-2 

31 

9-49715 

07 

9-5I97I 

26 

0.48029 

9-97744 

69 

4 

9.6 

32 

9-49738 

•**5 

07 

9-51997 

or 

0.48003 

9-97741 

68 

5 

12.  0 

33 

9.49761 

•*o 
22 

9.52022 

*o 

25 

0.47978 

9-97739 

67 

6 

14-4 

34 

9-49783 

07 

9-52047 

26 

0.47953 

9-97736 

66 

7 

16.8 

35 

9.49806 

•**5 

9-52073 

or 

0.47927 

9-97734 

65 

8 

19.2 

36 

9.49829 

23 
23 

9.52098 

^o 

26 

0.47902 

9-97731 

64 

9 

21.6 

37 

9.49852 

O*J 

9.52124 

or 

0.47876 

9-97729 

63 

38 

9-49875 

*6 

9-52149 

•*o 

or 

0.47851 

9.97726 

62 

39 

9.49898 

23 
22 

9-52174 

*5 
26 

0.47826 

9.97723 

61 

23 

40 

9.49920 

23 

9.52200 

25 

0.47800 

9-97721 

60 

I 

2.3 

41 

9-49943 

0-3 

9.52225 

or 

0-47775 

9.97718 

59 

2 

4-6 
6n 

42 

9-49966 

*O 
07 

9.52250 

*O 
or 

0.47750 

9.97716 

58 

3 

•  9 

43 

9.49989 

•^0 

22 

9-52275 

•*o 

26 

0.47725 

9-97713 

57 

4 
5 

9.2 
II.  5 

44 

9.50011 

07 

9-52301 

or 

0.47699 

9.97711 

56 

6 

13.8 

45 

9-50034 

^o 

00 

9-52326 

•*5 
or 

0.47674 

9.97708 

55 

7 

16.1 

46 

9-50057 

•**i 

23 

9-52351 

*O 

25 

0.47649 

9.97706 

54 

8 

18.4 

47 

9.50080 

22 

9.52376 

26 

0.47624 

9-97703 

53 

9 

20.7 

48 

9.50102 

00 

9.52402 

or 

0.47598 

9.97701 

53 

49 

9  -50125 

A5 
23 

9.52427 

*j 
25 

0.47573 

9.97698 

51 

50 

9.50148 

9.52452 

0.47548 

9.97696 

50 

Cos 

d. 

Cot 

d.  C. 

Tan 

Sin 

P.P. 

108 


71 ( 


(135) 


18 ' 


161' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

l              P.  P. 

50 

9.50148 

22 

9.52452 

25 

0.47548 

9.97696 

50 

Si 

9.50170 

23 

9-52477 

25 

0-47523 

9.97693 

49 

52 

9.50I93 

23 

9.52502 

26 

0.47498 

9.97691 

48 

53 

9.50216 

22 

9.52528 

25 

0-47472 

9.97688 

47 

25 

54 

9.50238 

23 

9-52553 

25 

0.47447 

9.97686 

46 

I 

2.5 

55 

9.50261 

22 

9.52578 

2^ 

0.47422 

9.97683 

45 

2 

S.o 

56 

9-50283 

23 

9-52603 

^O 
25 

0-47397 

9.9768o 

44 

3 

7-5 

57 

9.50306 

22 

9.52628 

OC 

0-47372 

9.97678 

43 

4 

IO.O 

58 

9-50328 

00 

9-52653 

^5 

0-47347 

9.97675 

42 

5 

12-5 

59 

9.5035I 

^o 
23 

9-52678 

25 
25 

0.47322 

9.97673 

41 

6 

iS.o 

60 

9-50374 

22 

9-52703 

25 

0.47297 

9.97670 

40 

7 
g 

17-5 
20  o 

6z 

9.50396 

23 

9.52728 

25 

0.47272 

9.97668 

39 

9 

22.  5 

62 

9.50419 

22 

9-52753 

25 

0.47247 

9.97665 

38 

63 

9-50441 

23 

9.52778 

26 

0.47222 

9.97663 

37 

64 

9-50464 

22 

9-52804 

oC 

0.47196 

9.9766o 

36 

65 

9.50486 

22 

9.52829 

*o 
25 

0.47I7I 

9.97657 

35 

24 

66 

9-50508 

23 

9-52854 

25 

0.47146 

9-97655 

34 

I 

2.4 

6? 

9-50531 

22 

9-52879 

oe 

0.47121 

9.97652 

33 

2 

4-8 

68 

9-50553 

07 

9-52904 

*j 
or 

0.47096 

9.97650 

32 

3 

7-2 

69 

9.50576 

•*o 
22 

9-52929 

**) 
24 

0.47071 

9.97647 

31 

4 

9-6 

70 

9.50598 

22 

9  52953 

25 

0.47047 

9.97645 

30 

5 
g 

12.  0 

7i 

9.50620 

2T 

9.52978 

or 

0.47022 

9.97642 

29 

7 

14.4 

16.8 

72 

9-50643 

*o 

22 

9-53003 

•3 
2*r 

0.46997 

9.97640 

28 

8 

19.2 

73 

9-50665 

23 

9.53028 

*o 

25 

0.46972 

9.97637 

27 

9 

21.6 

74 

9.50688 

22 

9-53053 

or 

0.46947 

9.97634 

26 

75 

9.50710 

22 

9-53078 

•*O 
or 

o  .  46922 

9.97632 

25 

76 

9-50732 

23 

9-53103 

*O 

25 

0.46897 

9.97629 

24 

77 

9-50755 

22 

9-53128 

OC 

0.46872 

9.97627 

23 

23 

78 

9.50777 

22 

9-53153 

«9 
or 

0.46847 

9.97624 

22 

i 

2.3 

79 

9.50799 

22 

9.53178 

•O 
24 

o  .  46822 

9.97621 

21 

2 

4-6 

80 

9-50821 

23 

9-53202 

25 

0.46798 

9.97619 

20 

3 

6-9 

81 

9-50844 

22 

9-53227 

or 

0.46773 

9.976i6 

19 

4 

9-2 

82 

9.50866 

9-53252 

•*o 

0.46748 

9.97614 

18 

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ii  .  5 

j-2    Q 

83 

9.50888 

22 

9-53277 

25 

25 

0.46723 

9.97611 

17 

7 

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16.1 

84 

9  50910 

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9-53302 

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0.46698 

9.97609 

16 

8 

18.4 

85 

9.50933 

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9-53327 

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0.46673 

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9 

20.7 

86 

9.509S5 

22 

9-53351 

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25 

0.46649 

9-97603 

14 

87 

9.50977 

9.53376 

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9.97601 

13 

88 

9-50999 

22 
22 

9-53401 

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0.46599 

9.97598 

12 

89 

9.51021 

22 

9-53426 

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24 

0.46574 

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9-51043 

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9-53450 

25 

0.46550 

9-97593 

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2.2 

91 

9.51066 

22 

9-53475 

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0.46525 

9-97590 

09 

2 

4-4 

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92 

9.51088 

22 

9-53500 

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0.46500 

9-97588 

08 

3 

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93 

9.51110 

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9-53525 

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24 

0.46475 

9-97585 

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4 
5 

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94 

9-51132 

9-53549 

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0.46451 

9-97583 

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6 

13.2 

95 

9-5II54 

9-53574 

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0.46426 

9-97580 

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7 

15.4 

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9-5II76 

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9-53599 

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0.46401 

9-97577 

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8 

17.6 

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9.51198 

22 

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0.46377 

9-97575 

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19.8 

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9.51220 

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0.46352 

9-97572 

02 

99 

9-51242 

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9.53673 

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0.46327 

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9.51264 

9.53697 

0.46303 

9-97567 

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d. 

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9.51264 

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9.53697 

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0.46229 

9-97559 

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9.51352 

22 

9.53796 

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0.46204 

9-97557 

96 

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2.5 

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9-51374 

22 

9.53820 

25 

0.46180 

9-97554 

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9.-  51396 

22 

9.53845 

24 

0.46155 

9-97551 

94 

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9.5I4I8 

22 

9.53869 

25 

0.46131 

9-97549 

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5^%, 

TO   r 

08 
09 

9-5I440 
9.51462 

22 
22 

9.53894 
9-53918 

24 
25 

0.46106 
0.46082 

9.97546 
9-97543 

92 
91 

6 

7 

1-;  .  ^> 

15.0 
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10 

9.51484 

22 

9-53943 

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0.46057 

9-97541 

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9.51506 

21 

9.53967 

25 

0.46033 

9-97538 

89 

9 

22.5 

12 

9.5I527 

22 

9-53992 

O/l 

0.46008 

9.97536 

88 

13 

9-51549 

22 

9.54016 

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25 

0.45984 

9-97533 

87 

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14 

9.5I57I 

22 

9.54041 

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0.45959 

9-97530 

86 

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9-51593 

9-54065 

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0-45935 

9-97528 

85 

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2.4 

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9.5I6I5 

22 
22 

9.54090 

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24 

0.45910 

9-97525 

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9-5I637 

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0.45886 

9-97522 

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0.45861 

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9.51680 

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9.54163 

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0.45837 

9-97517 

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20 

9.51702 

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9.54I87 

25 

0.45813 

9-97515 

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14.4 

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9.51724 

9.54212 

0.45788 

9-97512 

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19.2 

22 

9-51745 

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9.54236 

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0.45764 

9-97509 

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21.6 

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9.54261 

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0-45739 

9.97507 

77 

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9.51789 

22 

9.54285 

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0.45715 

9-97504 

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25 

9.5i8n 

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9.54309 

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0.45691 

9-97501 

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0.45666 

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27 

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9-54358 

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0.45642 

9.97496 

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0.45618 

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29 

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0.45593 

9-97491 

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9.5I9I9 

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9-54431 

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0.45569 

9-97488 

70 

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4-4 
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9-54455 

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0.45545 

9-97485 

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8.8 

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9.51962 

22 

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0.45520 

9-97483 

68 

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II.  0 

33 

9.51984 

22 

9-54504 

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24 

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9.52027 

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9-54552 

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0.45448 

9-97475 

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9.52049 

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9-54577 

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9.97472 

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9 

19.8 

37 

9.52070 

22 

9.546oi 

0-45399 

9.97469 

63 

38 

9.52092 

21 

9-54625 

24 

0-45375 

9.97467 

62 

39 

9.52H3 

22 

9.54649 

24 
24 

0.45351 

9.97464 

61 

21 

40 

9-52135 

21 

9.54673 

25 

0.45327 

9.9746i 

60 

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2.X 

41 

9.52I56 

22 

9.54698 

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0.45302 

9-97459 

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2 

4.2 

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42 

9.52178 

21 

9-54722 

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0.45278 

9-97456 

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9.52199 

22 

9.54746 

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0.45254 

9-97453 

57 

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9-52221 

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9-54770 

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0.45230 

9-97451 

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9-54794 

24 

0.45206 

9.97448 

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7 

14.7 

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9.52264 

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9.54818 

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0.45182 

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9.52285 

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0.45157 

9-97443 

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18.9 

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9-52307 

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9.54867 

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0.45133 

9-97440 

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49 

9.52328 

22 

9.54891 

24 
24 

0.45109 

9-97437 

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9.52350 

9.549IS 

0.45085 

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Cos 

d. 

Cot 

d.  c.  '     Tan 

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109s 


70  < 


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d. 

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50 

9-52350 

21 

9-54915 

24 

0.45085 

9-97435 

50 

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9-52371 

21 

9-54939 

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0.45061 

9-97432 

49 

52 

9-52392 

22 

9.54963 

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24 

0.45037 

9-97429 

48 

53 

9.S24I4 

21 

9.54987 

24 

0.45013 

9.97427 

47 

24 

54 

9-52435 

21 

9-550II 

VA 

0.44989 

9-97424 

46 

i 

2.4 

55 

9-52456 

9.55035 

mQ 

0.44965 

9.97421 

45 

2 

4-8 

56 

9-52478 

9-55059 

24 

0.44941 

9-97419 

44 

3 

7-2 

57 

9-52499 

21 

9-55083 

24 
24 

0.44917 

9.97416 

43 

4 
5 

9.6 

12.0 

58 

9-52520 

22 

9-55107 

24 

0.44893 

9-97413 

42 

6 

14.4 

59 

9.52542 

21 

9-55I3I 

24 

0.44869 

9.97410 

41 

7 

16.8 

60 

9-52563 

21 

9-55155 

24 

0.44845 

9.97408 

40 

8 

19.2 

61 

9.52584 

9-55179 

0.44821 

9.97405 

39 

9 

21.6 

62 

9.52606 

21 

9-55203 

24 
OA 

0.44797 

9-97402 

38 

63 

9.52627 

21 

9-55227 

~4 
24 

0-44773 

9.97400 

37 

An 

64 

9-52648 

21 

9-55251 

*yA 

0.44749 

9-97397 

36 

23 

65 

9-52669 

21 

9.55275 

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0.44725 

9-97394 

35 

I 

2.3 

66 

9.52690 

22 

9.55299 

*4 

24 

0.44701 

9.97392 

34 

2 

4-6 

6- 

67 

9-52712 

21 

9-55323 

0.44677 

9.97389 

33 

3 

•9 

68 

9-52733 

9-55347 

24 

0.44653 

9.97386 

32 

4 

9-2 

69 

9-52754 

21 

9-55371 

24 
24 

0.44629 

9.97383 

31 

5 
g 

ZX.f 

17  8 

70 

9-52775 

21 

9-55395 

23 

0.44605 

9.97381 

30 

7 

J.J.O 

16.1 

71 

9.52796 

22 

9-55418 

fylt 

0.44582 

9-97378 

29 

8 

18.4 

72 

9.52818 

21 

9-55442 

~4 

0.44558 

9-97375 

28 

9 

20.7 

73 

9.52839 

21 

9-55466 

24 
24 

0.44534 

9-97373 

27 

74 

9.52860 

21 

9-55490 

O1 

0.44510 

9-97370 

26 

75 

9.52881 

21 

9-55514 

^4 

0.44486 

9-97367 

25 

76 

9.52902 

21 

9.55538 

24 
24 

0.44462 

9.97364 

24 

77 

9-52923 

21 

9-55562 

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0.44438 

9.97362 

23 

21 

78 

9-52944 

21 

9-55585 

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0.44415 

9-97359 

22 

79 

9.52965 

21 

9.55609 

~4 
24 

0.44391 

9-97356 

21 

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2.1 

80 

9.52986 

21 

9.55633 

24 

0.44367 

9-97353 

20 

2 

3 

4-2 

6.3 

81 

9.53007 

21 

9-55657 

0.44343 

9-97351 

19 

4 

8-4 

82 

9.53028 

9.55680 

23 

0.44320 

9-97348 

18 

5 

10.5 

83 

9-53049 

22 

9-55704 

24 

24 

0.44296 

9-97345 

17 

6 

12.6 

84 

9-5307I 

21 

9.55728 

0.44272 

9-97343 

16 

7 

14.7 

85 

9.53092 

9-55752 

24 

0.44248 

9-97340 

15 

8 

16.8 

86 

9-53H2 

21 

9-55775 

23 

24 

0.44225 

9-97337 

14 

9 

18.9 

87 

9.53133 

21 

9-55799 

2/1 

0.44201 

9-97334 

13 

88 

9-53154 

21 

9-55823 

44 

24 

0.44177 

9-97332 

12 

89 

9-53175 

21 

9.55847 

21 

0.44153 

9.97329 

II 

20 

90 

9.53196 

21 

9.55870 

^o 

24 

0.44130 

9.97326 

10 

i 

2.0 

9i 

9-53217 

9.55894 

0.44106 

9.97323 

09 

2 

4.0 

fi  n 

92 

9-53238 

21 

9-55918 

24 

23 

0.44082 

9-97321 

08 

3 

A 

o.o 

8.0 

93 

9-53259 

21 

9-55941 

24 

0.44059 

9-97318 

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5 

10.  0 

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9-53280 

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9-55965 

24 

0.44035 

9-97315 

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6 

12.0 

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9-53301 

9.55989 

0.44011 

9-97312 

05 

7 

14.0 

96 

9-53322 

21 

9.56012 

23 
24 

0.43988 

9-97310 

04 

8 

16.0 

97 

9-53343 

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9.56036 

91 

0.43964 

9-97307 

03 

9 

18.0 

98 

9.53363 

21 

9-56059 

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0.43941 

9.97304 

02 

99 

9.53384 

21 

9-56083 

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24 

0.43917 

9-97301 

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100 

9-53405 

9.56107 

0.43893 

9.97299 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.  P. 

109 


70  < 


20 < 


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d. 

Tan 

d.  c. 

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9.56107 

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9-97299 

100 

01 

9-53426 

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0.43870 

9.97296 

99 

02 

9-53447 

21 

9.56154 

~*\ 
23 

0.43846 

9-97293 

98 

03 

9-53468 

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9.56177 

24 

0.43823 

9.97290 

97 

24 

04 

9.53488 

21 

9.56201 

23 

0.43799 

9.97288 

96 

I 

2.4 

05 

9-53509 

9.56224 

0.43776 

9-97285 

95 

2 

4-8 

06 

9-53530 

21 

9.56248 

24 

23 

0.43752 

9.97282 

94 

3 

A 

7-2 

q  6 

07 

9-53551 

20 

9.56271 

24 

0.43729 

9.97279 

93 

y  •  ^ 
12  .0 

08 

9-53571 

21 

9-56295 

27 

0.43705 

9.97276 

92 

5 

Ty|          A 

09 

9-53592 

21 

9.56318 

•*o 

24 

0.43682 

9-97274 

9i 

7 

14  .  4 

16.8 

10 

9.536I3 

21 

9-56342 

23 

0.43658 

9.97271 

90 

8 

19-2 

II 

9.53634 

2O 

9-56365 

?A 

0.43635 

9.97268 

89 

9 

21.6 

12 

9.53654 

21 

9-56389 

*4 
27 

0.43611 

9.97265 

88 

13 

9.53675 

21 

9-56412 

*o 
24 

0.43588 

9'97263 

87 

14 

9.53696 

2O 

9.56436 

23 

0.43564 

9.97260 

86 

23 

IS 

9.537I6 

9.56459 

0.43541 

9-97257 

85 

I 

2.3 

16 

9-53737 

21 

9-56483 

24 

27 

0.43517 

9-97254 

84 

2 

4-6 

17 

9-53758 

2O 

9.56506 

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*>A 

0.43494 

9.9725I 

83 

3 

6-9 

18 

9-53778 

9.56530 

*4 

0.43470 

9.97249 

82 

4 

9.2 

19 

9-53799 

2O 

9.56553 

23 
23 

0-43447 

9.97246 

81 

5 

ii.  5 

T7    R 

20 

9.53819 

21 

9-56576 

24 

0.43424 

9.97243 

80 

7 

13-0 

16.1 

21 

9.53840 

21 

9.56600 

0"} 

0.43400 

9.97240 

79 

8 

18.4 

22 

9.53861 

20 

9-56623 

*o 
23 

0.43377 

9.97238 

78 

9 

20.7 

23 

9.53881 

21 

9.56646 

24 

0.43354 

9.97235 

77 

24 

9-53902 

20 

9-56670 

0-7 

0.43330 

9.97232 

76 

25 

9-53922 

9-56693 

•^o 

0.43307 

9.97229 

75 

26 

9-53943 

20 

9.56716 

23 

24 

0.43284 

9.97226 

74 

27 

9.53963 

21 

9.56740 

0-7 

0.43260 

9-97224 

73 

M 

28 

9.53984 

2O 

9-56763 

«J 

0.43237 

9.97221 

72 

mlL 

29 

9.54004 

21 

9-56786 

23 
24 

0.43214 

9.97218 

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2.1 

30 

9-54025 

2O 

9.56810 

23 

0.43190 

9.97215 

70 

2 

3 

4.2 

6.3 

31 

9.54045 

21 

9-56833 

*77 

0.43167 

9-97212 

69 

4 

8.4 

32 

9.54066 

2O 

9-56856 

•3 

2A 

0.43144 

9-97210 

68 

5 

10.5 

33 

9.54086 

21 

9-56880 

•**r 

23 

0.43120 

9.97207 

67 

6 

12.6 

34 

9-54107 

20 

9-56903 

0-7 

0.43097 

9.97204 

66 

7 

14-7 

35 

9-54127 

21 

9.56926 

Ai 

0.43074 

9-97201 

65 

8 

16.8 

36 

9.54148 

2O 

9.56949 

23 
24 

0.43051 

9.97198 

64 

9 

18.9 

37 

9.54168 

20 

9-56973 

0.43027 

9-97195 

63 

38 

9.54188 

9.56996 

23 

0.43004 

9.97I93 

62 

39 

9-54209 

20 

9.57019 

23 
23 

0.42981 

9.97190 

61 

20 

40 

9-54229 

21 

9.57042 

23 

0.42958 

9.97187 

60 

i 

2.0 

41 

9.54250 

2O 

9.57065 

0.42935 

9.97184 

59 

2 

4-0 

42 

9.54270 

20 

9-57089 

24 
23 

0.42911 

9.97i8i 

58 

3 

6.0 
8  o 

43 

9-54290 

21 

9.57112 

23 

0.42888 

9-97179 

57 

4 

5 

IO.O 

44 

9-543" 

20 

9.57135 

23 

0.42865 

9.97176 

56 

6 

12.  0 

45 

9-54331 

20 

9-57158 

00 

0.42842 

9.97173 

55 

7 

14.0 

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9-54351 

21 

9.57i8i 

^o 
23 

0.42819 

9.97170 

54 

8 

16.0 

47 

9-54372 

2O 

9-57204 

Oyf 

0.42796 

9.97167 

53 

9 

18.0 

48 

9-54392 

2O 

9.57228 

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23 

0.42772 

9.97164 

52 

49 

9.54412 

21 

9.57251 

23 

0.42749 

9.97162 

51 

50 

9-54433 

9.57274 

0.42726 

9.97159 

60 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

P.  P. 

110 ( 


(139) 


20' 


159' 


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d. 

Tan 

d.  c. 

Cot 

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p.p. 

50 

9.54433 

20 

9-57274 

23 

0.42726 

9-97159 

50 

5i 

9-54453 

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9-57297 

23 

0.42703 

9.97156 

49 

52 

9-54473 

20 

9-57320 

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9-97153 

48 

53 

9-54493 

21 

9-57343 

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23 

0.42657 

9-97150 

47 

23 

54 

9-54514 

9.57366 

0.42634 

9-97147 

46 

I 

2-3 

55 

9-54534 

9.57389 

23 

0.42611 

9-97145 

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37 
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29 
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26 
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24 
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9-96643 
9.96640 
9-96636 

9  96633 
9-96630 
9.96627 

3 
3 
3 
3 
4 
3 
3 
3 

79 
78 
77 
76 
75 
74 
73 
72 
71 

I 

2 

3 

4 
5 
6 
7 
8 
9 

19 

i-9 
3-8 

|:i 

9-5 
II.  4 
13  3 
15-2 
17.1 

30 

9.579I6 

9.61292 

0.38708 

9.96624 

70 

3i 

32 
33 
34 
35 
36 

37 
38 
39 

9-57935 
9-57953 
9-57972 

9-57990 
9.58008 
9.58027 

9-58045 
9.58064 
9.58082 

18 
19 
18 

18 
19 
18 

19 
18 

9-61314 
9.6I335 
9-61357 
9.61378 
9.61400 
9.  61422 

9.61443 
9-61465 
9.61486 

21 
22 
21 
22 
22 
21 
22 
21 
22 

0.38686 
0.38665 
0.38643 
0.38622 
0.38600 
0.38578 

0.38557 
0.38535 
0.38514 

9.96621 
9.96618 
9.96615 
9.96612 
9.96608 
9-96605 
9.96602 
9.96599 
9.96596 

3 
3 
3 
4 
3 
3 
3 
3 

69 
68 
67 
66 
65 
64 

63 
62 
61 

I 

2 

3 

4 

7 
8 
9 

18 

1.8 
3-6 
5-4 

7-2 

9-0 
10.8 

12.6 

14-4 
16.2 

40 

9.58101 

To 

9.61508 

0.38492 

9.96593 

60 

4i 
42 
43 
44 
45 
46 
47 
48 
49 

9.58H9 
9.58I37 
9-58156 

9-58I74 
9-58192 
9-58211 
9-58229 
9-58247 
9.58266 

18 
19 
18 

18 
19 
18 

18 
19 

fO 

9.61529 
9.6i55i 
9-61572 

9.61594 
9.61615 
9.61637 
9.61658 
9  .  61680 
9.61701 

22 
21 
22 
21 
22 
21 
22 
21 

0.38471 
0.38449 
0.38428 

0.38406 
0.38385 
0.38363 
0.38342 
0.38320 
0.38299 

9-96590 
9-96587 
9-96S83 
9.96580 
9.96577 
9-96574 
9.96571 
9.96568 
9.96565 

3 
3 
4 
3 
3 
3 
3 
3 
3 

59 
58 
57 
56 
55 
54 
53 

52 

5i 

I 

2 
3 

4 

7 
8 
9 

3 

0.3 
0.6 
0.9 

1.2 

1-5 
1.8 

2.1 
2.4 
2.7 

50 

9.58284 

9.61722 

0.38278 

9.96562 

50 

Cos 

d. 

Cot 

d.c. 

Tan 

Sin 

d. 

I 

>.  p. 

112° 


67 ( 


(143) 


22 


157' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

50 

9-58284 

18 

9.61722 

0.38278 

9-96562 

50 

Si 

9-58302 

9.6i744 

0.38256 

9.96558 

4 

49 

19 

52 

9-58321 

J9 

TQ 

9-61765 

21 

0.38235 

9.96555 

3 

48 

S3 

9.58339 

lo 
18 

9.61787 

22 
21 

0.38213 

9.96552 

3 

47 

I 
2 

2.2 

4-4 

54 

9.58357 

To 

9.61808 

0.38192 

9.96549 

46 

3 

6.6 

55 

9.58375 

lo 

9.61830 

22 

0.38170 

9.96546 

3 

45 

4 

8.8 

56 

9.58394 

*9 
18 

9.61851 

21 
21 

0.38149 

9.96543 

3 
3 

44 

5 
6 

II.  0 

13.2 

57 

9.58412 

TQ 

9.61872 

0.38128 

9.96540 

43 

7 

15-4 

58 

9.58430 

lo 

TQ 

9-61894 

22 

0.38106 

9.96536 

4 

42 

8 

17.6 

59 

9-5*448 

Jo 

10 

9-61915 

21 
21 

0.38085 

9.96533 

3 

41 

9 

19.8 

60 

9-58467 

*JF 

18 

9.61936 

0.38064 

9.96530 

3 

40 

61 

9.58485 

To 

9.61958 

0.38042 

9.96527 

3 

39 

21 

62 

9-58503 

lo 

To 

9.61979 

21 

0.38021 

9-96524 

3 

38 

i 

2.1 

63 

9-5852I 

lo 

18 

9.62001 

22 
21 

0-37999 

9.96521 

3 

4 

37 

2 

4-2 

6  i 

64 

9.S8539 

To 

9.62022 

0.37978 

9.96517 

36 

4 

**•  j 
8.4 

65 

9.58557 

lo 

9-62043 

21 

0-37957 

9.96514 

3 

35 

5 

10.5 

66 

9.58576 

!9 

TQ 

9  .  62065 

22 

0.37935 

9.965II 

3 

34 

6 

12.6 

67 

9-58594 

lo 

To 

9.62086 

21 

0.37914 

9.96508 

3 

33 

7 
8 

14.7 

16  8 

68 

9  58612 

lo 

TQ 

9.62107 

21 

0.37893 

9.96505 

3 

32 

9 

18.Q 

69 

9-58630 

lo 

18 

9.62128 

21 
22 

0.37872 

9-96502 

3 

31 

70 

9.58648 

18 

9.62150 

21 

0.37850 

9.96498 

4 

30 

71 

9.58666 

18 

9.62171 

0.37829 

9.96495 

29 

18 

72 

9-58684 

TQ 

9.62192 

21 

0.37808 

9.96492 

3 

28 

I 

1.8 

73 

9.58702 

lo 

9.62214 

22 

0.37786 

9-96489 

3 

27 

2 

3-6 

74 

9-58721 

J9 
18 

9-62235 

21 

O.37765 

9.96486 

3 

26 

3 

5-4 

75 

9.58739 

18 

9  .  62256 

21 

0.37744 

9-96483 

3 

25 

4 

5 

7-  2 
g  o 

76 

9.58757 

18 

9.62277 

21 
22 

0.37723 

9^479 

4 
3 

24 

6 

y  •  v 

10.8 

77 

9.58775 

To 

9-62299 

0.37701 

9.96476 

23 

7 

12.6 

78 

9.58793 

lo 

18 

9.62320 

21 

0.37680 

9-96473 

3 

22 

8 

14.4 
16.2 

79 

9.58811 

18 

9-62341 

21 
21 

0.37659 

9.96470 

3 

21 

80 

9-58829 

18 

9.62362 

21 

0.37638 

9.96467 

3 

20 

4f* 

81 

9-58847 

18 

9-62383 

0.37617 

9.96463 

19 

XI 

82 

9-58865 

18 

9-62405 

0.37595 

9.96460 

3 

18 

I 

i-7 

83 

9-58883 

18 

9.62426 

21 
21 

0-37574 

9-96457 

3 
3 

17 

3 

3-4 
5-1 

84 

9.58901 

18 

9.62447 

0.37553 

9.96454 

16 

4 

6.3 

85 

9-58919 

18 

9.62468 

0.37532 

9.96451 

3 

IS 

5 

8.5 

86 

9.58937 

18 

9.62489 

22 

0-375II 

9.96447 

4 
3 

14 

7 

10.  2 

11.9 

87 

9.58955 

18 

9.62511 

21 

0.37489 

9.96444 

13 

8 

13-6 

88 

9.58973 

18 

9-62532 

0.37468 

9.96441 

3 

12 

9 

15-3 

89 

9-5899I 

18 

9-62553 

21 

0.37447 

9-96438 

3 
3 

II 

90 

9-59009 

18 

9.62574 

21 

0.37426 

9.96435 

10 

9i 

9-59027 

18 

9-62595 

0.37405 

9.96432 

09 

4 

92 

9.59045 

18 

9.62616 

0.37384 

9.96428 

4 

08 

I 

0-4 

93 

9-59063 

18 

9-62637 

22 

0.37363 

9-96425 

3 

3 

07 

2 
3 

0.8 

1.2 

94 

9.59o8i 

T*7 

9.62659 

0-37341 

9.96422 

06 

4 

1.6 

95 

9-59098 

•*•/ 

18 

9.62680 

0.37320 

9.96419 

3 

05 

5 

2.0 

96 

9.59ii6 

18 

9.62701 

21 

0.37299 

9.96415 

4 
3 

04 

6 

7 

2-4 
2.8 

97 

9-59134 

18 

9  .  62722 

21 

0.37278 

9.96412 

03 

8 

32 

98 

9.59152 

18 

9-62743 

21 

0-37257 

9-96409 

3 

02 

9 

3-6 

99 

9.59I70 

18 

9.62764 

21 

0.37236 

9.96406 

3 
3 

01 

100 

9-59188 

9-62785 

0.37215 

9-96403 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

112* 


67' 


(144) 


23' 


156' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

01 
02 

03 
04 
05 
o6 

o? 
08 
09 
10 
ii 

12 
13 

14 

IS 
16 

17 
18 
19 
20 

21 
22 
23 

24 

25 
26 

27 

28 

29 
30 

31 
32 
33 
34 
35 
36 

37 
38 
39 
40 

4i 
42 
43 
44 
45 
46 

47 
48 
49 
50 

9.S9I88 

18 

17 
18 
18 
18 
18 
18 

17 
18 
18 
18 

17 
18 
18 
18 
17 
18 

18 
18 
I? 
18 
18 
17 
18 
18 
17 
18 

17 
18 
18 

17 
18 
17 
18 

18 
17 
18 

17 
18 
I? 
18 

17 
18 
17 
18 
17 
18 

17 
18 
17 

9.62785 

21 
21 
21 
21 
21 
22 
21 
21 
21 
21 
21 
21 
21 
21 
21 
2O 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
21 
2O 
21 
21 
21 
21 
21 
21 
20 
21 
21 
21 
21 
20 
21 
21 
21 
20 
21 
21 
21 
2O 
21 

0.37215 

9.96403 

4 
3 
3 
3 
3 
4 
3 
3 
3 
4 
3 
3 
3 
4 
3 
3 
3 
4 
3 
3 
3 
4 
3 
3 
3 
4 
3 
3 
3 
4 
3 
3 

4 
3 
3 
4 
3 
3 
3 
4 
3 
3 
3 
4 
3 
3 
4 
3 
3 

100 

99 
98 
97 
96 
95 
94 
93 

92 

9i 
90 

89 
88 
87 
86 
85 
84 

83 
82 
81 
80 

79 
78 
77 
76 
75 
74 
73 

72 

71 
70 

69 
68 
67 
66 
65 
64 

63 
62 
61 
60 

59 
58 
57 
56 
55 
54 
53 
52 
Si 
50 

I 

2 

3 
4 
5 
6 
7 
8 
9 

I 

2 

3 
4 
5 
6 
7 
8 
9 

I 

2 

3 

4 

I 
I 

9 

I 

2 

3 

4 

i 

I 

9 

I 

2 

3 

4 

7 
8 
9 

21 

2.1 
4.2 
6.3 
8.4 
10.5 
12.6 

14-7 
16.8 
18.9 

20 

2.0 

4-0 
6.0 
8.0 

10.  0 
12.  0 
IA.O 

16.0 
18.0 

18 

1.8 
3-6 

5-4 

7-2 
9.0 
10.8 

12.6 

14.4 
16.2 

17 

1-7 
3-4 

ii 

8.5 

10.2 

ii.  9 

13.6 
15.3 

3 

0-3 
0.6 
0.9 

1.2 
I-S 

1.8 

2.1 

2.4 
2.7 

9.59206 
9.59223 
9-S924I 
9-59259 
9-59277 
9-59295 
9-59313 
9-59330 
9-59348 

9.62806 
9.62827 
9.62848 
9.62869 
9  .  62890 
9.62912 

9-62933 
9.62954 
9-62975 

0.37194 
0.37173 
0.37152 

0.37131 
0.37110 
0.37088 

0.37067 
0.37046 
0.37025 

9.96399 
9.96396 
9-96393 
9.96390 
9.96387 
9-96383 
9-96380 
9.96377 
9.96374 

9-59366 

9.62996 

0.37004 

9-96370 

9.59384 
9.59401 
9-59419 
9-59437 
9-59455 
9-59472 

9-59490 
9.59508 
9-59526 

9.63017 
9.63038 
9-63059 
9.63080 
9.63101 
9.63121 
9.63142 
9-63163 
9  63184 

0.36983 
0.36962 
0.36941 
0.36920 
0.36899 
0.36879 
0.36858 
0.36837 
0.36816 

9-96367 
9.96364 
9-96361 
9-96357 
9-96354 
9-9635I 
9.96348 
9-96344 
9.96341 

9-59543 

9-63205 

0.36795 

9-96338 

9-59561 
9-59579 
9-59596 

9-596I4 
9-59632 
9-59649 
9.59667 
9-59684 
9-59702 

9.63226 
9.63247 
9.63268 

9-63289 
9  63310 
9-6333I 
9-63352 
9  63373 
9-63393 

0.36774 
0.36753 
0.36732 
0.36711 
0.36690 
0.36669 
0.36648 
0.36627 
0.36607 

9-96335 
9-96331 
9-96328 

9-96325 
9.96322 
9-96318 

9-96315 
9-96312 
9-96309 

9.59720 

9-59737 
9-59755 
9-59772 

9-5979° 
9.59808 
9.59825 

9-59843 
9.5986o 
9.59878 

9  63414 

0.36586 

9-96305 

9-63435 
9-63456 
9-63477 
9.63498 
9-63519 
9-63539 
9-63560 
9-63581 
9.63602 

0.36565 
0.36544 
0.36523 

0.36502 
0.36481 
0.36461 
0.36440 
0.36419 
0.36398 

9-96302 
9.96299 
9-96296 
9.96292 
9.96289 
9.96286 
9.96282 
9.96279 
9.96276 

9-59895 

9  63623 

0.36377 

9-96273 

9-59913 
9-59930 
9-59948 
9.59965 
9-59983 
9.60000 

9.60018 
9-60035 
9-60053 

9-63643 
9-63664 
9-63685 
9.63706 
9-63726 
9-63747 
9.63768 
9.63789 
9-63809 

0.36357 
0.36336 
0.36315 
0.36294 
0.36274 
0.36253 
0.36232 
0.36211 
0.36191 

9.96269 
9.96266 
9.96263 
9.96260 
9.96256 
9-96253 
9.96250 
9.96246 
9-96243 

9.60070 

9-63830 

0.36170 

9.96240 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

113' 


66' 


(H5) 


156' 


Sin 

d. 

Tan 

d.c. 

Cot 

Cos 

d. 

p 

P. 

50 

9.60070 

9.63830 

0.36170 

9.96240 

50 

Si 

53 

53 

54 
55 
56 

57 

58 
59 

9.60087 
9  .  60105 
9.60122 
9.60140 
9.60157 
9.60174 

9.60192 
9.60209 
9  .  60227 

18 
17 
18 

17 
17 
18 

17 

18 

9-63851 
9.63872 
9-63892 

9.639I3 
9-63934 
9-63954 
9.63975 
9.63996 
9.64016 

21 
2O 
21 
21 
20 
21 
21 
20 

0.36149 
0.36128 
0.36108 
0.36087 
0.36066 
0.36046 

0.36025 
0.36004 
0.35984 

9-96236 
9-96233 
9-96230 
9-96227 
9-96223 
9.96220 

9.96217 
9-96213 
9.96210 

3 
3 
3 

4 
3 
3 
4 
3 

49 
48 
47 
46 
45 
44 

43 

42 
41 

I 

2 
3 

4 

7 
8 
9 

21 

2.1 

ti 

8.4 
10.5 
12.6 
14-7 
16.8 
18.9 

60 

9.60244 

9.64037 

0.35963 

9.96207 

40 

61 
62 
63 
64 
65 
66 

6? 
68 
69 

9.60261 
9.60279 
9.60296 

9-60313 
9-60331 
9-60348 

9-60365 
9.60382 
9.60400 

18 
I? 
17 
18 
17 
I? 

17 
18 

9.64058 
9.64078 
9.64099 
9  .  64120 
9.64140 
9.64161 
9.64182 
9  .  64202 
9-64223 

20 
21 
21 
2O 
21 
21 
20 
21 

0-35942 
0.35922 
0.35901 
0.35880 
0.35860 
0.35839 
0.35818 
0.35798 
0.35777 

9-96203 
9.96200 
9.96197 

9.96I93 
9.96190 
9-96187 
9.96184 
9.96180 
9.96177 

3 
3 

4 
3 
3 
3 
4 
3 

39 
38 
37 
36 
35 
34 
33 
32 
31 

I 

2 

3 

4 
5 
6 
7 
8 
9 

20 

2.0 
4-0 
6.0 
8.0 

10.  0 
12.  0 

14.0 
16.0 
18.0 

70 

9.60417 

9.64243 

0.35757 

9.96174 

30 

71 

72 

73 
74 

75 
76 

77 
78 
79 

9.60434 
9-60451 
9-60469 
9.60486 
9.60503 
9.60520 
9-60538 
9.60555 
9-60572 

17 
18 
17 
17 
17 
18 

17 
17 

9.64264 
9-64285 
9-64305 
9-64326 
9.64346 
9.64367 

9-64387 
9.64408 
9-64429 

21 
20 
21 
20 
21 
20 
21 
21 

0.35736 
0.35715 
0.35695 
0.35674 
0.35654 
0.35633 
0.35613 
0.35592 
0.35571 

9.96170 
9-96167 
9.96164 
9.96160 
9.96157 
9.96I54 
9-96150 
9.96147 
9.96144 

3 
3 
4 
3 
3 
4 
3 
3 

29 
28 
27 
26 

25 

24 
23 

22 
21 

I 

2 
3 

4 

I 

7 
8 
9 

18 

1.8 
3.6 
5-4 

7-2 

9.0 
10.8 

12.6 

14.4 
16.2 

80 

9-60589 

9.64449 

0.35551 

9.96140 

-1 

20 

17 

81 
82 
83 
84 
85 
86 

87 
88 
89 

9.60606 
9.60624 
9.60641 
9.60658 
9-60675 
9.60692 

9.60709 
9.60726 
9.60744 

18 
17 
17 
17 
17 
17 

17 
18 

9.64470 
9.64490 
9-64511 
9.64531 
9.64552 
9.64572 
9.64593 
9.64613 
9-64634 

20 
21 
20 
21 
20 
21 
20 
21 
20 

0.35530 
0.35510 
0.35489 
0.35469 
0.35448 
0.35428 

0.35407 
0.35387 
0.35366 

9-96I37 
9.96134 
9.96130 
9.96127 
9-96123 
9.96120 

9.96117 
9.96113 
9.96110 

3 
4 
3 
4 
3 
3 
4 
3 
3 

19 
18 
17 
16 
15 
14 
13 

12 
II 

I 

2 

3 

4 
5 
6 
7 
8 
9 

1.7 
3.4 

1:1 

8.5 
IO.2 

II.  9 

13.6 
15.3 

90 

9.60761 

9.64654 

2O 

0.35346 

9.96107 

10 

9i 
92 
93 
94 
95 
96 
97 
98 
99 

9.60778 
9-60795 
9.60812 

9.60829 
9.60846 
9.60863 
9.60880 
9.60897 
9.60914 

17 
17 
17 
I? 
17 
17 
17 
17 
17 

9-64674 
9-64695 
9.647I5 
9.64736 
9.64756 
9.64777 

9.64797 
9.64818 
9-64838 

21 

20 
21 
2O 
21 
20 
21 
20 
20 

0.35326 
0-35305 
0.35285 
0.35264 
0.35244 
0.35223 

0.35203 
0.35182 
0.35162 

9.96103 
9.96100 
9.96097 

9.96093 
9.96090 
9.96087 
9  96083 
9.96080 
9-96076 

3 
3 
4 
3 
3 
4 
3 
4 
3 

09 
08 

07 
06 
05 
04 
03 

02 
OI 

2 

3 

4 
5 
6 
7 
8 
9 

4 

0.4 
0.8 

1.2 

1.6 

2.0 
2-4 
2.8 
32 

3-6 

100 

9-60931 

9-64858 

0.35142 

9-96073 

00 

Cos 

d. 

Cot 

d.c. 

Tan 

Sin 

d. 

F 

.  P. 

113' 


66' 


(146) 


165< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

F 

.P. 

00 

9-60931 

9-64858 

0.35142 

9-96073 

100 

01 
02 
03 
04 

05 
06 

o? 
08 
09 

9.60948 
9-60965 
9.60982 
9.60999 
9.61016 
9-61033 
9.61050 
9.61067 
9.61084 

17 
17 
17 
17 
17 
17 
17 
17 

9.64879 
9.64899 
9-649I9 
9.64940 
9.64960 
9.64981 
9.65001 
9.65021 
9-65042 

20 
20 
21 
20 
21 
2O 
20 
21 

0.35121 
0.35101 
0.35081 
0.35060 
0.35040 
0.35019 

0.34999 
0.34979 
0.34958 

9.96070 
9.96066 
9-96063 
9.96060 
9.96056 
9-96053 

9.96049 
9.96046 
9-96043 

4 
3 
3 
4 
3 
4 
3 
3 

99 
98 
97 
96 
95 
94 
93 

92 

9i 

I 

2 

3 

4 
5 
6 
7 
8 
9 

21 

2.1 

4-2 

6.3 

8.4 
10.5 

12.6 

14-7 
16.8 
18.9 

10 

9.61101 

9  .  65062 

0.34938 

9-96039 

90 

ii 

12 
13 
14 
15 
16 

17 

18 
19 

9.61118 
9-6II35 
9.61152 

9.61169 
9.61186 
9.61203 
9.61220 
9.61236 
9  61253 

17 
17 
17 
17 
17 
17 
16 
17 

9.65082 
9-65103 
9-65123 

9-65143 
9.65164 
9.65184 
9.65204 
9.65224 
9-65245 

21 

20 
20 
21 
20 
20 
20 
21 

0.34918 
0.34897 
0.34877 
0.34857 
0.34836 
0.34816 
0.34796 
0.34776 
0.34755 

9-96036 
9-96032 
9.96029 
9.96026 
9.96022 
9-96019 
9.96015 
9.96012 
9.96009 

4 
3 
3 
4 
3 
4 
3 
3 

89 
88 
87 
86 
85 
84 

83 
82 

81 

I 

2 
3 

4 

7 
8 
9 

20 

2.0 
4-0 

6.0 
8.0 

10.  0 
12.0 

14-0 

16.0 
18.0 

20 

9.61270 

9-65265 

0.34735 

9.96005 

80 

21 
22 
23 
24 
25 
26 

27 
28 
29 

9.61287 
9.61304 
9.61321 

9.61338 
9-61354 
9.61371 
9.61388 
9.61405 
9.61422 

17 
17 
17 
16 
17 
17 
17 
17 
16 

9-65285 
9.65306 
9-65326 

9.65346 
9.65366 
9-65387 
9.65407 
9.65427 
9-65447 

21 
2O 
20 
20 
21 
20 
20 
20 

0-34715 
0.34694 
0.34674 
0.34654 
0.34634 
0.34613 
0-34593 
0-34573 
0.34553 

9.96002 
9-95998 
9-95995 
9-95992 
9-95988 
9^5985 
9-95981 
9-95978 
9-95974 

4 
3 
3 
4 
3 
4 
3 
4 

79 
78 
77 
76 
75 
74 
73 

72 

7i 

I 

2 
3 

4 

I 

7 
8 
9 

17 

1-7 
3-4 
5-1 
6.8 
8.5 

IO.2 
II.9 

13-6 
15-3 

30 

9-61438 

9-65467 

0.34533 

9-95971 

3 

70 

3i 
32 
33 
34 
35 
36 

37 
38 
39 

9.61455 
9.61472 
9-61489 
9.61506 
9.61522 
9-61539 
9-6I556 
9-61573 
9-61589 

17 
17 
17 
16 
17 
17 

17 
16 

9-65488 
9.65508 
9-65528 

9-65548 
9-65568 
9.65589 
9.65609 
9-65629 
9-65649 

20 
20 
20 
20 
21 
2O 
20 
20 

0.34512 
0,34492 
0.34472 
0.34452 
0.34432 
0.34411 

0-34391 
0.34371 
0.34351 

9-95968 
9.95964 
9.9S96I 

9-95957 
9-95954 
9-95950 

9-95947 
9-95944 
9-95940 

3 

4 
3 
4 
3 
4 
3 
3 
4 

69 
68 
67 
66 
65 
64 

63 
62 
61 

I 

2 

3 

4 
5 
6 

7 
8 
9 

16 

1.6 

3-2 

4-8 
6.4 
8.0 
9.6 

II.  2 
12.8 
14.4 

40 

9.61606 

9-65669 

0-34331 

9-95937 

3 

60 

41 
42 
43 
44 
45 
46 

47 
48 
49 

9.61623 
9.61639 
9.61656 

9.61673 
9.61689 
9.61706 

9.61723 
9-61739 
9.61756 

16 
I? 
17 
16 
17 
17 
16 
17 

9.65689 
9-65710 
9-65730 
9  65750 
9.65770 
9.65790 
9.65810 
9.65830 
9-65850 

21 

20 
20 
2O 
2O 
20 
2O 
2O 

0.343H 
0.34290 
0.34270 
0.34250 
0.34230 
0.34210 

0.34190 
0.34170 
0.34150 

9-95933 
9-95930 
9.95926 

9-95923 
9.95920 
9.95916 
9-95913 
9.95909 
9.95906 

3 
4 
3 
3 
4 
3 
4 
3 

59 
58 
57 
56 
55 
54 
53 

52 

Si 

I 

2 

3 
4 
5 
6 
7 
8 
9 

3 

0.3 
0.6 
0.9 

1.2 

1.5 
1.8 

2.1 

2.4 

2.7 

50 

9-61773 

9-65870 

0.34130 

9-95902 

4 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

I 

'.p. 

65< 


d47) 


165< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

I 

>.  P. 

50 

9-61773 

16 

9-65870 

0.34130 

9-95902' 

50 

Si 

52 

53 
54 
55 
56 

57 
58 
59 

9-61789 
9.61806 
9.61823 

9.61839 
9.61856 
9.61872 
9.61889 
9.61906 
9.61922 

16 

16 
17 

17 
16 

9-65890 
9-65911 
9.65931 
9.65951 
9.65971 
9.6599I 
9.66011 
9.66031 
9.66051 

21 
2O 
2O 
20 
2O 
20 
20 
20 

0.34110 
0.34089 
0.34069 

0.34049 
0.34029 
0.34009 

0.33989 
0.33969 
0.33949 

9.95899 
9.95895 
9-95892 
9-95888 
9.95885 
9.95882 

9-95878 
9.95875 
9.9587I 

4 
3 
4 
3 
3 
4 
3 
4 

49 
48 
47 
46 

45 
44 
43 
42 
41 

i 

2 

3 

4 

i 

7 
8 
9 

20 

2.0 

4.0 
6.0 
8.0 

IO.O 
12.  0 

14.0 

16.0 
18.0 

60 

9.61939 

16 

9.66071 

0.33929 

9-95868 

40 

fa 

62 
63 
64 
65 
66 

67 
68 
69 

9.61955 
9.61972 
9.61988 
9.62005 
9.62021 
9.62038 
9.62054 
9.62071 
9.62087 

16 
17 
16 
17 

16 

17 
16 

9  .  66091 
9.66111 
9.66131 
9.66151 
9.66171 
9.66191 
9.66211 
9.66231 
9.66251 

20 
20 
20 
2O 
20 
20 
20 
2O 

0.33909 
o  .  33889 
0.33869 

0.33849 
0.33829 
0.33809 

0.33789 
0.33769 
0.33749 

9.95864 
9.9586i 
9-95857 
9.95854 
9.95850 
9-95847 

9.95843 
9.95840 
9-95836 

3 

4 
3 
4 
3 
4 
3 
4 

39 
38 
37 
36 
35 
34 
33 
32 
31 

i 

2 

3 

4 

I 

7 
8 
9 

19 

19 
3-8 

& 

9-5 
ii.  4 
13  3 
15-2 
17.1 

70 

9.62104 

rfi 

9.66271 

20 

0.33729 

9.95833 

30 

71 

72 

73 

74 
75 
76 

77 
78 
79 

9.62120 
9-62137 
9-62153 
9.62170 
9.62186 
9.62203 
9.62219 
9-62235 
9.62252 

17 
16 
17 
16 
17 
16 

16 

17 

9.66291 
9.66311 
9.66331 
9-6635I 
9.66371 
9-66391 
9.66411 
9.66430 
9.66450 

2O 
20 
20 
2O 
20 
20 

19 
2O 

0.33709 
0.33689 
0.33669 

0.33649 
0.33629 
0.33609 
0.33589 
0.33570 
0-33550 

9-95829 
9-95826 
9-95822 

9-958I9 
9.95815 
9-95812 
9.958o8 
9.95805 
9.958oi 

3 

4 
3 
4 
3 
4 
3 
4 

29 
28 
27 
26 
25 
24 
23 

22 
21 

I 

2 

3 

4 

I 

9 

17 

1-7 
3-4 
5-1 
6.8 
8.5 

10.2 

ii.  9 

13.6 
15.3 

80 

9.62268 

9.66470 

6.33530 

9-95798 

20 

81 
82 
83 
84 
85 
86 

87 
88 
89 

9.62285 
9.62301 
9.62317 
9-62334 
9.62350 
9-62367 
9  62383 
9.62399 
9.62416 

16 
16 
17 
16 

16 
16 

9.66490 
9.66510 
9.66530 
9.66550 
9-66570 
9.66590 
9.66609 
9.66629 
9-66649 

20 
20 
20 
20 
20 
19 
20 
20 

0.33510 
0.33490 
0.33470 
0.33450 
0.33430 
0.33410 

0.33391 
0-33371 
0.33351 

9-95794 
9-95791 
9-95787 

9-95784 
9.95780 
9-95777 
9-95773 
9-95770 
9.95766 

3 

4 
3 
4 
3 
4 
3 
4 

19 
18 
17 
16 
15 
14 
13 

12 
II 

i 

2 
3 
4 
5 
6 

I 

9 

16 

1.6 

3-2 

4-8 
6.4 
8.0 
9-6 
ii.  a 

12.8 

14.4 

90 

9-62432 

Tr. 

9.66669 

0.33331 

9.95763 

10 

92 
93 
94 
95 
96 

97 
98 
99 

9.62448 
9.62465 
9.62481 

9-62497 
9-62513 
9.62530 
9.62546 
9.62562 
9.62579 

i? 

16 
16 
17 
16 

16 

Tfi 

9.66689 
9-66709 
9-66729 

9.66748 
9.66768 
9.66788 
9.66808 
9.66828 
9.66847 

20 
2O 
19 
20 
20 
20 
2O 
19 

0-333II 
0.33291 
0.33271 
0.33252 
0.33232 
0.33212 

0.33192 
0.33172 
0.33153 

9-95759 
9-95756 
9-95752 

9-95749 
9-95745 
9-95742 
9  95738 
9-95735 
9.95731 

3 

4 
3 
4 
3 

4 
3 

4 

09 
08 
07 
06 
05 
04 
03 

02 
01 

i 

2 

3 

4 

I 

7 
8 
9 

4 

0.4 
0.8 

1.2 

1.6 

2.0 
2.4 
2.8 
3-2 

100 

9-62595 

9.66867 

20 

0.33133 

9.95728 

00 

Cos 

d 

Cot 

d.  c. 

Tan 

Sin 

d. 

F 

.p. 

114° 


65' 


(148) 


25< 


154 ' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

I 

'.  P. 

00 

9.62595 

rfi 

9.66867 

0.33133 

9-95728 

100 

OI 

02 
03 
04 
05 
06 

07 
08 
09 

9.62611 
9  .  62627 
9.62644 
9.62660 
9.62676 
9.62692 
9.62708 
9.62725 
9.62741 

16 

17 

16 
16 
16 
16 

17 
16 
16 

9.66887 
9-66907 
9.66927 

9.66946 
9.66966 
9.66986 
9.67006 
9-67025 
9.67045 

20 
20 
19 
20 
2O 
2O 

19 

2O 

0.33H3 
0.33093 
0.33073 
0.33054 
0.33034 
0.33014 

0.32994 
0.32975 
0-32955 

9.95724 
9.95720 
9-95717 
9-95713 
9.95710 
9-95706 

9-95703 
9.95699 
9-95696 

4 
3 
4 
3 
4 
3 
4 
3 

99 
98 
97 
96 
95 
94 
93 
92 
9i 

I 

2 

3 

4 

1 

7 
8 
9 

20 

2.0 

4.0 
6.0 
8.0 

IO.O 
12.0 
14.0 

16.0 
18.0 

10 

9-62757 

rfi 

9-67065 

0.32935 

9-95692 

90 

ii 

12 
13 

14 
IS 
if 

17 
18 
19 

9-62773 
9.62789 
9.62806 
9.62822 
9.62838 
9.62854 
9.62870 
9.62886 
9  .  62902 

16 
17 
16 
16 
16 
16 
16 
16 
16 

9-67085 
9.67104 
9.67124 

9.67144 
9-67163 
9-67183 
9-67203 
9-67223 
9.67242 

19 

20 
2O 

19 
2O 
20 
2O 
19 

0.32915 
0.32896 
0.32876 
0.32856 
0.32837 
0.32817 
0.32797 
0.32777 
0.32758 

9-95689 
9.95685 
9-95681 
9.95678 
9-95674 
9-95671 
9-95667 
9.95664 
9-9566o 

3 

4 
4 
3 
4 
3 
4 
3 
4 

89 
88 
87 
86 
85 
84 

83 
82 
81 

I 

2 

3 

4 

1 
1 

9 

19 

i-9 
3-8 

1:1 

9-5 
ii.  4 
13-3 
15.2 
17.1 

20 

9.62918 

9.67262 

0.32738 

9.95657 

80 

21 
22 
23 
24 
25 
26 

27 
28 
29 

9-62935 
9-62951 
9.62967 

9-62983 
9.62999 
9-63015 
9-63031 
9-63047 
9-63063 

17 
16 
16 
16 
16 
16 
16 
16 
16 
16 

9.67282 
9-67301 
9-67321 

9-6734I 
9-67360 
9-67380 

9.67399 
9.674I9 
9.67439 

19 
2O 
2O 

19 

20 
19 
2O 
2O 

0.32718 
0.32699 
0.32679 
0.32659 
0.32640 
0.32620 
0.32601 
0.32581 
0.32561 

9-95653 
9-95649 
9-95646 

9-95642 
9.95639 
9.95635 
9-95632 
9-95628 
9.95624 

4 
4 
3 
4 
3 
4 
3 
4 
4 

79 
78 
77 
76 
75 
74 
73 

72 
71 

i 

2 

3 

4 
5 
6 
7 
8 
9 

17 

1-7 
3-4 
5-1 
6.8 
8.5 
10.2 

ii.  9 
13-6 
15-3 

30 

9-63079 

-rf. 

9.67458 

0.32542 

9-95621 

70 

31 
32 
33 
34 
35 
36 

37 
38 
39 

9-63095 
9.63111 
9-63127 
9.63I43 
9-63I59 
9.63I75 
9.63191 
9-63207 
9-63223 

16 
16 
16 
16 
16 
16 
16 
16 
16 

9.67478 
9.67498 
9.67517 
9.67537 
9.67S56 
9.67576 
9.67596 
9-67615 
9-67635 

2O 
19 
20 

19 
20 
20 

19 
20 

0.32522 
0.32502 
0.32483 

0.32463 
0.32444 
0.32424 
0.32404 
0.32385 
0.32365 

9.956I7 
9-95614 
9.956io 

9.956o6 
9-95603 
9-95599 
9  95596 
9-95592 
9-95588 

4 
3 
4 
4 
3 
4 
3 
4 
4 

69 
68 
67 
66 
65 
64 

63 
62 
61 

i 

2 

3 

4 
5 
6 
7 
8 
9 

16 

1.6 

3-2 

4.8 
6.4 
8.0 
9.6 

II.  2 
12.8 
14-4 

40 

9-63239 

16 

9.67654 

0.32346 

9.95S85 

60 

4i 
42 
43 
44 
45 
46 

47 
48 
49 

9-63255 
9.63271 
9-63287 

9-63303 
9-63319 
9-63335 
9.6335I 
9-63367 
9-63383 

16 
16 
16 
16 
16 
16 
16 
16 

9.67674 
9.67693 
9.677I3 
9.67732 
9.67752 
9.67772 

9.67791 
9.67811 
9.67830 

19 

2O 

19 
2O 
2O 
19 
2O 
19 

0.32326 
0.32307 
0.32287 
o  .  32268 
0.32248 
0.32228 

0.32209 
0.32189 
0.32170 

9.9558I 
9-95578 
9-95574 
9-95570 
9-95567 
9.95563 
9.9556o 
9-95556 
9-95552 

3 

4 
4 
3 
4 
3 
4 
4 

59 
58 
57 
56 
55 
54 
53 

52 

Si 

I 
2 
3 
4 
5 
6 
7 
8 
9 

3 

•3 

.9 
.2 

•  5 
.8 
.1 

•  4 
•  7 

50 

9-63398 

9-67850 

0.32150 

9-95549 

3 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

\ 

.  P. 

64' 


(149) 


26< 


154' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

f 

.  P. 

60 

9.63398 

16 

9-67850 

0.32150 

9-95549 

50 

Si 

52 

53 
54 
55 
56 

57 
58 
59 

9.63414 
9.63430 
9-63446 
9-63462 
9.63478 
9-63494 
9-63SIO 
9.63525 
9-6354I 

16 
16 
16 
16 
16 
16 

IS 
16 
16 

9.67869 
9.67889 
9.67908 
9.67928 
9-67947 
9.67967 
9.67986 
9.68005 
9.68025 

19 

20 
19 
20 

19 

2O 
19 

19 

2O 

0.32131 
0.32111 
0.32092 
0.32072 
0.32053 
0.32033 

0.32014 
0.31995 
0.31975 

9-95545 
9-95542 
9-95538 

9-95534 
9-95531 
9-95527 

9-95523 
9-95520 
9.95516 

4 
3 
4 
4 
3 
4 
4 
3 
4 

49 
48 
47 
46 
45 
44 

43 
42 
41 

I 

2 

3 

4 
5 
6 
7 
8 
9 

20 

2.0 

4-o 
6.0 
8.0 

10.  0 
12.  0 
14.0 

16.0 
18.0 

60 

9-63557 

16 

9.68044 

0.31956 

9-95513 

40 

61 
62 
63 
64 
65 
66 

67 
68 
69 

9-63573 
9.63589 
9.63604 

9.63620 
9.63636 
9.63652 
9.63668 
9.63683 
9.63699 

16 
15 
16 

16 
16 
16 

IS 
16 
16 

9.68064 
9.68083 
9.68103 
9.68122 
9.68142 
9.68161 
9.68180 
9.68200 
9.68219 

19 

2O 

19 
20 
19 
19 
20 
19 

0.31936 
0.31917 
0.31897 
0.31878 

0.31858 
0.31839 
0.31820 
0.31800 

0.31781 

9.95509 
9-95505 
9-95502 

9-95498 
9-95494 
9-95491 
9.95487 
9.95483 
9.95480 

4 
3 
4 
4 
3 
4 
4 
3 

39 
38 
37 
36 
35 
34 
33 
32 
31 

I 

2 

3 

4 
5 
6 
7 
8 
9 

19 

i-9 
3-8 

\l 

9-5 
II.  4 
13-3 
IS-2 
I7-I 

70 

9.63715 

16 

9.68239 

0.31761 

9-95476 

30 

71 

72 

73 
74 
75 
76 

77 
78 
79 

9.6373I 
9.63746 
9.63762 

9.63778 
9-63794 
9.63809 

9-63825 
9-63841 
9-63856 

IS 
16 
16 
16 
IS 
16 

16 
IS 
16 

9.68258 
9.68277 
9-68297 
9.68316 
9.68336 
9-68355 
9.68374 
9-68394 
9-68413 

19 

20 
19 
20 
19 
19 
20 

19 

0.31742 
0.31723 
0.31703 
0.31684 
0.31664 
0.31645 
0.31626 
0.31606 
0.31587 

9-95473 
9.95469 
9.95465 
9.95462 
9-95458 
9-95454 
9-95451 
9-95447 
9-95443 

4 
4 
3 
4 
4 
3 
4 
4 

29 

28 
27 
26 

25 

24 

23 
22 
21 

I 

2 

3 

4 

i 

7 
8 
9 

16 

1.6 

ii 

6.4 
8.0 
9-6 

II.  2 
12.8 
14-4 

80 

9.63872 

16 

9-68432 

0.31568 

9-95440 

20 

81 
82 
83 
84 
85 
86 

87 
88 
89 

9.63888 
9-63903 
9.639I9 
9-63935 
9.63950 
9.63966 
9-63982 
9-63997 
9-64013 

IS 
16 
16 

IS 
16 
16 

IS 
16 

9.68452 
9.68471 
9.68490 

9.68510 
9.68529 
9.68548 
9.68568 
9.68587 
9.68606 

19 
19 

20 

19 
19 

20 

19 
19 

0.31548 
0.31529 
0.31510 

0.31490 
0.31471 
0.31452 
0.31432 
0.31413 
0.31394 

9-95436 
9-95432 
9-95429 

9-95425 
9-95421 
9.95418 

9-95414 
9-95410 
9-95407 

4 
3 
4 
4 
3 
4 
4 
3 

19 

18 
17 
16 
15 
14 
13 

12 
II 

2 
3 

4 

7 
8 
9 

15 

1-5 
3-0 
4-5 
6.0 
7-5 
9-0 
10.  s 

12.0 

13-5 

90 

9.64028 

16 

9.68626 

0.31374 

9-95403 

10 

9i 

92 

93 
94 
95 
96 

97 
98 
99 

9.64044 
9.64060 
9.64075 
9.64091 
9.64106 
9.64122 
9-64138 
9-64I53 
9.64169 

16 
IS 
16 

IS 

16 
16 

IS 
16 

9-68645 
9.68664 
9.68683 
9-68703 
9.68722 
9.68741 
9.68760 
9.68780 
9-68799 

19 
19 
20 

19 
19 
19 
20 

19 

0.31355 
0.31336 
0.31317 
0.31297 
0.31278 
0.31259 
0.31240 
0.31220 
0.31201 

9-95399 
9-95396 
9-95392 
9-95388 
9-95384 
9-95381 
9-95377 
9-95373 
9-95369 

3 

4 
'    4 
4 
3 
4 
4 
4 

09 
08 
07 
06 
05 
04 

03 

02 
01 

I 

2 
3 

4 

I 

7 
8 
9 

4 

-4 
.2 

.6 
.0 
•  4 
.8 

3-2 

3-6 

100 

9.64184 

9.68818 

0.31182 

9-95366 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P 

.P. 

115° 


64' 


(150) 


26< 


153< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

I 

J.  P. 

00 

9.64184 

16 

9.68818 

0.31182 

9.95366 

100 

OI 
02 

03 

04 

OS 
06 

07 
08 
09 

9.64200 
9-64215 
9.64231 
9.64246 
9.64262 
9.64277 

9-64293 
9-64308 
9-64324 

15 
16 
15 
16 
15 
16 

15 
16 

9-68837 
9-68857 
9.68876 

9-68895 
9.68914 
9-68934 

9-68953 
9-68972 
9-68991 

20 
19 
19 

19 
20 
19 
19 
19 

0.31163 
0.3H43 
0.31124 

0.31105 
0.31086 
0.31066 

0.31047 
0.31028 
o  .  31009 

9.9S362 
9-95359 
9-95355 
9-95351 
9-95348 
9-95344 
9-95340 
9-95336 
9-95333 

3 

4 
4 
3 
4 
4 
4 
3 

99 
98 
97 
96 
95 
94 
93 

92 

9i 

2 

3 

4 

7 
8 
9 

20 

2.0 

4-0 
6.0 
8.0 

IO.O 
12.  0 
I4.O 

16.0 
18.0 

10 

9-64339 

16 

9  .  69010 

0.30990 

9-95329 

90 

ii 

12 
13 

14 

IS 
16 

17 
18 
19 

9.64355 
9.64370 
9-64386 
9.64401 
9.64417 
9.64432 

9-64447 
9-64463 
9.64478 

15 
16 
IS 
16 
IS 
IS 
16 
IS 
16 

9-69029 
9.69049 
9.69068 

9.69087 
9.69106 
9-69125 

9.69144 
9-69164 
9-69183 

20 
19 
19 
19 
19 
19 
20 
19 

0.30971 
0.30951 
0.30932 

0.30913 
0.30894 
0.30875 

0.30856 
0.30836 
0.30817 

9-95325 
9-95322 
9.95318 

9-95314 
9-95310 
9.95307 
9-95303 
9.95299 
9.95295 

3 

4 
4 
4 
3 

4 
4 
4 

89 
88 
87 
86 
85 
84 

83 
82 
81 

i 

2 
3 

4 

i 
l 

9 

19 

i-9 
3-8 
5-7 
7.6 
9-5 
11.4 
13-3 
15.2 
17.1 

20 

9.64494 

It; 

9.69202 

0.30798 

9.95292 

80 

21 
22 
23 

24 

25 
26 

27 

28 
29 

9-64509 
9-64524 
9-64540 

9.64555 
9.6457I 
9-64586 

9.64601 
9.64617 
9.64632 

15 

16 
IS 
16 
15 
15 
16 
IS 
15 

9.69221 
9-69240 
9-69259 
9-69278 
9-69298 
9.693I7 
9.69336 
9.69355 
9.69374 

19 
19 
19 

2O 

19 
19 
19 
19 

0.30779 

0.30760 
0.30741 
0.30722 
0.30702 
0.30683 
o  .  30664 

0.30645 
0.30626 

9-95288 
9-95284 
9.95281 

9.95277 
9.95273 
9.95269 

9.95266 
9.95262 
9.95258 

4 
4 
3 
4 
4 
4 
3 
4 
4 

79 
78 
77 
76 
75 
74 
73 

72 

71 

i 

2 

3 

4 

i 

7 
8 
9 

16 

1.6 

3-2 

4-8 
6.4 
8.0 
9-6 

II.  2 
12.8 
14.4 

30 

9.64647 

16 

9.69393 

0.30607 

9-95254 

70 

3i 
32 
33 

34 
35 
36 

37 
38 
39 

9-64663 
9.64678 
9.64693 
9.64709 
9-64724 
9-64739 
9-64755 
9.64770 
9.64785 

is 
is 

16 

IS 
IS 
16 

IS 
IS 
15 

9.69412 
9.69431 
9-69450 

9.69469 
9.69488 
9.69507 
9-69526 
9.69545 
9-69565 

19 
19 
19 
19 
19 
19 
19 

20 

0.30588 
0.30569 
0.30550 

0.30531 
0.30512 
0.30493 
0.30474 
0.30455 
0.30435 

9.95251 
9.95247 
9-95243 

9.95239 
9.95236 
9-95232 
9.95228 
9-95224 
9-95221 

3 

4 
4 
4 
3 
4 
4 
4 
3 

69 
68 
67 
66 
65 
64 

63 
62 
61 

i 

2 

3 

4 
5 
6 
7 
8 
9 

15 

i.S 
3-0 
4-5 
6.0 
7-5 
9-0 
10.  S 
12.  0 
I3-S 

40 

9.64800 

16 

9.69584 

0.30416 

9.95217 

4 

60 

41 
42 
43 
44 
45 
46 

47 
48 
49 

9.64816 
9.64831 
9.64846 
9.64861 
9-64877 
9.64892 

9.64907 
9.64922 
9.64938 

IS 
IS 
IS 
16 
IS 
IS 

IS 
16 

9-69603 
9.69622 
9-69641 
9.69660 
9.69679 
9-69698 

9.697I7 
9.69736 
9.69755 

19 
19 
19 
19 
19 
19 
19 
19 

0.30397 
0.30378 
0.30359 
0.30340 
0.30321 
0.30302 
0.30283 
0.30264 
0.30245 

9-95213 
9.95209 
9.95206 

9-95202 
9.95198 
9.95I94 
9.95190 
9.95187 
9.95183 

4 

4 
3 
4 
4 
4 
4 
3 
4 

59 
58 
57 
56 
55 
54 
53 

52 

51 

i 

2 
3 

4 

7 
8 
9 

3 

0-3 
0.6 
o.9 

1.2 

i-S 
1.8 
2.1 
2.4 
2.7 

50 

9.64953 

9-69774 

0.30226 

9.95I79 

4 

50 

Cos 

d. 

Cot      j 

d.  C. 

Tan 

Sin 

d. 

p. 

p. 

(151) 


163' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

50 
51 

52 

53 

54 
55 
56 

57 
58 
59 
60 
6i 
62 
63 
64 
65 
66 

67 
68 
69 
70 
7i 

72 

73 

74 
75 
76 

77 
78 
79 
80 
81 
82 
83 
84 
85 
86 

87 
88 
89 
90 

9i 
92 
93 
94 
95 
96 
97 
98 
99 
100 

9-64953 

15 
15 

15 
16 

15 
IS 
15 
IS 
15 
15 
16 

15 
15 
15 
IS 
15 
IS 
IS 
IS 
15 
16 

15 
IS 
15 
15 
IS 
IS 
IS 
IS 
IS 
IS 
IS 
IS 
IS 
IS 
15 
15 
15 
IS 
IS 
IS 
14 
IS 
IS 
IS 
IS 
IS 
15 
15 
IS 

9-69774 

19 
19 
19 
19 
18 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
19 
18 
19 
19 
19 
19 
19 
19 

19 
18 
19 
19 
19 
19 
19 

19 
18 
19 
19 
19 
19 
18 
19 
19 
19 

19 
18 
19 
19 
19 
18 

19 
19 
19 

0.30226 

9-95179 

4 
3 

4 
4 
4 
4 
3 
4 
4 
4 
4 
3 
4 
4 
4 
4 
3 
4 
4 
4 
4 

3 

4 
4 
4 
4 
4 
3 
4 
4 
4 
4 
3 
4 

4 
4 
4 
4 
4 
3 
4 
4 
4 
4 
4 
3 
4 
4 
4 
4 

50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 

33 
32 
3i 
30 

29 

28 

27 

26 

25 

24 

23 
22 
21 

20 

19 
18 
17 
16 
15 
14 
13 

12 
II 

10 

09 
08 

07 
06 
05 
04 

03 
02 

OI 

00 

i 

2 

3 

4 
5 
6 
7 
8 
9 

I 

2 
3 
4 
5 
6 
7 
8 
9 

I 

2 
3 
4 
5 
6 
7 
8 
9 

I 

2 

3 

4 
5 
6 
7 
8 
9 

I 

2 
3 

4 

1 

9 

19 

1-9 
3-8 
5-7 
7.6 
9-5 
11.  4 
13-3 

IS-  2 
I7.I 

18 

1.8 
3-6 

5-4 

7-2 

9-0 
10.8 

12.6 

14-4 
16.2 

15 

i-S 
3-0 
4-5 
6.0 
7-5 
9-0 
10.5 

12.0 

13-5 

14 

1-4 

2.8 

4-2 
5-6 
7-0 
8.4 
9-8 

II.  2 
12.6 

4 

0.4 
0.8 

1.2 

1.6 

2.O 
2.4 
2.8 

1:1 

9.64968 
9-64983 
9.64998 

9.65014 
9-65029 
9-65044 
9-65059 
9-65074 
9-65089 

9.69793 
9.69812 
9-69831 
9-69850 
9.69868 
9.69887 
9.69906 
9-69925 
9-69944 

0.30207 
o  .  30188 
0.30169 
0.30150 
0.30132 
0.30113 
0.30094 
0.30075 
0.30056 

9-95175 
9.9SI72 
9.95168 

9.95164 
9.95i6o 
9.95I56 
9-95153 
9-95149 
9-95145 

9-65104 

9.69963 

0.30037 

9.95I4I 

9.65120 
9-65I35 
9-65I50 
9.65165 
9.65180 
9-65I95 
9.65210 
9-65225 
9-65240 

9.69982 
9.70001 
9  .  70020 
9.70039 
9-70058 
9.70077 
9.70096 
9.70114 
9-70133 

0.30018 
0.29999 
0.29980 

0.29961 
0.29942 
0.29923 
0.29904 
0.29886 
0.29867 

9.95137 
9-95134 
9-95I30 
9-95126 
9-95122 
9-95II8 

9-95115 
9-95III 
9-95107 

9-65255 

9.70152 

0.29848 

9-95103 

9-65271 
9.65286 
9-6530I 
9-653I6 
9.65331 
9-65346 
9-6536I 
9-65376 
9-65391 

9.70171 
9.70190 
9-70209 
9.70228 
9.70247 
9.70265 
9.70284 
9-70303 
9-70322 

0.29829 
0.29810 
0.29791 
0.29772 
0.29753 
0.29735 

0.29716 
0.29697 
0.29678 

9-95099 
9-95096 
9.95092 
9-95088 
9-95084 
9.9So8o 

9-95076 
9-95073 
9-95069 

9.65406 

9-70341 

0.29659 

9-95065 

9.65421 
9-65436 
9-65451 
9.65466 
9-65481 
9-65496 

9-655II 
9.65526 
9-6554I 

9-70360 
9-70379 
9-70397 
9.70416 
9.70435 
9-70454 
9.70473 
9.70491 
9.70510 

0.29640 
0.29621 
0.29603 

0.29584 
0.29565 
0.29546 
0.29527 
0.29509 
0.29490 

9.95o6i 
9-95057 
9.95054 
9.950SO 
9.95046 
9.95042 

9.95038 
9-95034 
9.95030 

9-65556 

9-70529 

0.29471 

9-95027 

9-6557I 
9-65585 
9.65600 

9-65615 
9-65630 
9-65645 
9.65660 
9-65675 
9-65690 

9.70548 
9-70567 
9-70585 
9.70604 
9-70623 
9.70642 
9.70660 
9.70679 
9-70698 

0.29452 
0.29433 
0.29415 
0.29396 
0.29377 
0.29358 

0.29340 
0.29321 
0.29302 

9-95023 
9.95019 
9-95015 
9  -9501  I 
9.95007 
9.95004 
9-95000 
9.94996 
9.94992 

9.65705 

9.70717 

o  .  29283 

9-94988 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

116° 


63' 


(152) 


27' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

9-65705 

9.70717 

18 

0.29283 

9.94988 

100 

01 

9-65720 

15 

9-70735 

0.29265 

9.94984 

4 

99 

10 

02 

9-65734 

14 

9.70754 

19 

0.29246 

9.94980 

4 

98 

03 

9-65749 

15 
15 

9-70773 

19 
19 

0.29227 

9-94976 

4 
3 

97 

I 

2 

19 
3-8 

04 

9.65764 

9.70792 

_Q 

0.29208 

9-94973 

96 

3 

5-7 

05 

9-65779 

15 

9.70810 

lo 

0.29190 

9.94969 

4 

95 

4 

7-6 

ob 

9-65794 

15 
15 

9-70829 

19 

0.29171 

9-94965 

4 
4 

94 

6 

9-5 
11.4 

07 

9-65809 

9.70848 

0.29152 

9.94961 

93 

7 

13  3 

08 

9-65823 

14 

9.70866 

18 

0.29134 

9-94957 

4 

92 

8 

IS-2 

09 

9-65838 

15 

9.70885 

19 

0.29115 

9-94953 

4 

91 

9 

I7.I 

10 

9.65853 

15 

9.70904 

TQ 

0.29096 

9-94949 

4 

90 

ii 

9.65868 

15 

9.70922 

lo 

0.29078 

9.94946 

3 

89 

18 

12 

9-65883 

15 

9.70941 

19 

0.29059 

9.94942 

4 

88 

I 

1.8 

13 

9-65898 

15 

9.70960 

19 

TQ 

0.29040 

9.94938 

4 

87 

2 

3-6 

14 

9-65912 

14 

9.70978 

IS 

o  .  29022 

9-94934 

4 

86 

3 

4 

5-4 

7-2 

15 

9.65927 

15 

9.70997 

19 

0.29003 

9-94930 

4 

85 

5 

9.0 

16 

9-65942 

15 

9.71016 

19 

0.28984 

9-94926 

4 

84 

6 

10.8 

17 

9-65957 

15 

9-71034 

18 

0.28966 

9.94922 

4 

83 

7 
g 

12.6 

18 

9.65971 

14 

9-71053 

19 

0.28947 

9.94918 

4 

82 

14.4 
16.2 

19 

9.65986 

15 

9.71072 

19 

T  ft 

0.28928 

9.94914 

4 

81 

20 

9.66001 

15 

9.71090 

lo 

0.28910 

9.949H 

3 

80 

21 

9.66016 

15 

9.71109 

!9 

0.28891 

9.94907 

4 

79 

IB 

22 

9.66030 

14 

9.71128 

19 

0.28872 

9.94903 

4 

78 

23 

9-66045 

15 
15 

9.71146 

18 

0.28854 

9.94899 

4 

A 

77 

2 

1.5 

3-0 

24 

9.66060 

9.7H65 

0.28835 

9.94895 

76 

3 

4-5 

25 

9-66075 

15 

9.71184 

19 

0.28816 

9.94891 

4 

75 

4 

6.0 

26 

9.66089 

14 
15 

9.71202 

18 
19 

0.28798 

9-94887 

4 
4 

74 

1 

7-5 
9.0 

27 

9  .  66104 

9.71221 

0.28779 

9.94883 

73 

7 

10-5 

28 

9.66119 

15 

9-71239 

18 

0.28761 

9.94879 

4 

72 

8 

12.0 

29 

9  66133 

14 
IS 

9-71258 

19 

0.28742 

9.94875 

4 

71 

9 

13-5 

30 

9.66148 

9.71277 

To 

0.28723 

9.94871 

4 

70 

31 

9.66163 

IS 

9-7I295 

lo 

0.28705 

9-94868 

3 

69 

14 

32 

9.66177 

14 

9.7I3I4 

19 

0.28686 

9.94864 

4 

68 

i 

M 

33 

9.66192 

IS 

9-7I332 

18 

0.28668 

9.94860 

4 

67 

2 

2.8 

34 

9.66207 

15 

9.7I35I 

19 

0.28649 

9.94856 

4 

66 

3 

4 

4.2 

5-6 

35 

9.66221 

14 

9.71370 

19 

0.28630 

9.94852 

4 

65 

7-0 

36 

9.66236 

IS 

9.71388 

18 

0.28612 

9.94848 

4 

64 

6 

8.4 

37 

9.66251 

15 

9.71407 

19 

0.28593 

9.94844 

4 

63 

7 

9-8 

II.  2 

38 

9.66265 

14 

9.71425 

18 

0.28575 

9.94840 

4 

62 

9 

12.6 

39 

9.66280 

15 

T  C 

9.71444 

19 
18 

0.28556 

9.94836 

4 

61 

40 

9.66295 

•0 

T  A 

9.71462 

0.28538 

9.94832 

4 

60 

4i 

9.66309 

14 

9.7I48I 

J9 

0.28519 

9.94828 

4 

59 

3 

42 

9-66324 

15 

9.71499 

18 

o  .  28501 

9.94824 

4 

58 

I 

O.3 

43 

9-66338 

14 

9-7I5I8 

19 

0.28482 

9.94820 

4 

57 

2 

0.6 

44 

9-66353 

15 

9.7IS37 

19 

0.28463 

9.94817 

3 

56 

3 

0.9 

45 

9-66368 

15 

9.7I5S5 

18 

0.28445 

9.94813 

4 

55 

4 

1.2 

46 

9.66382 

14 
IS 

9-71574 

19 
18 

o  .  28426 

9.94809 

4 
4 

54 

5 
6 

1-5 

1.8 

47 

9.66397 

9.71592 

0.28408 

9.94805 

53 

7 

2.1 

48 

9.66411 

14 

9.71611 

19 

0.28389 

9.94801 

4 

52 

8 

2.4 

49 

9.66426 

15 

9.71629 

18 

0.28371 

9-94797 

4 

5i 

9 

2.7 

50 

9.66441 

15 

9.71648 

19 

0.28352 

9-94793 

4 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

117* 


62' 


d53) 


27< 


162  * 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

50 

9.66441 

T  A 

9.71648 

18 

0.28352 

9-94793 

50 

5i 

9-66455 

14 

9.71666 

0.28334 

9.94789 

4 

49 

1Q 

52 

9.66470 

15 

9.71685 

19 

,Q 

0.28315 

9.94785 

4 

48 

53 

9.66484 

14 
15 

9.7I703 

lo 

19 

0.28297 

9.94781 

4 
4 

47 

I 

2 

!-9 

3-8 

54 

9.66499 

9.71722 

TQ 

0.28278 

9-94777 

46 

3 

5-7 

55 

9.66513 

14 

9.71740 

lo 

0.28260 

9-94773 

4 

45 

4 

7-6 

56 

9.66528 

15 
14 

9-71759 

19 
18 

0.28241 

9-94769 

4 
4 

44 

I 

9-5 
11.4 

57 

9-66542 

9.71777 

0.28223 

9.94765 

43 

7 

13-3 

58 

9.66557 

15 

9.71796 

19 

To 

0.28204 

9.94761 

4 

42 

8 

15-2 

59 

9.66571 

14 

TC 

9.71814 

lo 

TO 

0.28186 

9-94757 

4 

41 

9 

17.1 

60 

9.66586 

lo 

9.71833 

xy 

TQ 

0.28167 

9-94753 

4 

40 

61 

9.66600 

14 

9.7I85I 

lo 

-rO 

0.28149 

9-94749 

4 

39 

18 

62 

9.66615 

15 

9.71869 

lo 

0.28131 

9-94745 

4 

38 

i 

1.8 

63 

9.66629 

14 

9.71888 

19 

To 

0.28112 

9-94741 

4 

37 

2 

3-6 

64 

9.66644 

15 

9-71906 

lo 

0.28094 

9-94737 

4 

36 

3 

4 

5-4 

7-2 

65 

9.66658 

14 

9.71925 

19 

o  .  28075 

9  94734 

3 

35 

5 

9.0 

66 

9-66673 

IS 

9-71943 

18 

0.28057 

9-94730 

4 

34 

6 

10.8 

67 

9.66687 

14 

9-71962 

19 

To 

0.28038 

9.94726 

4 

33 

7 
g 

12.6 

14  4 

68 

9.66702 

15 

9.71980 

lo 

TQ 

o  .  28020 

9.94722 

4 

32 

9 

16^2 

69 

9.66716 

14 

9.71998 

lo 

o  .  28002 

9.94718 

4 

31 

70 

9-66731 

15 

T  A 

9.72017 

19 

18 

0.27983 

9.94714 

4 

30 

71 

9-66745 

A4 

9-72035 

0.27965 

9.94710 

4 

29 

15 

72 

9.66759 

14 

9-72054 

19 

-rQ 

0.27946 

9.94706 

4 

28 

J 

Ie 

73 

9.66774 

15 
14 

9.72072 

lo 

19 

0.27928 

9.94702 

4 
4 

27 

2 

•  5 

3-0 

74 

9.66788 

9-72091 

0.27909 

9.94698 

26 

3 

4-5 

75 

9.66803 

15 

9.72109 

18 

TQ 

0.27891 

9.94694 

4 

25 

4 

6.0 

76 

9.66817 

14 
14 

9.72127 

lo 

19 

0.27873 

9.94690 

4 
4 

24 

1 

7-5 
9-o 

77 

9.66831 

9.72146 

TQ 

0.27854 

9.94686 

23 

7 

10.  s 

78 

9.66846 

15 

9.72164 

lo 

0.27836 

9.94682 

4 

22 

8 

12.0 

79 

9.66860 

14 

9.72182 

18 

0.27818 

9  94678 

4 

21 

9 

13-5 

80 

9-66875 

15 

9  .  72201 

J9 
18 

0.27799 

9.94674 

4 

20 

81 

9.66889 

14 

9-72219 

0.27781 

9.94670 

4 

19 

14 

82 

9.66903 

14 

9-72238 

19 

o  .  27762 

9-94666 

18 

I 

1-4 

83 

9.66918 

15 

14 

9.72256 

18 
18 

0.27744 

9.94662 

17 

2 
3 

2.8 
4-2 

84 

9-66932 

9.72274 

0.27726 

9.94658 

16 

4 

5-6 

85 

9.66946 

14 

9.72293 

19 

0.27707 

9.94654 

15 

s 

7.o 

86 

9.66961 

15 

14 

9-723II 

18 
18 

0.27689 

9-94650 

14 

6 

n 

8.4 
o  8 

87 

9-66975 

9.72329 

0.27671 

9.94646 

13 

8 

y-° 

II   2 

88 

9.66989 

14 

9.72348 

19 

0.27652 

9.94642 

4 

12 

9 

12^6 

89 

9.67004 

15 

T  A 

9.72366 

18 
18 

0.27634 

9.94638 

4 

II 

90 

9.67018 

A4 

T  A 

9.72384 

TO 

0.27616 

9.94634 

4 

10 

9i 

9-67032 

14 

9-72403 

*9 

•rQ 

0.27597 

9.94630 

4 

09 

4 

92 

9.67047 

15 

9.72421 

lo 

0.27579 

9-94626 

4 

08 

j 

0.4 

93 

9.67061 

14 

9-72439 

18 

0.27561 

9.94622 

4 

07 

2 

0.8 

94 

9.67075 

14 

9-72458 

*9 

0.27542 

9.94618 

4 

06 

3 

1.2 
_   r 

95 

9-67090 

IS 

9.72476 

18 

0.27524 

9.94614 

4 

05 

4 

1.0 

96 

9.67104 

14 

9.72494 

18 

0.27506 

9.946io 

4 

04 

6 

2.4 

97 

9.67118 

14 

9.725I3 

19 

0.27487 

9.94606 

4 

03 

7 

2.8 

98 

9-67132 

14 

9-72531 

18 

0.27469 

9.94602 

4 

02 

8 

I'l 

99 

9.67147 

IS 

9-72549 

18 
18 

0.27451 

9-94598 

4 

OI 

9 

3-0 

100 

9.67161 

14 

9.72567 

0.27433 

9-94593 

5 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

117' 


62  < 


(154) 


161' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

9.67161 

9.72567 

0.27433 

9-94593 

100 

01 

9-67I75 

14 

9-72586 

TQ 

0.27414 

9.94589 

99 

10 

O2 

9.67189 

14 

9.72604 

lo 

0.27396 

9.94585 

4 

98 

03 

9.67204 

15 
14 

9.72622 

18 
19 

0.27378 

9.94581 

4 
4 

97 

I 

2 

1-9 
3-8 

04 

9.67218 

9.72641 

TO 

0.27359 

9-94577 

96 

3 

5-7 

05 

9-67232 

14 

9-72659 

18 

0.27341 

9-94573 

4 

95 

4 

7.6 

06 

9-67246 

14 
15 

9.72677 

18 
18 

0.27323 

9.94569 

4 

4 

94 

5 
6 

9-5 
11.4 

07 

9.67261 

9-72695 

0.27305 

9-94565 

93 

7 

13-3 

08 

9.67275 

14 

9.72714 

19 

0.27286 

9.94561 

4 

92 

8 

15-2 

09 

9-67289 

14 

9-72732 

18 
18 

0.27268 

9-94557 

4 

9 

17.1 

10 

9.67303 

14 

9-72750 

18 

0.27250 

9-94553 

4 

90 

ii 

9.67317 

14 

9.72768 

0.27232 

9-94549 

4 

89 

18 

12 

9.67332 

15 

9.72787 

19 

0.27213 

9-94545 

4 

88 

i 

1.8 

13 

14 

9-72805 

18 

0.27195 

9-94541 

4 

87 

2 

3-6 

14 

9-67360 

14 

9.72823 

18 

_Q 

0.27177 

9-94537 

4 

86 

3 

4 

5-4 

7-2 

IS 

9.67374 

14 

9-72841 

lo 

0.27159 

9-94533 

4 

85 

5 

9-o 

16 

9-67388 

14 

18 

0.27141 

9-94529 

4 

84 

6 

10.8 

17 

9.67402 

14 

9.72878 

19 

•rQ 

0.27122 

9-94525 

4 

83 

7 
a 

12.6 

18 

9.67417 

15 

9.72896 

lo 

0.27104 

9-94521 

4 

82 

16^2 

19 

9.6743I 

14 

9.72914 

18 
18 

0.27086 

9-94517 

4 

81 

20 

9.67445 

14 

9.72932 

18 

0.27068 

9-94513 

4 

80 

21 

9-67459 

14 

9.72950 

0.27050 

9-94508 

79 

IB 

22 

9-67473 

T4 

9.72969 

19 

0.27031 

9-94504 

4 

78 

If* 

23 

9.67487 

14 

14 

9.72987 

18 
18 

0.27013 

9.94500 

4 
4 

77 

2 

•  5 

3-0 

24 

9.67501 

9-73005 

0.26995 

9.94496 

76 

3 

4-5 

25 

9.675I5 

14 

9-73023 

18 

0.26977 

9-94492 

4 

75 

4 

6.0 

26 

9-67530 

15 

14 

9.7304I 

18 
19 

0.26959 

9.94488 

4 
4 

74 

5 

6 

7-5 
9.0 

27 

9-67544 

9.73o6o 

xy 

0.26940 

9-94484 

73 

7 

10.5 

28 

9.67558 

14 

9.73078 

18 

0.26922 

9.94480 

4 

72 

8 

12.0 

29 

9-67572 

14 

9.73096 

18 
18 

0.26904 

9-94476 

4 

71 

9 

13-5 

30 

9-67586 

14 

9-73II4 

18 

0.26886 

9.94472 

4 

70 

31 

9.67600 

14 

9.73132 

_0 

0.26868 

9.94468 

4 

69 

14 

32 

9.67614 

14 

9-73150 

lo 

0.26850 

9.94464 

4 

68 

I 

1-4 

33 

9.67628 

14 
14 

9-73I69 

19 
18 

0.26831 

9.94460 

4 
5 

67 

2 

3 

2.8 
4-2 

34 

9.67642 

9.73187 

TQ 

0.26813 

9-94455 

66 

4 

5-6 

35 

9-67656 

T4  . 

9-73205 

lo 

0.26795 

9-94451 

4 

65 

5 

7-0 

36 

9.67670 

14 

9-73223 

18 

0.26777 

9-94447 

4 

64 

6 

8.4 

37 

9.67684 

14 

9-73241 

18 

_Q 

0.26759 

9-94443 

4 

63 

7 
g 

9-8 

II.  2 

38 

9-67698 

14 

9-73259 

lo 

0.26741 

9-94439 

4 

62 

9 

12.6 

39 

9.67712 

14 

9-73277 

18 

18 

0.26723 

9-94435 

4 

61 

40 

9.67726 

T  A 

9.73295 

o  .  26705 

9-94431 

4 

60 

41 

9.67740 

•"•4 

9-73314 

TQ 

0.26686 

9.94427 

4 

59 

4 

42 

9-67754 

14 

9-73332 

lo 

TQ 

0.26668 

9-94423 

4 

58 

I 

0  4 

43 

9.67768 

I4 

9-73350 

lo 
18 

0.26650 

9.94419 

4 

57 

2 

o'.S 

44 

9.67782 

9-73368 

o  .  26632 

9-94415 

56 

3 

1.2 

45 

9.67796 

14 

9-73386 

18 

0.26614 

9.94410 

5 

55 

4 

1.6 

2  O 

46 

9.67810 

14 
14 

9-73404 

18 

0.26596 

9.94406 

4 
4 

54 

6 

2.4 

47 

9.67824 

9-73422 

0.26578 

9.94402 

53 

7 

2.8 

48 
49 

9-67838 
9.67852 

14 
14 

9-73440 
9-73458 

18 

18 

18 

0.26560 
0.26542 

9-94398 
9-94394 

4 

4 

52 
Si 

8 
9 

1:1 

50 

9-67866 

9-73476 

0.26524 

9-94390 

4 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

118' 


(155) 


28( 


161  ' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

60 

9.67866 

. 

9-73476 

0.26524 

9-94390 

60 

Si 

9.67880 

14 

9-73495 

TQ 

0.26505 

9-94386 

4 

49 

1R 

52 

9.67894 

14 

9-73513 

lo 

TQ 

0.26487 

9-94382 

4 

48 

IQ 

53 

9-67908 

14 
14 

9-73531 

lo 

18 

0.26469 

9-94377 

5 
4 

47 

I 
2 

.5 

3-6 

54 

9.67922 

9-73549 

1-Q 

0.26451 

9-94373 

46 

3 

5-4 

55 

9-67936 

14 

9-73567 

lo 

0.26433 

9-94369 

4 

45 

4 

7.2 

56 

9-67950 

14 
14 

9.73585 

18 
18 

0.26415 

9-94365 

4 
4 

44 

1 

9-0 
10.8 

57 

9.67964 

9-73603 

,0 

0.26397 

9-94361 

43 

7 

12.6 

58 

9.67978 

14 

9-73621 

Xo 

_Q 

0.26379 

9-94357 

4 

42 

8 

14.4 

59 

9.67992 

14 

9.73639 

lo 
18 

0.26361 

9-94353 

4 

41 

9 

16.2 

60 

9.68006 

9-73657 

18 

0.26343 

9-94349 

4 

40 

6i 

9.68020 

4 

9.73675 

To 

0.26325 

9-94344 

39 

17 

62 

9-68033 

13 

9.73693 

lo 

To 

o  .  26307 

9-94340 

4 

38 

i 

1.7 

63 

9.68047 

14 
14 

9-737H 

lo 

18 

0.26289 

9-94336 

4 
4 

37 

2 
3 

3-4 
5  I 

64 

9.68061 

9.73729 

T0 

0.26271 

9-94332 

36 

4 

6^8 

65 

9-68075 

14 

9-73747 

lo 

,0 

0.26253 

9-94328 

4 

35 

5 

8.5 

66 

9.68089 

14 

9-73765 

lo 

TQ 

0.26235 

9-94324 

4 

34 

6 

10.2 

67 

9.68103 

14 

9.73783 

IB 

TQ 

0.26217 

9.94320 

4 

33 

7 
g 

ii.  9 
13.6 

68 

9-68117 

14 

9.738oi 

lo 

To 

0.26199 

9-94315 

5 

32 

9 

69 

9.68130 

13 

9.73819 

lo 

18 

0.26181 

9-943H 

4 

3i 

70 

9.68144 

9.73837 

18 

0.26163 

9-94307 

4 

30 

71 

9.68158 

9-73855 

To 

0.26145 

9-94303 

29 

14 

73 

9.68172 

14 

9-73873 

lo 

18 

0.26127 

9.94299 

4 

28 

i 

1-4 

73 

9.68186 

14 
14 

9-7389I 

18 

0.26109 

9-94295 

4 
4 

27 

2 

2.8 

74 

9.68200 

9-73909 

To 

0.26091 

9.94291 

26 

3 

JJ 

75 

9.68213 

13 

9-73927 

lo 

To 

0.26073 

9.94286 

5 

25 

4 
c 

5.0 

7.0 

76 

9.68227 

14 
14 

9-73945 

lo 

18 

0.26055 

9.94282 

4 
4 

24 

6 

77 

9.68241 

9.73963 

TQ 

0.26037 

9.94278 

23 

7 

9-8 

78 
79 

9-68255 
9.68269 

14 
14 
14 

9-73981 
9-73999 

lo 

18 
18 

0.26019 
0.26001 

9.94274 
9.94270 

4 
4 
4 

22 
21 

8 
9 

II.  2 
12.6 

80 

9.68283 

9.74017 

18 

0.25983 

9.94266 

20 

4  A 

81 

9.68296 

3 

9-74035 

18 

0.25965 

9.94261 

19 

M 

82 

9.68310 

14 
14 

9-74053 

18 

0.25947 

9.94257 

4 
4 

18 

I 

2 

1:1 

83 

9-68324 

14 

9.74071 

18 

0.25929 

9-94253 

4 

17 

3 

3.9 

84 

9.68338 

9.74089 

18 

0.25911 

9.94249 

16 

4 

5-2 

85 

9  68351 

13 

9.74107 

18 

0.25893 

9-94245 

4 

15 

5 

6.5 

86 

9-68365 

14 
14 

9-74125 

17 

0.25875 

9.94241 

4 
5 

14 

7 

7-8 

87 

9-68379 

9.74142 

18 

0.25858 

9  .  94236 

13 

8 

10.4 

88 

9.68393 

14 

9.74160 

18 

0.25840 

9.94232 

4 

12 

9 

II.  7 

89 

9.68406 

14 

9.74178 

18 

0.25822 

9.94228 

4 

4 

ii 

90 

9  .  68420 

9.74196 

18 

o  .  25804 

9.94224 

10 

9i 

9-68434 

9-74214 

18 

0.25786 

9.94220 

• 

09 

6 

92 

9.68448 

9.74232 

18 

0.25768 

9.94215 

08 

i 

o.S 

93 

9.68461 

14 

9.74250 

18 

0.25750 

9.94211 

4 
4 

07 

2 

I.O 

94 

9.68475 

14 

9.74268 

18 

0.25732 

9.94207 

4 

06 

3 

4 

1-5 

2.O 

95 

9-68489 

T7 

9-74286 

18 

0.25714 

9.94203 

4 

05 

5 

2-5 

96 

9.68502 

AO 
14 

9-74304 

18 

0.25696 

9.94199 

4 

04 

6 

3-0 

97 

9.68516 

9.74322 

0.25678 

9.94I95 

03 

7 

3-5 

98 
99 

9.68530 
9.68543 

13 
14 

9-74339 
9-74357 

18 
18 

0.25661 
0.25643 

9.94190 
9.94186 

5 
4 
4 

02 

01 

8 
9 

4-0 
4-5 

100 

9-68557 

9-74375 

o  .  25625 

9.94182 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

118* 


61' 


(156) 


29< 


150' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

9.68557 

9-74375 

18 

0.25625 

9.94182 

100 

01 

9-68571 

14 

9-74393 

To 

0.25607 

9.94178 

99 

18 

02 

9-68584 

13 

9.74411 

lo 

TO 

0.25589 

9.94174 

4 

98 

T    K 

03 

9-68598 

14 
14 

9-74429 

lo 
18 

0.25571 

9.94169 

5 
4 

97 

X 

2 

I  .0 

3-6 

04 

9.68612 

9-74447 

TQ 

0.25553 

9.94I6S 

96 

3 

5-4 

05 

9.68625 

13 

9.74465 

lo 

0.25535 

9.94161 

4 

95 

4 

7-2 

06 

9-68639 

14 
14 

9.74482 

17 
18 

0.25518 

9-94157 

4 

s 

94 

I 

9.0 
10.8 

07 

9-68653 

9.74500 

To 

0.25500 

9-94152 

93 

7 

12.6 

08 

9.68666 

13 

9.74518 

lo 

1-0 

0.25482 

9.94148 

4 

92 

8 

14.4 

09 

9.68680 

14 

9.74536 

lo 
18 

0.25464 

9.94144 

4 

9i 

9 

16.2 

10 

9.68694 

J-4 

T7 

9-74554 

18 

0.25446 

9.94140 

90 

ii 

9-68707 

••••$ 

9-74572 

0.25428 

9.94I36 

89 

17 

12 

9.68721 

14 

9-74589 

17 

_Q 

0.25411 

9-94I3I 

5 

88 

I 

1-7 

13 

9-68734 

13 
TA 

9.74607 

lo 
18 

0.25393 

9.94127 

4 
4 

87 

2 

3-4 

ST  ' 

14 

9.68748 

*n 

9-74625 

,  0 

0.25375 

9-94123 

86 

4 

.  X 

6.8 

15 

9.68762 

14 

9-74643 

lo 

_Q 

0.25357 

9-94II9 

4 

85 

8.5 

16 

9.68775 

13 
14 

9.74661 

lo 

18 

0.25339 

9.94114 

5 

4 

84 

IO.2 

TT    O 

17 

9.68789 

9-74679 

0.25321 

9.94110 

83 

8 

11.  y 
13-6 

18 

9.68802 

13 

9.74696 

I? 

TQ 

0.25304 

9.94106 

4 

82 

9 

15-3 

19 

9.68816 

14 
T7 

9.74714 

lo 

18 

0.25286 

9-94102 

4 

81 

20 

9.68829 

lO 
Tyt 

9-74732 

18 

0.25268 

9.94098 

• 

80 

21 

9-68843 

•••4 

9-74750 

TQ 

0.25250 

9-94093 

79 

14 

22 

9-68857 

14 

9-74768 

lo 

0.25232 

9.94089 

4 

78 

I 

1.4 

23 

9.68870 

13 
14 

9.74785 

17 
18 

0.25215 

9.94085 

4 
4 

77 

2 

2.8 

24 
25 

9.68884 
9-68897 

13 

9.74803 
9.7482I 

18 

To 

0.25197 
0.25179 

9.94081 
9.94076 

5 

76 
75 

3 

4 
5 

4-2 

5-6 
7  o 

26 

9.68911 

J-4 

13 

9.74839 

.     1° 

17 

0.25161 

9.94072 

4 
4 

74 

i 

8.4 

27 

9.68924 

9.74856 

18 

0.25144 

9.94068 

73 

Z 

9.8 

28 

9-68938 

14 

9.74874 

18 

0.25126 

9.94064 

4 

72 

0 

II.  2 
12.6 

29 

9-68951 

13 

TA 

9.74892 

18 

0.25108 

9-94059 

71 

30 

9-68965 

•^ 

T-7 

9.74910 

17 

0.25090 

9-94055 

4 

70 

4O 

31 

9-68978 

1»J 

14 

9-74927 

18 

0.25073 

9.94051 

4 

69 

j 

*• 
T    1 

32 

9.68992 

T-J 

9-74945 

18 

0.25055 

9.94047 

68 

2 

\l 

33 

9-69005 

lO 

14 

9-74963 

18 

0.25037 

9-94042 

4 

67 

3 

3-9 

34 

9.69019 

9.74981 

0.25019 

9.94038 

66 

4 

5-2 

35 

9.69032 

13 

9-74998 

I? 

To 

0.25002 

9.94034 

4 

65 

5 

6.5 

36 

9.69046 

J-4 

13 

9-75016 

IO 

18 

0.24984 

9.94030 

4 
5 

64 

6 
7 

7.8 
9-1 

37 

9.69059 

T  A 

9.75034 

18 

0.24966 

9.94025 

63 

8 

10.4 

38 

9-69073 

14 

9.75052 

0.24948 

9-94021 

62 

9 

II.  7 

39 

9.69086 

13 
TA 

9.75069 

17 
18 

0.24931 

9.94017 

4 

61 

40 

9.69100 

IH 
13 

9.75087 

18 

0.24913 

9.94012 

4 

60 

41 

9-69113 

9-75105 

18 

0.24895 

9-94008 

59 

4 

42 

9.69127 

*4 

9-75123 

TT 

0.24877 

9.94004 

4 

58 

X 

0.4 

43 

9.69140 

13 
13 

9-75I40 

»f 

18 

0.24860 

9.94000 

4 

s 

57 

2 

0.8 

44 

9.69IS3 

9-75158 

18 

o  .  24842 

9-93995 

56 

3 

1.2 

1.6 

45 

9.69167 

J-4 

9-75I76 

TT 

o  .  24824 

9-93991 

55 

4 
5 

2.0 

46 

9.69180 

13 

14 

9-75193 

*7 

18 

0.24807 

9.93987 

4 
4 

54 

6 

2-4 

47 

9.69194 

T-2 

9  -7521  I 

18 

0.24789 

9.93983 

53 

7 

2.8 

48 

9.69207 

•••o 
13 

9-75229 

18 

0.24771 

9-93978 

4 

52 

8 

3.2 
3.6 

49 

9  .  69220 

14 

9-75247 

17 

0.24753 

9-93974 

4 

Si 

BO 

9-69234 

9.75264 

0.24736 

9.93970 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

119* 


60e 


(157) 


150< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

] 

3.  P. 

50 

9.69234 

9-75264 

18 

0.24736 

9-93970 

50 

Si 

52 

53 
54 
55 
56 

57 
58 
59 

9-69247 
9.69261 
9.69274 
9-69287 
9-69301 
9.69314 
9-69328 
9.69341 
9-69354 

14 
13 
13 
14 
13 
14 
13 
13 
14 

9.75282 
9-75300 
9-75317 
9-75335 
9-75353 
9-75370 
9.75388 
9.75406 
9-7542.3 

18 
17 
18 
18 
17 
18 
18 
17 
18 

0.24718 
0.24700 
0.24683 
0.24665 
0.24647 
0.24630 

0.24612 
0-24594 
0.24577 

9.93965 
9.9396i 
9-93957 
9-93953 
9.93948 
9-93944 
9-93940 
9-93935 
9-93931 

4 
4 
4 
5 
4 
4 
5 
4 

49 
48 
47 
46 
45 
44 

43 
42 
41 

I 

2 
3 
4 

1 

7 
8 
9 

18 

1.8 
3-6 

5-4 
7.2 
9-o 
10.8 

12.6 

14.4 
16.2 

60 

9-69368 

9-75441 

18 

0.24559 

9-93927 

40 

61 
62 
63 
64 
65 
66 

67 
68 
69 

9-69381 
9.69394 
9-69408 

9-69421 
9.69434 
9.69448 

9.69461 
9.69474 
9-69487 

13 
14 
13 
13 
14 
13 
13 
13 

9-75459 
9-75476 
9-75494 
9-75511 
9.75529 
9-75547 
9.75564 
9-75582 
9.756oo 

17 
18 
17 
18 
18 
17 
18 
18 

0.24541 
0.24524 
0.24506 

0.24489 
0.24471 
0.24453 
0.24436 
0.24418 
0.24400 

9-93922 
9.93918 
9.93914 
9.93909 
9.93905 
9-93901 

9.93897 
9.93892 
9-93888 

4 
4 
5 

4 
4 
4 
5 
4 

39 
38 
37 
36 
35 
34 
33 
32 
31 

I 

2 

3 

4 

1 
I 

9 

17 

1.7 
3-4 
5-1 
6.8 
8.5 

IO.2 

ii.  9 

13.6 
15.3 

70 

9-69501 

9.75617 

18 

0.24383 

9.93884 

30 

71 

72 

73 
74 
75 
76 

77 
78 
79 

9-69514 
9-69527 
9.69541 
9.69554 
9-69567 
9-69580 

9.69594 
9.69607 
9.69620 

13 
14 
13 
13 
13 
14 
13 
13 
I"? 

9.75635 
9.75652 
9.75670 
9-75688 
9-75705 
9-75723 
9-75740 
9-75758 
9.75776 

17 
18 
18 

17 
18 
17 
18 
18 
I? 

0.24365 
0.24348 
0.24330 
0.24312 
0.24295 
0.24277 
0.24260 
0.24242 
0.24224 

9.93879 
9.93875 
9.93871 
9-93866 
9.93862 
9.93858 
9-93853 
9.93849 
9-93845 

4 
4 
5 
4 
4 
5 
4 
4 

29 
28 

27 

26 
25 
24 

23 
22 
21 

I 

2 

3 

4 
5 
6 
7 
8 
9 

14 

1-4 
2.8 
4.2 
5-6 
7-0 
8.4 
9-8 

II.  2 
12.6 

80 

9-69633 

9-75793 

18 

0.24207 

9-93840 

20 

81 
82 
83 
84 
85 
86 

87 
88 
89 

9.69647 
9.69660 
9.69673 
9.69686 
9.69699 
9.69713 
9.69726 
9.69739 
9.69752 

13 
13 
13 
13 
14 
13 
13 
13 

J-7 

9.758U 
9.75828 
9-75846 
9.75863 
9.75881 
9.75899 
9.759!6 
9-75934 
9-75951 

17 
18 
17 
18 
18 
17 
18 
17 
18 

0.24189 
0.24172 
0.24154 

0.24137 
0.24119 
0.24IOI 
0.24084 
0.24066 
0.24049 

9-93836 
9.93832 
9-93827 
9.93823 
9.93819 
9.938I4 
9.93810 
9.93805 
9.938oi 

4 
5 
4 
4 
5 
4 
5 
4 

i9 
18 
17 
16 
IS 
14 
13 

12 
II 

2 

3 
4 

I 

7 
8 
9 

IS 

1-3 
2.6 

3-9 

5-2 

6.5 

7-8 
9-1 
10.4 
ii.  7 

90 

9-69765 

14 

9.75969 

17 

0.24031 

9-93797 

5 

10 

91 

92 

93 
94 
95 
96 

97 
98 
99 

9.69779 
9.69792 
9-69805 

9.69818 
9.69831 
9.69844 
9-69858 
9.69871 
9.69884 

13 
13 
13 
13 
13 
14 
13 
13 
13 

9.75986 
9.76004 
9.76021 

9.76039 
9.76056 
9.76074 

9-76091 
9.76109 
9.76126 

18 
17 

18 

17 
18 
17 
18 
17 
18 

0.24014 
0.23996 
0.23979 

0.23961 
0.23944 
0.23926 

0.23909 
0.23891 
0.23874 

9-93792 
9-93788 
9.93784 
9-93779 
9-93775 
9-93771 
9.93766 
9.93762 
9-93757 

4 
4 
5 
4 
4 
5 
4 
5 

09 
08 

07 
06 
05 
04 

03 

02 

OI 

I 

2 

3 

4 
5 
6 
7 
8 
9 

5 

0.5 

I.O 

i.S 

2.0 
2.5 

3-0 
35 
4-0 
4-5 

100 

9.69897 

9-76144 

0.23856 

9-93753 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P. 

P. 

119' 


(158) 


30C 


149< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.P. 

00 

9.69897 

9.76144 

T*7 

0.23856 

9-93753 

100 

01 

9.69910 

13 

9.76161 

A7 
T-Q 

0.23839 

9-93749 

4 

99 

10 

02 

9.69923 

13 

9.76179 

lo 

0.23821 

9-93744 

5 

98 

T     ft 

03 

9-69936 

13 
13 

9.76196 

17 

18 

0.23804 

9-93740 

4 
4 

97 

I 
2 

I.O 

3-6 

04 

9.69949 

9-76214 

0.23786 

9.93736 

96 

3 

5-4 

OS 

9.69963 

14 

9-76231 

17 

0.23769 

9-93731 

5 

95 

4 

7.2 

06 

9.69976 

13 
13 

9-76249 

18 
17 

0.23751 

9-93727 

4 
5 

94 

5 
6 

9.0 

10.8 

07 

9.69989 

9.76266 

To 

0.23734 

9.93722 

93 

7 

12.6 

08 

9.70002 

13 

9.76284 

lo 

0.23716 

9-93718 

4 

92 

8 

14.4 

09 

9-70015 

13 

T1 

9.76301 

17 

18 

0.23699 

9-93714 

4 

9i 

9 

16.2 

10 

9  .  70028 

Ao 

9-76319 

TT 

0.23681 

9-93709 

90 

ii 

9.70041 

13 

9.76336 

A7 

TQ 

0.23664 

9-93705 

4 

89 

17 

12 

9-70054 

13 

9.76354 

lo 

0.23646 

9-93700 

5 

88 

i 

1-7 

13 

9.70067 

13 

9.76371 

17 

TQ 

0.23629 

9.93696 

4 

87 

2 

3-4 

14 

9.70080 

13 

9-76389 

lo 

0.23611 

9.93692 

4 

86 

3 

4 

1:1 

IS 

9.70093 

13 

9.76406 

I? 
-Q 

0.23594 

9.93687 

5 

85 

5 

8.5 

16 

9.70106 

13 

9.76424 

lo 

0.23576 

9-93683 

4 

84 

6 

10.2 

17 

9.70119 

13 

9.76441 

17 

0.23559 

9.93678 

5 

83 

7 
g 

ii.  9 
T-I  5 

18 

9-70132 

13 

9.76458 

17 

TQ 

0.23542 

9-93674 

4 

82 

9 

AO.U 
IS..1 

19 

9-70145 

13 

Tyi 

9-76476 

lo 
17 

0.23524 

9.93670 

4 

81 

20 

9-70159 

A4 

9-76493 

*•  i 

18 

0.23507 

9.93665 

80 

21 

9.70172 

13 

9.76511 

0.23489 

9.93661 

4 

79 

14 

22 

9.70185 

13 

9-76528 

17 

18 

0.23472 

9-93656 

5 

78 

I 

1-4 

23 

9-70198 

13 
13 

9.76546 

17 

0.23454 

9-93652 

4 

A 

77 

2 

2.8 

24 

9.70211 

9-76563 

0.23437 

9.93648 

76 

3 

4i 

25 

9.70224 

13 

9-76580 

i? 

0.23420 

9-93643 

5 

75 

4 

5-6 

26 

9.70237 

13 
13 

9-76598 

18 
17 

0.23402 

9-93639 

4 
5 

74 

I 

7.0 
8.4 

27 

9.70250 

9-76615 

TQ 

0.23385 

9.93634 

73 

7 

9-8 

28 

9-70263 

13 

9  76633 

IS 

0.23367 

9.93630 

4 

72 

8 

II.  2 

29 

9.70276 

13 

12 

9.76650 

17 
18 

0.23350 

9.93625 

5 

71 

9 

12.6 

30 

9.70288 

9.76668 

TT 

0.23332 

9.93621 

4 

70 

31 

9.70301 

13 

9-76685 

A7 

0.23315 

9.93617 

4 

69 

13 

32 

9.70314 

13 

9.76702 

17 

TQ 

0.23298 

9.93612 

5 

68 

I 

1-3 

33 

9.70327 

13 

9.76720 

lo 

TT 

0.23280 

9.936c8 

4 

67 

2 

2.6 

1    Q 

34 

9.70340 

13 

9.76737 

•"•7 

0.23263 

9-93603 

5 

66 

4 

o-y 
5-2 

35 

9-70353 

13 

9.76754 

17 

TQ 

0.23246 

9-93599 

4 

65 

5 

6.5 

36 

9.70366 

13 

9.76772 

lo 

0.23228 

9-93594 

5 

64 

6 

7.8 

37 

9-70379 

13 

9.76789 

J7 

To 

0.23211 

9-93590 

4 

63 

7 
8 

9-1 

10.4 

38 

9.70392 

13 

9.76807 

lo 

0.23193 

9-93585 

5 

62 

9 

II.  7 

39 

9.70405 

13 

TO 

9.76824 

17 

T*7 

0.23176 

9-93581 

4 

61 

40 

9.70418 

•*-o 

9.76841 

*/ 
TQ 

0.23159 

9-93577 

4 

60 

41 

9-70431 

13 

9-76859 

lo 

0.23141 

9-93572 

5 

59 

4 

42 

9.70444 

13 

9.76876 

17 

0.23124 

9-93568 

4 

58 

f\      A 

43 

9-70457 

13 
13 

9.76893 

17 

18 

0.23107 

9-93563 

5 

A 

57 

2 

u-4 
0.8 

44 

9.70470 

9.76911 

0.23089 

9-93559 

56 

3 

1.2 

45 

9.70482 

12 

9.76928 

17 

0.23072 

9-93554 

5 

55 

4 

1.6 

46 

9-70495 

13 
13 

9-76945 

17 
18 

0.23055 

9-93550 

4 

5 

54 

g 

2.O 
2-4 

47 

9-70508 

9-76963 

0.23037 

9-93545 

53 

7 

2.8 

48 

9.70521 

13 

9.76980 

I? 

0.23020 

9-93541 

4 

52 

8 

3-2 

49 

9-70534 

13 

T^ 

9.76998 

18 

0.23002 

9-93537 

4 

51 

9 

3.6 

50 

9-70547 

*J 

9-77015 

^7 

0.22985 

9-93532 

5 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

120 


69° 


(159) 


30< 


149  ' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

50 

9.70547 

9-77015 

0.22985 

9-93532 

60 

Si 

9.70560 

13 

T7 

9.77032 

J7 
18 

0.22968 

9.93528 

4 

49 

18 

52 

9-70573 

AO 

9.77050 

0.22950 

9-93523 

48 

T      ft 

53 

9-70585 

12 
13 

9.77067 

17 
17 

0.22933 

9-93519 

4 
5 

47 

i 

2 

I  .  O 

3-6 

54 

9.70598 

9.77084 

0.22916 

9.93514 

46 

3 

5-4 

55 

9.70611 

13 

9.77101 

17 

0.22899 

9-935IQ 

4 

45 

4 

7-2 

56 

9.70624 

13 
13 

9.77119 

18 

17 

0.22881 

9.93505 

5 

4 

44 

| 

9.0 
10.8 

57 

9.70637 

9-77I36 

0.22864 

9-93501 

43 

7 

12.6 

58 

9.70650 

13 

9-77153 

I? 

0.22847 

9-93496 

5 

42 

8 

14.4 

59 

9.70662 

12 

T1 

9-77I7I 

18 

0.22829 

9-93492 

4 

41 

9 

16.2 

60 

9.70675 

*O 

TO 

9.77188 

^7 

T7 

0.22812 

9-93487 

5 

40 

61 

9.70688 

*O 

9.77205 

•*•  / 

0.22795 

9.93483 

39 

17 

62 

9.70701 

13 

9.77223 

18 

0.22777 

9-93478 

5 

38 

i 

1-7 

63 

9.70714 

13 

TO 

9.77240 

17 

T7 

0.22760 

9-93474 

4 

37 

2 

3-4 

5T 

64 

9.70727 

AO 

9-77257 

•*•/ 

0.22743 

9.93469 

36 

4 

•   A 

6.8 

65 

9-70739 

12 

9.77274 

17 

0.22726 

9.93465 

4 

35 

5 

8.5 

66 

9-70752 

13 

9.77292 

18 

0.22708 

9.93460 

5 

34 

6 

10.2 

6? 

9.70765 

13 

9-77309 

17 

0.22691 

9.93456 

4 

33 

I 

II.  0 

13.6 

68 

9.70778 

13 

9-77326 

17 

TQ 

0.22674 

9-93451 

5 

32 

9 

15-3 

69 

9.70790 

12 

9-77344 

Io 

0.22656 

9-93447 

4 

31 

70 

9-70803 

13 

T7. 

9.77361 

17 
T*7 

0.22639 

9-93442 

5 

80 

7i 

9.70816 

AO 

9-77378 

•!•/ 

0.22622 

9-93438 

4 

29 

13 

72 

9.70829 

13 

9-77395 

I? 

TQ 

0.22605 

9-93433 

5 

28 

i 

I  3 

73 

9.70842 

13 

9-77413 

Io 

0.22587 

9  93429 

4 

27 

2 

2.6 

74 

9-70854 

12 

9-77430 

17 

0.22570 

9-93424 

5 

26 

3 

3-9 

75 

9.70867 

13 

9-77447 

17 

0.22553 

9.93420 

4 

25 

4 

e 

1.1 

76 

9.70880 

13 
12 

9.77464 

17 
18 

0.22536 

9-93415 

5 
4 

24 

6 

V.  o 

7-8 

77 

9.70892 

9.77482 

0.22518 

9  -9341  i 

23 

I 

9-i 

78 

9-70905 

13 

9-77499 

i? 

0.22501 

9.93406 

5 

22 

8 

10.4 

79 

9-70918 

13 

9.77516 

17 

0.22484 

9-93402 

4 

21 

9 

11.7 

80 

9.70931 

13 

9-77533 

17 
18 

0.22467 

9-93397 

5 

20 

81 

9.70943 

12 

9-77551 

0.22449 

9-93393 

4 

19 

12 

82 

9-70956 

13 

9-77568 

i? 

0.22432 

9-93388 

5 

18 

i 

1.2 

83 

9.70969 

13 
12 

9-77585 

17 
17 

0.22415 

9-93384 

4 
5 

17 

2 

3 

11 

84 

9.70981 

9.77602 

0.22398 

9-93379 

16 

4 

4-8 

85 

9-70994 

13 

9.77619 

i? 

TQ 

0.22381 

9-93375 

4 

15 

6.0 

86 

9.71007 

13 

9-77637 

Io 

0.22363 

9-93370 

5 

14 

" 

7.2 

8, 

87 

9.71020 

13 

9.77654 

17 

0.22346 

9.93366 

4 

13 

I 

•4 
9-6 

88 

9.71032 

12 

9.77671 

17 

o  .  22329 

9.93361 

5 

12 

9 

10.8 

89 

9-71045 

13 

9.77688 

17 

18 

0.22312 

9-93357 

4 

II 

90 

9.71058 

13 

9.77706 

TT 

0.22294 

9-93352 

10 

9i 

9.71070 

12 

9-77723 

A7 

0.22277 

9-93347 

09 

5 

92 

9-71083 

13 

9-77740 

17 

o  .  22260 

9-93343 

4 

08 

i 

0.5 

93 

9.71096 

13 

9-77757 

17 

0.22243 

9-93338 

5 

07 

2 

I.O 

94 

9.71108 

12 

9-77774 

I? 

0.22226 

9-93334 

4 

06 

3 

1-5 

95 

9.71121 

13 

9-77791 

17 

_Q 

o  .  22209 

9-93329 

5 

05 

4 
5 

2.O 
2.5 

96 

9-7II33 

12 
17 

9.77809 

Io 

I? 

0.22191 

9-93325 

4 
5 

04 

6 

3-0 

97 

9-7II46 

•••o 

9.77826 

0.22174 

9-93320 

03 

7 

35 

98 

9-7II59 

13 

9.77843 

17 

0.22157 

9-93316 

4 

02 

8 

4.0 

4r 

99 

9.71171 

12 

9.77860 

I? 

0.22140 

9-933H 

5 

OI 

9 

•5 

100 

9.71184 

J3 

9.77877 

^7 

0.22123 

9-93307 

4 

00 

Cos 

d. 

Cot        d.  c. 

Tan 

Sin 

d. 

P.  P. 

120  < 


59 ' 


(160) 


31' 


148 ' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

9.71184 

9-77877 

18 

0.22123 

9.93307 

100 

OI 

9.71197 

13 

9-77895 

0.22105 

9-93302 

99 

1ft 

02 

9.71209 

12 

9.77912 

I? 

0.22088 

9.93297 

5 

98 

I 

I  8 

03 

9.71222 

13 
12 

9.77929 

17 

0.22071 

9.93293 

5 

97 

2 

3-6 

04 

9-71234 

9-77946 

0.22054 

9.93288 

96 

3 

5-4 

05 

9.71247 

13 

9.77963 

17 

0.22037 

9.93284 

4 

95 

4 

7-2 

06 

9.71260 

13 
12 

9.77980 

17 
17 

O.2202O 

9.93279 

5 
4 

94 

1 

9-o 
10.8 

07 

9.71272 

9.77997 

O.22O03 

9-93275 

93 

7 

12.6 

08 

9-71285 

13 

9-78015 

18 

0.21985 

9.93270 

5 

92 

8 

14.4 

09 

9.71297 

12 

9-78032 

17 

T7 

0.21968 

9-93265 

5 

9 

16.2 

10 

9.7i3io 

12 

9.78049 

*-  1 

0.2I95I 

9.93261 

90 

ii 

9-71322 

9.78066 

17 

0.21934 

9-93256 

89 

17 

12 

9.7I335 

13 

9-78083 

17 

O.2I9I7 

9.93252 

4 

88 

I 

1-7 

13 

9.71348 

13 

9.78100 

17 

O.2I9OO 

9.93247 

5 

87 

2 

3-4 

14 

9.71360 

12 

9.78117 

17 

0.21883 

9-93243 

4 

86 

3 

4 

11 

15 

9.71373 

13 

9-78I35 

18 

0.21865 

9.93238 

5 

85 

5 

8.S 

16 

9.7I385 

12 

9.78I52 

i? 

0.21848 

9-93233 

5 

84 

6 

10.2 

17 

9.71398 

13 

9.78169 

17 

0.2I83I 

9.93229 

4 

83 

J 

ii.  9 
13.6 

!8 

9.71410 

12 

9.78186 

17 

O.2I8I4 

9-93224 

5 

82 

9 

15.3 

19 

9-7I423 

13 
12 

9.78203 

17 

T*7 

0.21797 

9-93220 

4 

81 

20 

9-71435 

9.78220 

*•  / 

O.2I78O 

9-93215 

80 

21 

9.71448 

13 

9.78237 

i? 

0.21763 

9-932II 

4 

79 

18 

22 

9.71460 

12 

9-78254 

17 

O.2I746 

9.93206 

5 

78 

i 

X  3 

23 

9-71473 

13 

12 

9.78271 

i? 
18 

0.21729 

9-93201 

5 

77 

2 

Ii 

24 

9.71485 

9.78289 

0.2I7II 

9-93197 

76 

3 

3-9 

25 

9.71498 

13 

9.78306 

17 

O.2I694 

9.93192 

5 

75 

4 

K 

26 

9-7i5io 

12 
13 

9-78323 

17 
17 

0.21677 

9.93188 

4 

s 

74 

i 

0.5 
7.8 

27 

9-7I523 

9.78340 

0.21660 

9.93183 

73 

7 

9-1 

28 

9-71535 

12 

9.78357 

17 

0.21643 

9.93I78 

5 

72 

8 

10.4 

29 

9-71548 

13 
12 

9-78374 

i? 

0.21626 

9-93174 

4 

5" 

71 

9 

11.7 

30 

9-7i56o 

9.7839I 

17 

0.2I6O9 

9.93I69 

70 

31 

9-71573 

13 

9.78408 

17 

0.21592 

9.93165 

4 

69 

12 

32 

9-7I585 

12 

9.78425 

i? 

0.21575 

9.93i6o 

5 

68 

i 

i.a 

33 

9.7I598 

13 
12 

17 

0.21558 

9-93155 

5 
4 

67 

2 

3 

2.4 
3-6 

34 

9.71610 

9.78459 

0.2I54I 

9-93I5I 

66 

4 

4-8 

35 

9.71622 

12 

9.78476 

17 

0.21524 

9.93I46 

5 

65 

5 

6.0 

36 

9.7I635 

13 
12 

9.78493 

17 
17 

0.21507 

9-93I4I 

5 
4 

64 

6 
7 

7.2 
8-4 

37 

9.71647 

9.78510 

O.2I49O 

9-93137 

63 

8 

9-6 

38 

9.71660 

13 

9-78528 

18 

O.2I472 

9.93I32 

5 

62 

9 

10.8 

39 

9-71672 

12 

9.78545 

i? 

0.21455 

9.93128 

4 

61 

40 

9-71685 

13 

9-78562 

17 

0.21438 

9-93123 

60 

4i 

9.71697 

9.78579 

17 

0.21421 

9.93118 

5 

59 

4 

42 

9.71709 

12 

9.78596 

17 

0.21404 

9-93II4 

4 

58 

0.4 

43 

9.71722 

13 

9-78613 

i? 

0.21387 

9.93I09 

5 

57 

2 

0.8 

44 

9-71734 

12 

9.78630 

17 

0.21370 

9.93104 

5 

56 

3 

1.2 

•r      £ 

45 

9.71747 

13 

9.78647 

17 

0.21353 

9-93100 

4 

55 

4 

I.O 

46 

9-71759 

12 
12 

9.78664 

i? 
i? 

0.21336 

9-93095 

5 

4 

54 

I 

2.4 

47 

9.71771 

9.78681 

0.21319 

9.93091 

53 

7 

2.8 

48 

9.71784 

13 

9.78698 

17 

0.21302 

9-93086 

5 

52 

8 

11 

49 

9.71796 

12 

9.78715 

17 

0.21285 

9.93081 

5 

Si 

9 

3-6 

50 

9.71809 

13 

9-78732 

0.21268 

9-93077 

4 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

121* 


58 c 


(161) 


ar 


148  ' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

50 

9.71809 

9.78732 

0.21268 

9.93077 

50 

51 

9.71821 

9.78749 

^7 

0.21251 

9.93072 

•   5 

49 

<"7 

52 

9.71833 

12 

9.78766 

17 

0.21234 

9-93067 

5 

48 

At 

53 

9.71846 

13 
12 

9.78783 

17 
17 

0.21217 

9-93063 

4 
5 

47 

I 

2 

1-7 
3-4 

54 

9-7I858 

9.78800 

O.2I2OO 

9.93058 

46 

3 

5-1 

55 

9.71870 

12 

9-78817 

17 

0.2II83 

9-93053 

5 

45 

4 

6.8 

56 

9-71883 

13 
12 

9-78834 

17 
i? 

O.2II66 

9-93049 

4 
5 

44 

j? 

8.5 
IO.2 

57 

9.7I89S 

9-78851 

0.2II49 

9.93044 

43 

7 

II.9 

58 

9.71907 

12 

9.78868 

17 

0.2II32 

9-93039 

5 

42 

8 

13-6 

59 

9.71920 

13 

9-78885 

17 

TT 

0.21115 

9-93035 

4 

41 

9 

15-3 

60 

9.71932 

12 

9.78902 

** 
TT 

0.21098 

9.93030 

5 

40 

61 

9.71944 

9.78919 

-1  / 

0.21081 

9-93025 

5 

39 

16 

62 

9-71957 

13 

9-78936 

17 

o?2io64 

9-93021 

4 

38 

I 

1.6 

63 

9.VI969 

12 

9.78953 

I? 

0.21047 

9.93016 

5 

37 

2 

32 

64 

9.71981 

12 

9.78970 

17 

0.21030 

9-930II 

5 

36 

3 

4 

4-8 
6.4 

65 

9.7I994 

13 

9.78987 

17 

0.21013 

9.93007 

4 

35 

5 

8.0 

66 

9.72006 

12 

9.79004 

17 

0.20996 

9-93002 

5 

34 

6 

9.6 

67 

9.72018 

12 

9.79021 

17 

0.20979 

9.92997 

5 

33 

1 

II.  2 
12.8 

68 

9-72030 

12 

9.79038 

I? 

0.20962 

9.92993 

4 

32 

9 

14.4 

69 

9.72043 

13 
12 

9.79055 

17 
T7 

0.20945 

9-92988 

5 

31 

70 

9-72055 

12 

9.79072 

A  / 
T7 

0.20928 

9-92983 

5 

30 

71 

9.72067 

9.79089 

A  / 

0.20911 

9.92979 

4 

29 

13 

73 

9.72079 

12 

9.79io6 

17 

0.20894 

9-92974 

5 

28 

J 

T    Q 

73 

9.72092 

13 

9.79122 

16 

0.20878 

9.92969 

5 

27 

2 

2.1 

74 

9.72104 

12 

9-79139 

J7 

0.20861 

9-92965 

4 

26 

3 

3-9 

75 

9.72116 

12 

9.79156 

i? 

0.20844 

9-92960 

5 

25 

4 

5-2 

6r 

76 

9.72128 

12 
13 

9.79173 

17 
17 

0.20827 

9-92955 

5 

4 

24 

5 
6 

•5 
7.8 

77 

9.72141 

9.79190 

0.20810 

9.92951 

23 

7 

9-1 

78 

9-72153 

12 

9.79207 

i? 

0.20793 

9.92946 

5 

22 

8 

10.4 

79 

9-72165 

12 
12 

9.79224 

17 

17 

0.20776 

9.92941 

5 

21 

9 

11.7 

80 

9.72177 

9.79241 

•*•  / 
T7 

0.20759 

9.92936 

20 

81 

9.72190 

13 

9.79258 

A7 

0.20742 

9.92932 

19 

12 

82 

9.72202 

12 

9-79275 

17 

o  .  20725 

9.92927 

5 

18 

I 

1.2 

83 

9.72214 

12 

12 

9.79292 

17 
17 

0.20708 

9.92922 

5 
4 

17 

2 

3 

3i6 

84 

9.72226 

9-79309 

0.20691 

9-92918 

16 

4 

4-8 

85 

9-72238 

12 

9.79326 

17 

0.20674 

9.92913 

5 

15 

5 

6.0 

86 

9-72251 

13 
12 

9-79343 

17 

16 

0.20657 

9-92908 

5 
5 

14 

6 

7 

7-2 

8.4 

87 

9.72263 

9-79359 

0.20641 

9.92903 

13 

8 

9-6 

88 

9.72275 

12 

9.79376 

J-7 

0.20624 

9.92899 

4 

12 

9 

10.8 

89 

9.72287 

12 
12 

9-79393 

i? 

T7 

0.20607 

9-92894 

5 

II 

90 

9-72299 

9-79410 

*  / 

0.20590 

9-92889 

10 

9i 

9-72312 

13 

9.79427 

!7 

0.20573 

9.92885 

4 

09 

5 

92 

9.72324 

12 

9-79444 

17 

0.20556 

9.92880 

5 

08 

i 

0.5 

93 

9.72336 

12 

9.79461 

I? 

0.20539 

9.92875 

5 

07 

2 

I.O 

94 

9.72348 

12 

9.79478 

I? 

0.20522 

9.92870 

5 

06 

3 

1-5 

95 

9.72360 

12 

9-79495 

17 

_/• 

0.20505 

9.92866 

4 

05 

4 

2.0 

2.5 

96 

9.72372 

12 
13 

9-795II 

It) 
17 

0.20489 

9.92861 

5 
5 

04 

6 

3-0 

97 

9-72385 

9-79528 

0.20472 

9.92856 

03 

7 

35 

98 

9-72397 

12 

9-79545 

I? 

0.20455 

9-92852 

4 

02 

8 

4-0 

99 

9.72409 

12 

9.79562 

I? 

0.20438 

9.92847 

5 

01 

9 

4-5 

100 

9.72421 

12 

9-79579 

17 

0.20421 

9.92842 

00 

Cos 

d. 

Cot 

d.  C. 

Tan 

Sin          d. 

P.  P. 

121 ' 


58' 


(162) 


32 ' 


147' 


Sin 

d. 

Tan   d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

9.72421 

9-79579 

0.20421 

9.92842 

100 

ox 

9  72433 

12 

9-79596 

I? 

0.20404 

9-92837 

99 

17 

02 

9-72445 

12 

9.79613 

i? 

0.20387 

9.92833 

4 

98 

i 

1-7 

03 

9-72457 

12 
12 

9.79630 

17 
16 

0.20370 

9.92828 

5 
5 

97 

2 

3-4 

04 

9-72469 

9-79646 

0.20354 

9.92823 

96 

3 

5-1 

05 

9.72482 

13 

9-79663 

i? 

0.20337 

9.92818 

5 

95 

4 

6.8 

06 

9-72494 

12 

12 

9.79680 

i? 
17 

0.20320 

9-92814 

4 
5 

94 

5 
6 

8.5 

10.2 

07 

9.72506 

9.79697 

0.20303 

9-92809 

93 

7 

ii.  9 

08 

9-725I8 

12 

9-79714 

17 

0.20286 

9.92804 

5 

92 

8 

13-6 

09 

9-72530 

12 

9-79731 

17 
16 

0.20269 

9.92799 

5 

9i 

9 

15-3 

10 

9.72542 

12 
12 

9-79747 

TT 

0.20253 

9-92795 

90 

ii 

9-72554 

9.79764 

-I/ 

0.20236 

9.92790 

89 

16 

12 

9.72566 

12 

9.79781 

17 

0.20219 

9.92785 

5 

88 

i 

1.6 

13 

9.72578 

12 
12 

9-79798 

I? 
17 

0.20202 

9-92780 

5 
4 

87 

2 
3 

\l 

U 

9.72590 

9-798I5 

O.2OI85 

9.92776 

86 

4 

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9-76300 

9.85182 

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9-76364 

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9.91014 

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9-76512 

9-85503 

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0.14497 

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9.76533 

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0.14465 

9.90998 

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9.76544 

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0.14449 

9.90993 

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9.90987 

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9.76565 

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9-90982 

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9-76586 

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9.90971 

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9-76597 

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9-85631 

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0.14369 

9.90966 

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9-85647 

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0.14353 

9.90960 

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9.76618 

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0.14337 

9.90955 

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29 

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9.76628 

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9-85679 

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9.90949 

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9.76639 

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9.85695 

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0.14305 

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9.76649 

9.857H 

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0.14289 

9.90938 

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9.76660 

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9-85727 

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9.76670 

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9.76681 

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0.14241 

9-90922 

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9-85775 

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0.14225 

9.90916 

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9-76702 

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9.85791 

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0.14209 

9.90911 

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21 

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9.76712 

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9-85807 

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0.14193 

9.90906 

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9-76723 

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9.90900 

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9-85951 

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0.14049 

9-90856 

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9-85967 

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0.14033 

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9.76828 

9.85983 

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9.90845 

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9-76838 

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9-76859 

9.86030 

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9.90829 

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9.86046 

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0.13954 

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9.76922 

9.86126 

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0.13874 

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10 

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9.86142 
9.86158 
9.86174 
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9.86206 
9.86222 
9.86238 
9-86254 
9.86269 

16 
16 
16 
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15 
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0.13858 
0.13842 
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9.90790 
9-90785 
9.90779 

9-90774 
9.90768 
9.90763 

9-90757 
9-90752 
9.90746 

5 
6 
5 
6 
5 
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5 
6 

99 
98 
97 
96 
95 
94 
93 
92 
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2 
3 
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5 
6 
7 
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16 

1.6 

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9-6 

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10 

9.77026 

9.86285 

16 

O.I37I5 

9.90741 

6 

90 

ii 

12 
13 
14 
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16 

17 
18 
19 

9.77036 
9-77047 
9-77057 
9.77068 
9.77078 
9.77088 
9.77099 
9.77109 
9.77119 

II 

IO 

II 

10 
IO 

II 

10 

IO 

9.86301 
9-86317 
9-86333 

9-86349 
9-86365 
9.86381 

9-86397 
9-86413 
9.86429 

16 
16 
16 
16 
16 
16 
16 
16 
16 

0.13699 
0.13683 
0.13667 
0.13651 
0.13635 
0.13619 

0.13603 
0.13587 
O.I357I 

9-90735 
9.90730 
9.90724 
9.90718 
9-907I3 
9.90707 
9.90702 
9-90696 
9-90691 

5 
6 
6 

5 
6 
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83 
82 
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10.5 

12.0 

13  5   , 

20 

9.77130 

9-86445 

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0.13555 

9-90685 

80 

21 
22 
33 
24 

35 
26 

27 

28 
29 

9.77140 
9-77150 
9.77161 

9.77171 
9.77181 
9.77192 
9.77202 
9.77212 
9-77223 

10 

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10 
10 

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10 
10 

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9.86460 
9.86476 
9.86492 
9.86508 
9-86524 
9.86540 
9-86556 
9.86572 
9.86588 

16 
16 
16 
16 
16 
16 
16 
16 

0.13540 
0.13524 
0.13508 
0.13492 
0.13476 
0.13460 

0.13444 
0.13428 
0.13412 

9.90680 
9-90674 
9-90669 
9.90663 
9-90657 
9.90652 
9.90646 
9.90641 
9.90635 

6 
5 
6 
6 
5 
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5 
6 

79 
78 
77 
76 
75 
74 
73 
73 
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2 
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30 

9.77233 

9.86603 

16 

0.13397 

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5 

70 

31 
33 
33 

34 
35 
36 

37 
38 
39 

9.77243 
9-77254 
9.77264 

9.77274 
9.77285 
9-77295 

9-77305 
9.77316 
9.77326 

II 

10 
10 

II 

10 
10 

II 

IO 

9.86619 
9-86635 
9.86651 
9.86667 
9.86683 
9-86699 
9-86715 
9-86731 
9.86746 

16 
16 
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16 
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0.13381 
0.13365 
0.13349 
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9.90624 
9.90618 
9-90613 
9.90607 
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9-90596 

9.90591 
9.90585 
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6 
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7 
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6.0 
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40 

9.77336 

9.86762 

16 

0.13238 

9-90574 

g 

60 

41 
43 
43 
44 
45 
46 

47 
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9-77346 
9-77357 
9-77367 
9-77377 
9-77387 
9-77398 
9.77408 
9.77418 
9.77429 

II 

IO 
10 
10 

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10 
10 

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9.86778 
9-86794 
9.86810 

9.86826 
9.86842 
9-86857 

9.86873 
9.86889 
9.86905 

16 
16 
16 
16 
15 
16 
16 
16 
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0.13222 
0.13206 
0.13190 

O.I3I74 
0.13158 
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0.13127 
0.13111 
0.13095 

9-90568 
9-90563 
9-90557 
9-9055I 
9.90546 
9.90540 

9-90535 
9.90529 
9-90523 

5 
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9-77439 

9.86921 

0.13079 

9-905I8 

50 

Cos 

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126' 


53' 


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143' 


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p.  p. 

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9-77439 

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9-77449 

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0.13063 

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53 

9-77459 

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9-86953 

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0.13047 

9.90507 

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53 

9-77469 

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9.86968 

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0.13032 

9-90501 

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9.77480 

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9.77500 

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9.87016 

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16 

0.12984 

9.90484 

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57 

9.77510 

9-87032 

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0.12968 

9.90479 

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58 

9.77521 

11 

9.87048 

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0.12952 

9.90473 

42 

8 

12.8 

59 

9-77531 

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9-87063 

15 

16 

0.12937 

9.90467 

6 

41 

9 

14.4 

60 

9-77541 

10 

9  87079 

16 

0.12921 

9.90462 

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40 

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9-77551 

9-87095 

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0.12905 

9.90456 

39 

15 

62 

9-7756I 

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9.87111 

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0.12889 

9.90450 

38 

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63 

9-77572 

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9.87127 

10 
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0.12873 

9-90445 

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37 

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64 

9-77582 

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9.87143 

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0.12857 

9-90439 

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65 

9-77592 

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9-87158 

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0.12842 

9-90434 

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9.77602 

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9.87174 

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0.12826 

9.90428 

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9.77612 

9.87190 

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0.12810 

9.90422 

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9-77623 
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9.87206 
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9-90405 

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9-77653 

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9-77663 

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9-87269 

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0.12731 

9.90394 

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73 

9-77673 

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9-87285 

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0.12715 

9.90388 

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27 

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2.2 

74 

9-77684 

9.87301 

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0.12699 

9-90383 

26 

3 

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75 

9.77694 

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9-873I7 

10 

0.12683 

9.90377 

25 

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4-4 

76 

9-77704 

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9-87332 

15 
16 

0.12668 

9.90371 

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9-77714 
9.77724 

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9-87348 
9-87364 

16 

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0.12636 

9.90366 
9.90360 

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23 
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9-77734 

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9-87380 

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16 

0.12620 

9.90354 

6 

21 

9 

9-9 

80 

9-77744 

9-87396 

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0.12604 

9.90349 

20 

81 

9-77755 

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9.87412 

J.Q 

0.12588 

9.90343 

19 

10 

82 

9-77765 

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9.87427 

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0.12573 

9.90337 

6 

18 

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83 

9-77775 

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9-87443 

10 

16 

0.12557 

9-90332 

5 
6 

17 

2 
3 

2.O 

3-0 

84 

9-77785 

9-87459 

tFi 

0.12541 

9.90326 

6" 

16 

4 

4-o 

85 

9-77795 

10 

9-87475 

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0.12525 

9.90320 

15 

5 

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86 

9-77805 

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10 

9-87490 

15 
16 

0.12510 

9-903I5 

5 
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14 

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9-778I5 

9-87506 

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0.12494 

9-90309 

13 

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8.0 

88 

9-77825 

10 

9.87522 

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0.12478 

9-90303 

12 

9 

9.0 

89 

9.77835 

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9.87538 

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16 

0.12462 

9.90298 

5 
g 

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90 

9.77846 

10 

9-87554 

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0.12446, 

9.90292 

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10 

91 

9.77856 

9.87569 

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0.12431 

9.90286 

09 

6 

92 

9-77866 

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9.87585 

10 

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0.12415 

9.90280 

08 

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0.6 

93 

9.77876 

10 
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9.87601 

10 

16 

0.12399 

9-90275 

5 
6 

07 

2 

1.2 

1.8 

94 

9.77886 

9.87617 

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0.12383 

9.90269 

06 

4 

2.4 

95 

9.77896 

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9-87633 

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0.12367 

9.90263 

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3-0 

96 

9.77906 

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9.87648 

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0.12352 

9-90258 

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9.77916 

9.87664 

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0.12336 

9-90252 

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9.77926 

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9.90246 

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9-77936 

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0.12304 

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0.12289 

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Cos 

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Tan 

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d. 

P.P. 

126' 


53 


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37' 


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Cos 

d. 

P.  P. 

00 

9.77946 

9.87711 

16 

0.12289 

9-90235 

g 

100 

01 

9-77956 

9.87727 

16 

0.12273 

9-90229 

g 

99 

16 

02 

9.77966 

9.87743 

0.12257 

9.90223 

98 

03 

9.77976 

II 

9-87759 

16 

0.12241 

9.90218 

6 

97 

I 
2 

I.O 
3-2 

04 

9.77987 

9-87775 

0.12225 

9.90212 

g 

9b 

3 

4-8 

05 

9-77997 

9.87790 

IS 

O.I22IO 

9  .  90206 

95 

4 

6.4 

o6 

9.78007 

9.87806 

16 

O.I2I94 

9.90201 

6 

94 

5 

8.0 

9f. 

07 

9.78017 

9.87822 

O.I2I78 

9.90195 

93 

7 

II.  2 

08 

9.78027 

9.87838 

10 

O.I2I62 

9-90189 

92 

8 

12.8 

09 

9-78037 

9.87853 

15 
16 

0.12147 

9-90183 

9i 

9 

14-4 

10 

9-78047 

9.87869 

16 

0.12131 

9.90178 

6 

90 

ii 

9-78057 

9-87885 

0.12115 

9.90172 

89 

15 

12 

9.78067 

10 

9.87901 

0.12099 

9.90166 

88 

I 

1-5 

13 

9-78077 

9.87916 

15 

0.12084 

9.90160 

87 

2 

30 

14 

9.78087 

9-87932 

0.12068 

9.90155 

g 

86 

3 

45 
6  o 

15 

9-78097 

9-87948 

0.12052 

9-90149 

g 

85 

5 

7-5 

16 

9.78107 

10 

9.87964 

15 

0.12036 

9.90143 

6 

84 

6 

9-0 

17 
18 

9-78II7 
9.78127 
9.78I37 

IO 
10 

9-87979 
9-87995 
9.88011 

16 
16 

Ih 

O.I202I 
O.I2OO5 
0.11989 

9-90137 
9.90132 
9.90126 

5 

6 

83 
82 

81 

7 
8 
9 

10.5 

12.0 

13  5 

20 

9.78147 

9.88027 

O.II973 

9.90120 

6 

80 

21 

9-78157 

9.88042 

O.II958 

9.90114 

79 

11 

22 

9.78167 

9.88058 

O.II942 

9-90109 

5 

78 

23 

9.78177 

10 

9.88074 

IS 

O.II926 

9-90103 

6 

77 

2 

2.2 

24 

9.78187 

9.88089 

tfi 

O.II9II 

9-90097 

g 

7b 

3 

33 

25 

9.78197 

9.88105 

O.II895 

9.90091 

75 

4 

4-4 

26 

9.78207 

10 

9.88121 

16 

O.II879 

9.90086 

6 

74 

i 

o\6 

27 

9.78217 

9.88137 

O.II863 

9.90080 

73 

7 

7-7 

28 

9.78227 

9.88152 

IS 

O.II848 

9.90074 

72 

8 

8.8 

29 

9.78236 

9 

9.88168 

16 

O.II832 

9.90068 

71 

9 

9-9 

30 

9.78246 

9.88184 

rfi 

o.  11816 

9.90063 

g 

70 

31 

9.78256 

9.88200 

O.IISOO 

9.90057 

g 

69 

9 

32 

9.78266 

9.88215 

15 

O.II785 

9-90051 

68 

I 

0.9 

33 

9.78276 

10 

9.88231 

16 

O.II769 

9.90045 

6 

67 

2 
3 

1.8 

2.7 

34 

9.78286 

9.88247 

O.H753 

9.90039 

66 

4 

3-6 

35 

9.78296 

9.88262 

15 

O.II738 

9-90034 

65 

5 

4-5 

36 

9.78306 

10 

9.88278 

16 

O.II722 

9.90028 

6 

64 

6 

ol 

37 

9-78316 

9.88294 

O.II706 

9.90022 

63 

8 

7.2 

38 

9-78326 

9.88310 

O.II690 

9.90016 

62 

9 

8.1 

39 

9.78336 

9-88325 

15 
16 

O.II675 

9.90011 

5 
g 

61 

40 

9-78346 

9-88341 

16 

O.II659 

9.90005 

g 

60 

41 

9  78356 

9-88357 

O.II643 

9-89999 

59 

5 

42 

9-78366 

9.88372 

15 

O.II628 

9  89993 

58 

I 

0-5 

43 

9-78375 

9 

IO 

9.88388 

16 

o.  11612 

9.89987 

57 

2 

I.O 

44 

9-78385 

9.88404 

0.11596 

9.89982 

56 

3 

1-5 

45 

9-78395 

9.88420 

0.11580 

9.89976 

55 

2  5 

46 

9.78405 

10 

9.88435 

15 
16 

0.11565 

9.89970 

6 

54 

6 

3-0 

47 

9-784I5 

9-88451 

o.i  1549 

9.89964 

53 

7 

3-5 

48 

9.78425 

IO 

9.88467 

16 

O.H533 

9-89958 

52 

8 

4.0 

49 

9-78435 

9.88482 

15 
16 

0.11518 

9-89952 

51 

50 

9-78445 

9.88498 

0.11502 

9-89947 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

127' 


62° 


d73) 


37< 


142 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

50 

9-78445 

10 

9.88498 

16 

0.11502 

9.89947 

g 

50 

51 

9-78455 

9-88514 

0.11486 

9.89941 

49 

16 

52 

9.78464 

9 

9-88529 

15 

T-A 

0.11471 

9.89935 

48 

i  6 

53 

9.78474 

10 

IO 

9-88545 

IO 

16 

o  II455 

9.89929 

6 

47 

2 

3-2 

54 

9.78484 

9.88561 

-r£ 

0.11439 

9.89923 

46 

3 

4-8 

55 

9.78494 

IO 

9-88577 

10 

0.11423 

9.89918 

5 

45 

4 

6.4 

56 

9.78504 

10 
10 

9-88592 

15 

16 

0.11408 

9.89912 

6 

44 

5 
6 

8.0 
9.6 

57 

9-785I4 

9.88608 

Tfi 

0.11392 

9.89906 

43 

7 

II.  2 

58 

9-78524 

10 

9.88624 

10 

0.11376 

9.89900 

42 

8 

12.8 

59 

9-78533 

9 

9-88639 

15 

ifi 

o.  11361 

9.89894 

g 

41 

9 

14.4 

60 

9.78543 

10 

9-88655 

10 
16 

O.I  1345 

9.89888 

40 

61 

9-78553 

0 

9.88671 

0.11329 

9-89883 

39 

15 

62 

9.78563 

10 

9.88686 

15 

0.11314 

9.89877 

38 

I 

1-5 

63 

9-78573 

10 
10 

9.88702 

16 
16 

0.11298 

9.89871 

6 
6 

37 

2 

3 

3-0 

4  5 

64 

9.78583 

9.88718 

0.11282 

9.89865 

36 

4 

6.0 

65 

9-78592 

9 

9-88733 

IS 

T-A 

0.11267 

9-89859 

35 

5 

7-5 

66 

9.78602 

10 
IO 

9.88749 

10 

16 

0.11251 

9-89853 

6 

34 

6 

7 

9.0 
10.5 

67 

9.78612 

9.88765 

0.11235 

9.89847 

33 

8 

12.  O 

68 

9  .  78622 

IO 

9.88780 

IS 
Tr 

O.II22O 

9-89842 

5 

32 

9 

13.5 

69 

9-78632 

10 

9.88796 

IO 

16 

O.II204 

9-89836 

6 

31 

70 

9.78642 

10 

9.88812 

TC 

0.11188 

9-89830 

5 

30 

71 

9-786si 

9 

9.88827 

15 

rfi 

0.11173 

9.89824 

g 

29 

10 

72 

9.78661 

10 

9.88843 

10 

rf\ 

0.11157 

9.89818 

28 

I 

I.O 

73 

9.78671 

IO 
IO 

9.88859 

IO 
TC 

0.11141 

9.89812 

6 

27 

2 

2.0 

74 

9.78681 

9.88874 

AO 
T£ 

0.11126 

9.89806 

26 

3 

3-0 

75 

9.78691 

IO 

9.88890 

IO 

Tfi 

O.IIIIO 

9.89801 

5 
g 

25 

4 
5 

4.0 
5  o 

76 

9.78700 

9 

10 

9.88906 

IO 
15 

0.11094 

9-89795 

6 

24 

6 

6^0 

77 

9.78710 

9.88921 

*A 

0.11079 

9.89789 

23 

7 

7.0 

78 

9.78720 

10 

9-88937 

10 
ifi 

0.11063 

9-89783 

g 

22 

8 

8.0 

79 

9-78730 

IO 

9-88953 

IO 
T£ 

0.11047 

9-89777 

g 

21 

9 

9.0 

80 

9-78739 

9 

IO 

9.88968 

AO 
16 

0.11032 

9.89771 

6 

20 

81 

9-78749 

9.88984 

tfi 

0.11016 

9-8976S 

g 

19 

9 

82 

9  78759 

10 

9.89000 

10 

O.IIOOO 

9-89759 

18 

i 

83 

9.78769 

10 
10 

9-89015 

15 
16 

0.10985 

9-89754 

5 
6 

17 

2 
3 

18 

I  .  0 

2.7 

84 

9.78779 

9-89031 

0.10969 

9.89748 

g 

16 

4 

3.6 

85 

9.78788 

9 

9.89046 

IS 

0.10954 

9.89742 

15 

5 

4-5 

86 

9.78798 

10 
10 

9.89062 

16 
16 

0.10938 

9-89736 

6 

14 

7 

5-4 
6.3 

87 

9.78808 

9.89078 

0.10922 

9.89730 

g 

13 

8 

7-2 

88 

9.78818 

10 

9-89093 

15 

Tfi 

0.10907 

9.89724 

g 

12 

9 

8.1 

89 

9-78827 

9 

9-89109 

10 

rfi 

0.10891 

9.89718 

5 

II 

90 

9-78837 

xo 

9-89125 

xo 

TC 

0.10875 

9.89712 

g 

10 

9i 

9-78847 

10 

9.89140 

*5 
T£ 

0.10860 

9-89706 

09 

6 

92 

9.78856 

9 

9-89156 

10 

TJ\ 

0.10844 

9.89701 

5 

08 

I 

0.6 

93 

9.78866 

10 

9-89172 

10 

0.10828 

9.89695 

07 

2 

1.2 

94 

9.78876 

10 

9.89187 

15 

,/? 

0.10813 

9-89689 

g 

06 

3 

1.8 

95 

9.78886 

10 

9-89203 

ID 

0.10797 

9.89683 

g 

05 

4 
5 

2.  4 
3  ° 

96 

9-78895 

9 

10 

9.89218 

15 
16 

0.10782 

9.89677 

6 

04 

6 

3-'6 

97 

9-78905 

9.89234 

_£ 

0.10766 

9.89671 

03 

7 

4-2 

98 

9.78915 

10 

9-89250 

IO 

0.10750 

9-89665 

02 

8 

4-8 

99 

9.78924 

9 

9.89265 

15 
16 

0.10735 

9-89659 

g 

OI 

9 

5-4 

100 

9-78934 

IO 

9.89281 

0.10719 

9.89653 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

127° 


62  < 


(174) 


38' 


141' 


Sin          d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

9.78934 

9.89281 

16 

0.10719 

9  89653 

6 

100 

01 

9  78944 

9.89297 

0.10703 

9.89647 

99 

Ifi 

02 

9-78954 

10 

9-89312 

15 
if> 

0.10688 

9.89641 

98 

j 

1.6 

03 

9-78963 

9 

10 

9-89328 

10 

IS 

0.10672 

9.89635 

5 

97 

2 

32 

04 

9.78973 

9-89343 

rfi 

0.10657 

9  89630 

g 

96 

3 

4-8 

05 
o6 

9-78983 

10 

9 

IO 

9-89359 
9-89375 

10 

16 
15 

0.10641 
0.10625 

9-89624 
9.89618 

6 
6 

95 
94 

4 
5 
6 

6.4 

8.0 
9-6 

07 

9-79002 

9.89390 

ifi 

o.  10610 

9.89612 

g 

93 

7 

II.  2 

08 

9.79012 

10 

9.89406 

IO 

Ty- 

0.10594 

9.89606 

92 

8 

12.8 

09 

9.79021 

9 

9.89422 

10 

jr 

0.10578 

9.89600 

6 

9i 

9 

14-4 

10 

9.79031 

10 

9-89437 

AO 

16 

o  .  10563 

9-89594 

6 

90 

ii 

9.79041 

10 

9-89453 

0.10547 

9-89588 

89 

15 

12 

9.79050 

9 

9.89468 

IS 

T/r 

0.10532 

9-89582 

88 

5  i- 

1-5 

13 

9.79060 

10 
IO 

9.89484 

It) 

16 

0.10516 

9.89576 

6 

87 

2 

3-0 

A    r 

14 

9.79070 

9-89500 

0.10500 

9.89570 

86 

4 

6.1 

15 

9-79079 

9 

9-895I5 

IS 
ifi 

0.10485 

9-89564 

85 

5 

7-5 

16 

9-79089 

IO 

9-8953I 

IO 

0.10469 

9.89558 

84 

6 

9-0 

17 
18 

9.79099 
9.79108 

10 

9 

9.89546 
9.89562 

IS 

16 

Tfi 

0.10454 
0.10438 

9.89552 
9.89546 

6 

£ 

83 
82 

7 
8 
9 

10.5 

12.  0 

ti.if 

19 

9.79118 

IO 

10 

9.89578 

IO 
je 

0.10422 

9-89540 

O 

6 

81 

20 

9.79128 

9-89593 

AO 

16 

0.10407 

9-89534 

80 

21 

9-79137 

9 

9-89609 

0.10391 

9-89528 

79 

in 

22 

9-79147 

10 

9.89624 

IS 

rfi 

o  .  10376 

9.89522 

78 

j 

I   0 

33 

9.79156 

9 

10 

9.89640 

IO 

16 

0.10360 

9-89516 

6 

77 

2 

2.0 

24 

9.79166 

9-89656 

0.10344 

9-89510 

76 

3 

3-0 

25 

9.79176, 

10 

9.89671 

IS 

rfi 

0.10329 

9.89504 

75 

4 

4-0 

26 

9.79185 

9 

IO 

9-89687 

10 

IS 

0.10313 

9.89499 

5 
6 

74 

5 
6 

5-0 
6.0 

27 

9.79195 

9-89702 

jf. 

0.10298 

9-89493 

73 

7 

7-0 

28 

9-79204 

9 

9-89718 

IO 
ffi 

o  .  10282 

9.89487 

72 

8 

8.0 

29 

9.79214 

IO 
10 

9.89734 

10 

TC 

0.10266 

9-89481 

g 

71 

9 

9-0 

30 

9-79224 

9-89749 

AO 

16 

0.10251 

9.89475 

g 

70 

3i 

9-79233 

9 

9.89765 

0.10235 

9-89469 

69 

9 

32 

9-79243 

IO 

9.89780 

IS 
_£ 

O.I022O 

9-89463 

68 

i 

0-9 

33 

9 

IO 

9.89796 

10 

IS 

o  .  10204 

9.89457 

6 

67 

2 
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1.8 

2  7 

34 

9.79262 

9.89811 

rfi 

O.IOI89 

9-89451 

66 

o 

4 

3^6 

35 

9.79272 

IO 

9-89827 

10 
•rf\ 

O.IOI73 

9.89445 

65 

5 

4-5 

36 

9.79281 

9 

10 

9.89843 

10 
15 

O.IOI57 

9.89439 

6 

64 

6 

ii 

37 

9.79291 

9-89858 

rfi 

O.IOI42 

9-89433 

63 

7 
8 

0.3 

7  2 

38 

9-79300 

9 

9.89874 

IO 

O.IOI26 

9.89427 

62 

g 

8.1 

39 

9-79310 

10 

9.89889 

IS 

16 

O.IOIII 

9.89421 

61 

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9.79319 

9 

IO 

9.89905 

T^ 

0.10095 

9-89415 

5 

60 

4i 

9-79329 

9-89920 

ID 
T£ 

0.10080 

9.89409 

59 

6 

42 

9-79339 

IO 

9.89936 

IO 

tfi 

0.10064 

9.89403 

58 

I 

0.6 

43 

9.79348 

9 

IO 

9.89952 

IO 

IS 

0.10048 

9.89397 

6 

57 

2 

1.2 

44 

9-79358 

9.89967 

T/? 

0.10033 

9  89391 

56 

3 

1.8 

45 

9.79367 

9 

9-89983 

10 

0.10017 

9-89385 

55 

4 

2.4 

46 

9-79377 

IO 

9 

9.89998 

IS 
16 

O.IOO02 

9.89379 

6 

54 

S 
6 

3-0 
3-6 

47 

9.79386 

9  90014 

0.09986 

9.89373 

53 

7 

4.2 

48 

9.79396 

IO 

9.90029 

IS 

T/r 

0.09971 

9-89366 

7 

52 

8 

4.8 

49 

9-79405 

9 

IO 

9-90045 

IO 

16 

0.09955 

9-89360 

5 

51 

9 

5-4 

50 

9-79415 

9.90061 

0.09939 

9-89354 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

128* 


(175) 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

F 

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50 

9.79415 

9.90061 

0.09939 

9-89354 

g 

50 

51 

52 

53 
54 
55 
56 

57 
58 
59 

9-79424 
9-79434 
9-79444 
9-79453 
9-79463 
9-79472 
9.79482 
9-79491 
9-79501 

10 

10 

9 

10 

9 

10 

9 
10 

9.90076 
9-90092 
9.90107 
9.90123 
9-90138 
9.90154 
9.90169 
9.90185 
9.90200 

16 
15 
16 

15 
16 
15 
16 
15 
16 

0.09924 
0.09908 
0.09893 

0.09877 
0.09862 
0.09846 
0.09831 
0.09815 
0.09800 

9.89348 
9.89342 
9.89336 
9.89330 
9.89324 
9-89318 
9-89312 
9-89306 
9-89300 

6 
6 
6 
6 
6 
6 
6 
6 
g 

49 
48 
47 
46 
45 
44 
43 

42 

41 

I 

2 

3 

4 

I 

7 
8 
9 

16 

1.6 

J:l 

6-4 
8.0 
9-6 

II.  2 
12.8 
14-4 

60 

9-79510 

9.90216 

16 

0.09784 

9.89294 

40 

61 
62 
63 
64 
65 
66 

67 

68 
69 

9-79520 
9-79529 
9-79539 
9-79548 
9-79558 
9-79567 
9-79576 
9-79586 
9-79595 

9 
10 
9 

10 

9 
9 

10 

9 

9.90232 
9.90247 
9-90263 
9.90278 
9.90294 
9.90309 
9-90325 
9.90340 
9-90356 

IS 
16 
15 
16 
15 
16 

15 
16 

0.09768 
0.09753 
0.09737 

0.09722 
0.09706 
0.09691 

0.09675 
0.09660 
0.09644 

9.89288 
9.89282 
9.89276 
9.89270 
9.89264 
9-89258 
9-89252 
9.89246 
9.89239 

6 
6 
6 
6 
6 
6 
6 

7 
g 

39 
38 
37 
36 
35 
34 
33 

32 

31 

I 

2 

3 

4 

I 

7 
8 
9 

15 

l-S 
3-0 
4-5 
6.0 
7-5 
9-0 
10.5 

12.0 

13  5 

70 

9-79605 

9  90371 

16 

0.09629 

9-89233 

6 

30 

71 

72 

73 
74 
75 
76 

77 
78 
79 

9-796I4 
9.79624 
9.79633 
9.79643 
9-79652 
9.79662 

9.79671 
9.7968o 
9.79690 

10 
9 

10 

9 
10 
9 

9 
10 

9.90387 
9-90403 
9.90418 

9.90434 
9.90449 
9.90465 
9.90480 
9.90496 
9.90511 

16 
15 
16 

15 
16 
15 
16 
IS 

l6 

0.09613 
0.09597 
0.09582 
0.09566 
0.09551 
0-09535 
0.09520 
0.09504 
0.09489 

9.89227 
9.89221 
9-892I5 
9.89209 
9.89203 
9.89197 

9.89191 
9-89185 
9.89179 

6 
6 
6 
6 
6 
6 
6 
6 
6 

29 

28 

27 

26 

25 
24 

23 

22 
21 

I 

2 

3 
4 
5 
6 
7 
8 
9 

10 

I.O 
2.0 

3-0 
4.0 
5-0 
6.0 
7-0 
8.0 
9-o 

80 

9.79699 

9 

9.90527 

0.09473 

9.89173 

20 

81 
82 
83 
84 
85 
86 

87 
88 
89 

9-79709 
9-79718 
9.79728 

9-79737 
9-79746 
9-79756 
9-79765 
9-79775 
9.79784 

9 

10 

9 
9 

10 

9 
10 
9 

9.90542 
9.90558 
9-90573 
9-90589 
9.90604 
9.90620 

9-90635 
9.90651 
9.90666 

16 
IS 
16 

15 
16 
IS 
16 
IS 
16 

0.09458 
0.09442 
0.09427 
0.09411 
0.09396 
0.09380 

0.09365 
0.09349 
0.09334 

9.89166 
9.89160 
9-89I54 
9.89148 
9-89142 
9-89136 
9.89130 
9.89124 
9.89118 

6 

6 
6 
6 
6 
6 
6 
6 
g 

19 

18 
17 
16 
IS 
14 
13 

12 

ii 

I 

2 
3 
4 
5 
6 
7 
8 
9 

9 

0.9 
1.8 

1:1 

4-5 
5-4 
6-3 
7.2 
8.1 

90 

9-79793 

9 

9.90682 

0.09318 

9.89112 

10 

9i 
92 
93 
94 
95 
96 
97 
98 
99 

9.79803 
9.79812 
9.79822 

9-7983I 

9.79840 
9.79850 

9.798S9 
9.79868 
9.79878 

9 

10 

9 
9 

10 

9 
9 

10 

9.90697 
9-90713 
9.90728 

9.90744 
9-90759 
9-90775 
9.90790 
9.90806 
9.90821 

16 
IS 
16 

IS 

16 
IS 
16 
IS 
16 

0.09303 
0.09287 
0.09272 
0.09256 
0.09241 
0.09225 
0.09210 
0.09194 
0.09179 

9-89105 
9.89099 
9-89093 
9.89087 
9.89081 
9-89075 
9.89069 
9-89063 
9-89056 

6 
6 
6 
6 
6 
6 
6 

7 
5 

09 
08 
07 
06 
05 
04 

03 
02 

OI 

I 

2 
3 
4 
5 
6 
7 
8 
9 

7 

0-7 
i-4 

2.1 
2.8 

3-5 

4-2 

4-9 
5-6 
6-3 

100 

9.79887 

9-90837 

0.09163 

9.89050 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

I 

5.  P. 

128* 


61° 


39' 


140' 


Sin     d. 

Tan 

d.  c.    Cot 

Cos 

d. 

P.  P. 

00 

9.79887 

9.90837 

0.09163 

9-89050 

g 

100 

ox 

9.79897 

IO 

9.90852 

15 

Tfi 

0.09148 

9.89044 

g 

99 

16 

02 

9.79906 

9 

9.90868 

IO 

0.09132 

9.89038 

98 

T 

1.6 

03 

9.799IS 

9 

IO 

9.90883 

15 
16 

0.09117 

9.89032 

6 

97 

2 

3-2 

04 

9-79925 

9.90899 

0.09101 

9.89026 

96 

3 

4.8 

05 

9-79934 

9 

9-90914 

15 
-*• 

0.09086 

9.89020 

95 

4 

6.4 

8_ 

06 

9-79943 

9 

IO 

9-90930 

IO 

IS 

0.09070 

9.89013 

7 
6 

94 

5 
6 

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9-6 

07 

9-79953 

9-90945 

_/- 

0.09055 

9.89007 

93 

7 

II.  2 

08 

9.79962 

9 

9.90961 

10 

0.09039 

9.89001 

92 

8 

12.8 

09 

9-79971 

9 

9.90976 

IS 
rfi 

0.09024 

9-88995 

5 

9i 

9 

14.4 

10 

9.79981 

IO 

9.90992 

IO 

yr 

0.09008 

9-88989 

5 

90 

ii 

9-79990 

9 

9.91007 

•o 

T£ 

0.08993 

9-88983 

89 

15 

12 

9-79999 

9 

9.91023 

10 

0.08977 

9.88976 

7 

88 

I 

I-  5 

13 

9.80009 

10 

y 

9.91038 

15 
16 

0.08962 

9.88970 

6 

87 

2 
3 

3-0 
4-5 

14 

9.80018 

9-91054 

0.08946 

9-88964 

86 

4 

6.0 

IS 

9.80027 

9 

9.91069 

15 

0.08931 

9.88958 

85 

5 

7-5 

16 

9-80037 

10 

9.91085 

16 

0.08915 

9.88952 

84 

6 

9.0 

17 

9.80046 

9 

9.91100 

15 

1-£ 

0.08900 

9.88946 

83 

7 
8 

10.  5 

12.  0 

If 

9.80055 

9 

9.91116 

IO 

0.08884 

9-88939 

7 
g 

82 

9 

I3-S 

19 

9.80064 

9 

9.9H3I 

15 
16 

0.08869 

9-88933 

g 

81 

20 

9.80074 

9-9"47 

Tg 

0.08853 

9.88927 

g 

80 

21 

9.80083 

9.91162 

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T£ 

0.08838 

9.88921 

79 

10 

22 

9.80092 

9 

9.91178 

10 

0.08822 

9-88915 

78 

1 

1.0 

23 

9.80102 

IO 

9-9II93 

15 

16 

0.08807 

9-88909 

1 

77 

2 

2.0 

24 

9.80111 

9-91209 

0.08791 

9.88902 

76 

3 

3-0 

25 

9.80120 

9 

9.91224 

IS 

0.08776 

9.88896 

g 

75 

4 
5 

4.0 
5  o 

26 

9.80129 

9 

10 

9.91239 

15 
16 

0.08761 

9.88890 

6 

74 

6 

6.0 

27 

9-80139 

9-91255 

0.08745 

9.88884 

73 

7 

7.0 

28 

9.80148 

9 

9.91270 

15 

,c 

0.08730 

9.88878 

72 

8 

8.0 

29 

9.80157 

9 

9.91286 

10 

0.08714 

9.88871 

7 
g 

71 

9 

9.0 

30 

9.80166 

9 

IO 

9.91301 

15 

16 

0.08699 

9.88865 

g 

70 

3i 

9.80176 

9.9I3I7 

0.08683 

9-88859 

69 

9 

32 

9.80185 

9 

9-9I332 

15 

_/• 

0.08668 

9.88853 

68 

I 

33 

9.80194 

9 

IO 

9.91348 

10 

15 

0.08652 

9.88847 

7 

67 

2 
3 

18 
I.o 

2.7 

34 

9.80204 

9-9I363 

T£ 

0.08637 

9.88840 

66 

4 

3-6 

35 

9.80213 

9 

9.91379 

IO 

0.08621 

9-88834 

65 

5 

4-5 

36 

9  .  80222 

9 
9 

9.9I394 

15 
16 

0.08606 

9.88828 

6 

64 

6 
7 

5-4 
6.3 

37 

9.80231 

9.91410 

0.08590 

9.88822 

63 

8 

7-2 

38 

9  .  80240 

9 

9.91425 

15 

tfi 

0.08575 

9.88815 

7 

62 

9 

8.1 

39 

9.80250 

IO 

9.91441 

IO 

0.08559 

9.88809 

g 

61 

40 

9-80259 

9.9I456 

IS 

T(- 

0.08544 

9.88803 

g 

60 

41 

9.80268 

9.91471 

10 

0.08529 

9-88797 

59 

6 

42 

9.80277 

9 

9.91487 

16 

0.08513 

9-88791 

6 

58 

I 

0.6 

43 

9.80287 

IO 

9 

9-91502 

15 
16 

0.08498 

9.88784 

7 
6 

57 

2 

1.2 

44 

9.80296 

9-9I5I8 

0.08482 

9-88778 

56 

3 

1.8 

45 
46 

9-80305 
9-80314 

9 

9 
9 

9.9I533 
9-91549 

15 
16 
IS 

0.08467 
0.08451 

9.88772 
9.88766 

6 

7 

55 

54 

4 

i 

2-4 

3-0 
3-6 

47 

9.80323 

9.91564 

T£ 

0.08436 

9-88759 

53 

7 

4.2 

48 

9-80333 

IO 

9.91580 

10 

0.08420 

9.88753 

52 

8 

4-8 

49 

9-80342 

9 

9-91595 

15 

TC 

0.08405 

9-88747 

g 

Si 

9 

5-4 

50 

9-80351 

9.91610 

AO 

0.08390 

9.88741 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

129' 


50C 


(177) 


140' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

50 

Si 

52 

53 

54 
55 
56 

57 
58 
59 
60 
61 
62 
63 
64 
65 
66 

67 
68 
69 
70 
71 

72 

73 
74 
75 
76 

77 
78 
79 
80 
81 
82 
83 
84 
85 
86 

87 
88 
89 
90 

9i 
92 
93 
94 
95 
96 

97 
98 
99 
100 

9-80351 

9 

9 
10 
9 
9 
9 
9 

10 

9 
9 
9 
9 
9 
9 
10 
9 
9 
9 
9 
9 
9 

10 

9 
9 
9 
9 
9 
9 
9 
9 

10 

9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
10 
9 
9 
9 
9 
9 

9.91610 

16 

15 
16 
15 
16 
IS 
16 

15 
15 
16 

IS 
16 
IS 
16 

IS 
IS 
16 

IS 
16 
IS 
16 

IS 
IS 
16 

IS 
16 
IS 

IS 
16 
IS 
16 

15 
16 
IS 

IS 
16 
IS 
16 
15 
IS 
16 

IS 
16 
IS 

IS 
16 
IS 
16 
IS 
IS 

0.08390 

9-88741 

7 
6 
6 
6 

7 
6 
6 
6 
7 
6 

6 

7 
6 
6 
6 
7 
6 

6 
7 
6 

6 
6 
7 
6 

6 
7 
6 

6 

7 
6 

6 
6 
7 
6 

6 
7 
6 

6 
7 
6 

6 

7 
6 
6 

7 
6 
7 
6 
6 
7 

50 

49 
48 
47 
46 
45 
44 

43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 

28 

27 

26 

25 
24 

23 
22 
21 

20 

19 
18 
17 
16 
15 
14 
13 

12 

II 
10 

09 
08 
07 
06 
05 
04 
03 

02 

01 

00 

I 

2 
3 

4 

7 
8 
9 

I 

2 

3 

4 
5 
6 
7 
8 
9 

I 

2 
3 

4 

I 
I 

9 

I 
a 
3 
4 

I 

7 
8 
9 

I 

2 
3 
4 

I 

7 
8 
9 

16 

1.6 

3-2 

4.8 
6-4 
8.0 
9-6 

II.  2 
12.8 
14-4 

15 

1-5 
3-0 
4-5 
6.0 
7-5 
9.0 
10.5 

12.  0 
13.5 

10 

I.O 
2.O 

3-0 
4.0 
5-0 
6.0 
7-0 
8.0 
9.0 

9 

SI 

1:1 

4-5 
5-4 
6.3 
7.2 
8.1 

7 

o-7 
1.4 
2.1 
2.8 
3-5 
4-2 

4.9 

5.6 

6.3 

9.80360 
9-80369 
9.80379 

9.80388 
9.80397 
9.80406 

9.80415 
9.80425 
9.80434 

9.91626 
9.91641 
9.9I657 
9.91672 
9.91688 
9.91703 
9.91719 
9.9I734 
9.91749 

0.08374 
0.08359 
0.08343 
0.08328 
0.08312 
0.08297 
0.08281 
0.08266 
0.08251 

9-88734, 
9.88728 
9.88722 
9.88716 
9.88709 
9-88703 

9.88697 
9.88691 
9.88684 

9.80443 

9-9I765 

0.08235 

9.88678 

9.80452 
9.80461 
9.80470 

9.80479 
9.80489 
9.80498 
9.80507 
9.80516 
9-80525 

9.91780 
9.91796 
9.91811 
9.91827 
9.91842 
9-9I857 
9-9I873 
9.91888 
9.91904 

0.08220 
o  .  08204 
0.08189 
0.08173 
0.08158 
0.08143 
0.08127 
o.  08112 
0.08096 

9.88672 
9.88665 
9.88659 
9-88653 
9.88647 
9.88640 

9-88634 
9.88628 
9.88621 

9.80534 

9.91919 

0.08081 

9.88615 

9-80543 
9-80553 
9.80562 

9-8057I 
9.80580 
9.80589 

9.80598 
9.80607 
9.80616 

9-91935 
9.91950 
9-9I965 
9.91981 
9.91996 
9.92012 

9.92027 
9-92042 
9-92058 

0.08065 
o  .  08050 
0.08035 
0.08019 
o  .  08004 
0.07988 
0.07973 
0.07958 
0.07942 

9.88609 
9.88603 
9-88596 
9-88590 
9.88584 
9-88577 
9.88571 
9-88565 
9-88558 

9.80625 

9.92073 

0.07927 

9-88552 

9.80635 
9.80644 
9.8o653 
9.80662 
9.80671 
9.80680 

9.80689 
9.80698 
9.80707 

9-92089 
9.92104 
9.92120 

9-92135 
9.92150 
9.92166 
9.92181 
9.92197 
9.92212 

0.07911 
0.07896 
0.07880 

0.07865 
0.07850 
0.07834 
0.07819 
0.07803 
0.07788 

9.88546 
9-88540 
9-88533 
9.88527 
9.88521 
9.88514 
9.88508 
9.88502 
9-88495 

9.80716 

9.92227 

0.07773 

9-88489 

9.80725 
9-80734 
9.80743 
9.80752 
9.80762 
9.80771 
9.80790 
9-80789 
9.80798 

9-92243 
9.92258 
9.92274 
9.92289 
9.92304 
9.92320 

9.92335 
9.9235I 
9.92366 

0.07757 
0.07742 
0.07726 
0.07711 
o  .  07696 
0.07680 

0.07665 
0.07649 
0.07634 

9.88483 
9.88476 
9.88470 
9.88464 
9.88457 
9.88451 
9.88444 
9-88438 
9.88432 

9.80807 

9.92381 

0.07619 

9.88425 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

129° 


6<r 


(178) 


40° 


139< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

OI 

02 
03 
04 
OS 
06 

07 
08 
09 
10 
ii 
la 
13 
14 
15 
16 

17 
18 
19 
20 

21 
22 
23 
24 
25 
26 

27 
28 
29 

30 

31 
32 
33 
34 
35 
36 

37 
38 
39 
40 

41 
42 
43 
44 
45 
46 

47 
48 
49 
50 

9.80807 

9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
8 

9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
9 
8 

9 
9 
9 
9 
9 
9 
9 
9 
8 

9-92381 

16 

15 
16 
15 

15 
16 
IS 
IS 
16 
IS 
16 

IS 
IS 
16 

IS 
16 
IS 
IS 
16 
IS 
IS 
16 
15 
16 

15 
IS 
16 

IS 
15 
16 

IS 
IS 
16 
IS 
16 
IS 
IS 
16 
IS 
IS 
16 

IS 
IS 
16 

IS 
IS 
16 

IS 
16 
IS 

0.07619 

9-88425 

6 
6 
7 
6 

6 

7 
6 

7 
6 
6 

7 
6 
6 
7 
6 
7 
6 

6 

7 
6 

7 
6 
6 
7 
6 
7 
6 

7 
6 
6 

7 
6 

7 
6 

7 
6 
6 

7 
6 
7 
6 

7 
6 
7 
6 
7 
6 

7 
6 
6 

100 

99 
98 
97 
96 
95 
94 
93 
92 
9i 
90 

89 
88 
87 
86 
85 
84 

83 
82 
81 
80 

79 
78 
77 
76 
75 
74 
73 

72 

71 
70 

69 
68 
67 
66 
65 
64 

63 
62 
61 
60 

59 
58 
57 
56 
55 
54 
53 

52 

Si 
50 

I 

2 

3 
4 
5 
6 
7 
8 
9 

2 

3 

4 
5 
6 
7 
8 
9 

2 

3 
4 
5 
6 
7 
8 
9 

I 

2 

3 
4 
5 
6 
7 
8 
9 

I 

2 

3 
4 
5 
6 
7 
8 
9 

16 

1.6 

11 
I:J 

9-6 

II.  2 
12.8 

14-4 

15 

1-5 
3-0 
4-5 
6.0 
7-5 
9-o 
10.  5 

12.  0 
13-5 

9 

0.9 
1.8 

2.7 

3-6 

4-5 
5-4 
6-3 

ii; 

8 

0.8 
1.6 
2.4 

3-2 

4.0 
4-8 
5.6 

6.4 

7-2 

7 

0.7 
i-4 

2.1 
2.8 
3-5 

4-2 

4.9 

5.6 
6.3 

9.80816 
9.80825 
9.80834 

9-80843 
9.80852 
9.80861 
9.80870 
9.80879 
9.80888 

9-92397 
9.92412 
9-92428 

9-92443 
9.92458 
9.92474 
9.92489 
9.92504 
9.92520 

0.07603 
0.07588 
0.07572 

0.07557 
0.07542 
0.07526 
0.07511 
0.07496 
0.07480 

9-88419 
9-88413 
9.88406 

9.88400 
9-88394 
9.88387 
9.88381 
9-88374 
9.88368 

9.80897 

9.92535 

0.07465 

9.88362 

9.80906 
9.80915 
9.80924 

9.80933 
9.80942 
9-80951 
9.80960 
9.80969 
9.80978 

9.92551 
9.92566 
9.92581 

9.92597 
9.92612 
9.92628 

9-92643 
9-92658 
9-92674 

0.07449 
0.07434 
0.07419 

0.07403 
0.07388 
0.07372 

0.07357 
0.07342 
o  .  07326 

9-88355 
9-88349 
9-88343 
9.88336 
9-88330 
9.88323 

9-88317 
9.88311 
9.88304 

9.80987 

9.92689 

0.07311 

9.88298 

9-80996 
9.81005 
9.81014 
9.81023 
9  .  81032 
9.81041 

9-81049 
9.81058 
9.81067 

9.92704 
9.92720 
9-92735 

9.92751 
9.92766 
9-92781 

9.92797 
9.92812 
9.92827 

0.07296 
0.07280 
o  .  07265 
0.07249 
0.07234 
0.07219 

0.07203 
0.07188 
0.07173 

9.88291 
9.88285 
9-88279 

9.88272 
9.88266 
9.88259 

9-88253 
9.88246 
9.88240 

9.81076 

9.92843 

0.07157 

9-88234 

9.81085 
9-81094 
9.81103 
9.81112 
9.81121 
9.81130 

9-8II39 
9.81148 
9-8II57 

9.92858 
9.92873 
9.92889 

9.92904 
9.92920 
9.92935 
9.92950 
9.92966 
9.92981 

0.07142 
0.07127 
0.07111 
0.07096 
0.07080 
0.07065 
0.07050 
0.07034 
0.07019 

9.88227 
9.88221 
9.88214 
9.88208 
9.88201 
9.88195 
9.88189 
9.88182 
9.88176 

9.81166 

9.92996 

0.07004 

9.88169 

9.81174 
9.81183 
9.81192 
9.81201 
9.81210 
9.81219 
9.81228 
9-81237 
9.81246 

9-93012 
9.93027 
9.93042 
9.93058 
9-93073 
9.93088 

9.93104 
9.93II9 
9-93135 

0.06988 
0.06973 
0.06958 
0.06942 
0.06927 
0.06912 
0.06896 
0.06881 
0.06865 

9.88163 
9.88156 
9.88150 

9-88143 
9-88137 
9.88130 
9.88124 
9.88117 
9.88111 

9.81254 

9.93I50 

0.06850 

9.88105 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

130* 


49( 


(179) 


40' 


139' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

] 

5.  P. 

50 

9-81254 

9.93I50 

0.06850 

9.88105 

50 

Si 

52 

53 

54 
55 
56 

57 
58 
59 

9.81263 
9.81272 
9.81281 
9.81290 
9.81299 
9.81308 
9.81316 
9-8I325 
9-81334 

9 
9 
9 
9 
9 
8 

9 
9 

9.93I65 
9.93i8i 
9.93I96 
9-932II 
9.93227 
9-93242 

9-9&2S7 
9-93273 
9-93288 

16 
IS 
IS 
16 
IS 
IS 
16 
IS 

0.06835 
0.06819 
0.06804 
0.06789 
0.06773 
0.06758 

0.06743 
0.06727 
0.06712 

9.88098 
9.88092 
9.88085 

9-88079 
9.88072 
9.88066 

9.88059 
9-88053 
9.88046 

7 
6 
7 
6 

7 
6 
7 
6 

7 

49 
48 
47 
46 
45 
44 
43 
42 
41 

i 

2 

3 

4 

i 

7 

8 
9 

16 

1.6 

32 

4-8 
6.4 
8.0 
9-6 

II.  2 
12.8 
14-4 

60 

9-81343 

9-93303 

16 

0.06697 

9.88040 

40 

6i 

63 

63 
64 
65 
66 

67 
68 
69 

9-81352 
9.81361 
9.81370 
9.8I378 
9-81387 
9.81396 
9.81405 
9-81414 
9.81422 

9 
9 
8 

9 
9 
9 

9 
8 

9-93319 
9-93334 
9-93349 
9-93365 
9-9338o 
9-93395 

9-934II 
9.93426 
9-93441 

15 
IS 
16 

IS 
IS 
16 

IS 
IS 
16 

0.06681 
0.06666 
0.06651 
0.06635 
0.06620 
0.06605 
0.06589 
0.06574 
0.06559 

9.88033 
9.88027 
9.88020 
9.88014 
9  .  88007 
9.88001 

9.87994 
9-87988 
9.87981 

6* 

7 
6 

7 
6 
7 
6 

7 

39 
38 
37 
36 
35 
34 
33 
32 
31 

i 

2 

3 

4 

7 
8 
9 

15 

1.5 
3-0 
4-5 
6.0 
7-5 
9.0 
lo.S 

12.  0 
I3.S 

70 

9-81431 

9-93457 

0.06543 

9.87975 

30 

71 
72 

73 
74 
75 
76 

77 
78 
79 

9.81440 
9-81449 
9.81458 

9.81467 
9-81475 
9.81484 

9.81493 
9.81502 
9.81510 

9 
9 
9 
8 
9 
9 

9 
8 

9-93472 
9-93487 
9-93503 
9-93518 
9-93533 
9-93549 
9.93564 
9-93579 
9-93595 

IS 
16 
IS 

IS 
16 
IS 

IS 
16 

0.06528 
0.06513 
0.06497 
0.06482 
0.06467 
0.06451 
0.06436 
0.06421 
0.06405 

9-87968 
9.87962 
9-87955 
9.87949 
9.87942 
9-87935 
9.87929 
9.87922 
9.87916 

7 
6 
7 
6 

7 
7 
6 

7 
6 

29 

28 
27 
26 
25 
24 
23 

22 
21 

I 

3 

4 
5 
6 
7 
8 
9 

8 

0.8 
1.6 
2.4 

3.2 
4.0 
4-8 
5-6 
6.4 

7-2 

80 

9.81519 

9  936io 

0.06390 

9.87909 

g 

20 

81 
82 
83 
84 
85 
86 

87 
88 
89 

9.81528 
9-81537 
9.81546 

9-81554 
9-81563 
9-81572 
9-81581 
9-81589 
9.81598 

9 
9 
8 

9 
9 
9 
8 
9 

9.93625 
9-9364I 
9-93656 

9.93671 
9-93687 
9-93702 

9-93717 
9-93733 
9-93748 

16 
IS 
IS 
16 
IS 
IS 
16 
IS 

0.06375 
0.06359 
0.06344 
0.06329 
0.06313 
0.06298 

0.06283 
0.06267 
0.06252 

9.87903 
9.87896 
9.87890 
9-87883 
9.87877 
9-87870 

9.87863 
9-87857 
9.87850 

7 
6 
7 
6 
7 
7 
6 

7 
g 

19 
18 
17 
16 
15 
14 
13 

12 
II 

i 

2 
3 

4 
5 
6 

I 

9 

7 

0.7 
1-4 

2.1 

2.8 

35 

4.2 

S.I 

6.3 

90 

9.81607 

9-93763 

0.06237 

9.87844 

10 

9i 

92 

93 
94 
95 
96 
97 
98 
99 

9.81616 
9.81624 
9-81633 
9.81642 
9.81651 
9-81659 
9.81668 
9.81677 
9.81686 

8 
9 
9 

9 
8 
9 
9 

9 
g 

9-93778 
9-93794 
9-93809 

9.93824 
9.93840 
9-93855 
9.93870 
9-93886 
9-93901 

16 
IS 
IS 
16 
IS 
IS 
16 
IS 

0.06222 
0.06206 
0.06191 
0.06176 
0.06160 
0.06145 
0.06130 
0.06114 
0.06099 

9-87837 
9-87831 
9.87824 

9.87817 
9.87811 
9-87804 

9.87798 
9.87791 
9.87785 

6 
7 
7 
6 
7 
6 

7 
6 

09 
08 
07 
06 
05 
04 

03 
02 

OI 

i 
a 
3 
4- 
5 
6 
7 
8 
9 

6 
0.6 

1.2 

1.8 

2.4 
3-0 
3-6 

4-2 

4-8 
5-4 

100 

9.81694 

9.93916 

0.06084 

9.87778 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P 

P. 

130' 


49' 


(i  80) 


138' 


Sin      |     d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

9.81694 

9.93916 

16 

0.06084 

9.87778 

100 

01 

9.81703 

9-93932 

0.06068 

9.87771 

7 

99 

16 

O2 

9.81712 

9 

9-93947 

15 

0.06053 

9.87765 

98 

f  ti 

03 

9.81720 

8 
9 

9.93962 

IS 
16 

o  .  06038 

.  9.87758 

7 
6 

97 

I 

2 

I.O 

3-2 

04 

9.81729 

9-93978 

0.06022 

9.87752 

96 

3 

4-8 

05 

9-81738 

9 

9-93993 

15 

0.06007 

9.87745 

7 

95 

4 

6-4 

06 

9-81747 

9 
8 

9.94008 

IS 
15 

0.05992 

9.87738 

7 
6 

94 

jj 

8.0 
9-6 

07 

9-81755 

9.94023 

_£ 

0.05977 

9.87732 

93 

7 

II.  2 

08 

9.81764 

9 

9.94039 

ID 

0.05961 

9.87725 

7 

93 

8 

12.8 

09 

9-81773 

9 
g 

9.94054 

IS 

0.05946 

9.87719 

B; 

91 

9 

14.4 

10 

9.81781 

9.94069 

15 

16 

0.05931 

9.87712 

7 

90 

ii 

9.81790 

9-94085 

0.05915 

9.87705 

7 

89 

15 

12 

9.81799 

9 

9-94100 

IS 

0.05900 

9.87699 

88 

i 

1-5 

13 

9.81807 

8 
9 

9-94H5 

IS 
16 

0.05885 

9.87692 

7 
6 

87 

2 

3-0 

4e 

14 

9.81816 

9.94I3I 

0.05869 

9.87686 

86 

fet 

4 

•  o 

6.0 

15 

9.81825 

9 

9.94146 

IS 

0.05854 

9.87679 

7 

85 

5 

7-5 

16 

9-81833 

8 

9.94i6i 

IS 

0.05839 

9.87672 

7 

84 

6 

9.0 

17 

9.81842 

9 

9.94176 

IS 
T£ 

0.05824 

9.87666 

6 

83 

7 
g 

10.5 

18 

9.81851 

9 

9.94192 

ID 

0.05808 

9.87659 

7 

82 

'_ 

19 

9.81859 

8 

9.94207 

15 

0.05793 

9-87652 

7 

81 

' 

20 

9.81868 

9 

9.94222 

IS 

16 

0.05778 

9.87646 

80 

21 

9.81877 

9.94238 

0.05762 

9.87639 

7 

79 

9 

22 

9.81885 

9-94253 

15 

0.05747 

9.87632 

7 

78 

33 

9.81894 

9 
9 

9.94268 

IS 
16 

0.05732 

9.87626 

6 

7 

77 

I 

2 

0.9 
1.8 

34 

9-81903 

9.94284 

0.05716 

9.87619 

76 

3 

2-7 

35 

9.81911 

9.94299 

IS 

0.05701 

9.87613 

6 

75 

4 

36 

26 

9.81920 

9 
9 

9-94314 

IS 
IS 

0.05686 

9.87606 

7 

7 

74 

\ 

4-5 

5-4 

37 

9.81929 

9.94329 

0.05671 

9-87599 

73 

7 

6.3 

28 

9-81937 

9-94345 

16 

0.05655 

9.87593 

6 

73 

8 

7-2 

39 

9-81946 

9 

9.94360 

15 

0.05640 

9-87586 

7 

71 

9 

8.1 

30 

9-81955 

g 

9-94375 

15 
16 

o  .  05625 

9-87579 

7 

70 

31 

9-81963 

9-94391 

0.05609 

9-87573 

69 

8 

33 

9-81972 

9 

9.94406 

15 

0.05594 

9.87566 

7 

68 

i 

0.8 

33 

9.81980 

9.94421 

IS 

0.05579 

9.87559 

7 

67 

2 

1.6 

34 

9.81989 

9 

9-94436 

IS 
_/• 

0.05564 

9-87553 

6 

66 

3 

4 

2.4 

3-2 

35 

9.81998 

9 

9-94452 

10 

0.05548 

9.87546 

7 

65 

5 

4-0 

36 

9.82006 

8 
9 

9.94467 

IS 

15 

0.05533 

9.87S39 

7 
6 

64 

6 

5.6 

37 

9.82015 

9.94482 

0.05518 

9.87533 

63 

7 
g 

6.  4 

38 

9.82023 

8 

9.94498 

16 

0.05502 

9-87526 

7 

62 

9 

7.2 

39 

9-82032 

9 

9-94513 

IS 

0.05487 

9-875I9 

7 

61 

40 

9.82041 

g 

9.94528 

IS 

0.05472 

9-875I3 

60 

41 

9.82049 

9-94543 

15 

-C 

0.05457 

9.87506 

7 

59 

7 

.43 

9  .  82058 

9 

9-94559 

IO 

0.05441 

9-87499 

7 

58 

0.7 

43 

9.82066 

9 

9-94574 

IS 
15 

0.05426 

9.87492 

7 
6 

57 

2 

1.4 

44 

9-82075 

9-94S89 

0.05411 

9-87486 

56 

3 

2.1 

45 

9.82084 

9 

9.94604 

15 

T/f 

0.05396 

9-87479 

7 

55 

4 

2.8 

46 

9.82092 

9 

9  .  94620 

10 
15 

0.05380 

9.87472 

7 
6 

54 

S 
6 

3-5 

4.2 

47 

9.82101 

9.94635 

0.05365 

9.87466 

53 

7 

4-9 

48 

9.82109 

8 

9.94650 

IS 

0.05350 

9-87459 

7 

53 

8 

5.6 

49 

9.82118 

9 
g 

9.94666 

16 

0.05334 

9.874S2 

7 

9 

6-3 

50 

9.82126 

9.94681 

0.05319 

9.87446 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.P. 

131' 


48° 


(181) 


138< 


Sin 

d. 

Tan 

d.c. 

Cot 

Cos 

d. 

P.P. 

50 

9.82126 

9.94681 

TC 

0.05319 

9.87446 

50 

Si 

9-82135 

9.94696 

AO 

0.05304 

9-87439. 

49 

1ft 

52 

9.82144 

9 
g 

9.94711 

15 

-rf. 

0.05289 

9.87432 

7 

48 

T    fi 

53 

9-82152 

9 

9-94727 

IO 

15 

0-05273 

9.87425 

7 
6 

47 

2 

I  .  O 
3-2 

54 

9.82161 

9-94742 

0.05258 

9.87419 

46 

3 

4-8 

55 

9.82169 

9-94757 

15 

0.05243 

9-87412 

7 

45 

4 

6.4 

56 

9.82178 

9 
8 

9-94772 

15 
16 

0.05228 

9.87405 

7 
6 

44 

5 
6 

8.0 
9.6 

57 

9.82186 

9-94788 

0.05212 

9.87399 

43 

7 

II.  2 

58 

9.82195 

9 

9.94803 

15 

0.05197 

9.87392 

7 

42 

8 

12.8 

59 

9.82203 

9.94818 

15 

16 

0.05182 

9-87385 

7 

4i 

9 

14  4 

60 

9.82212 

9.94834 

Tr 

0.05166 

9.87378 

5 

40 

61 

9.82221 

9-94849 

*O 

0.05151 

9.87372 

39 

15 

62 

9.82229 

9.94864 

15 

0.05136 

9.87365 

7 

38 

i 

1.5 

63 

9.82238 

9 
8 

9.94879 

15 

16 

0.05121 

9-87358 

7 

37 

2 

3-0 

A    e 

64 

9.82246 

9.94895 

0.05105 

9-87351 

36 

4 

c 

6.0 

65 

9-82255 

9 
g 

9.94910 

15 

0.05090 

9.87345 

6 

35 

5 

7-5 

66 

9.82263 

9.94925 

15 

0.05075 

9.87338 

7 

34 

6 

9-o 

67 

9.82272 

9 
g 

9.94940 

15 

rfi 

o  .  05060 

9.87331 

7 

33 

7 
g 

10.5 

12.0 

68 

9.82280 

9-94956 

10 

0.05044 

9.87325 

32 

9 

n.<; 

69 

9.82289 

9 
g 

9.94971 

IS 

0.05029 

9.87318 

7 

31 

70 

9.82297 

9.94986 

IS 

0.05014 

9.873H 

7 

30 

71 

9.82306 

g 

9-95001 

15 
_£ 

0.04999 

9-87304 

7 

29 

8 

72 

9-82314 

9.95017 

10 

0.04983 

9-87298 

28 

i 

o  8 

73 

9-82323 

9 

9.95032 

15 

0.04968 

9.87291 

7 

27 

2 

1.6 

74 

9-82331 

9-95047 

15 

0.04953 

9.87284 

7 

26 

3 

2.4 

75 

9-82340 

g 

9.95062 

15 

r£ 

0.04938 

9.87277 

7 

25 

4 

3-2 

76 

9-82348 

9 

9.95078 

IO 

15 

0.04922 

9.87270 

7 
6 

24 

6 

4-  o 
4-8 

77 

9-82357 

g 

9-95093 

0.04907 

9.87264 

23 

7 

5.6 

78 

9-82365 

9.95108 

15 

-rA 

0.04892 

9.87257 

7 

22 

8 

6.4 

79 

9-82374 

8 

9.95124 

IO 
Tr 

o  .  04876 

9.87250 

7 

*7 

21 

9 

7-2 

80 

9.82382 

9 

9-95139 

AO 

0.04861 

9.87243 

g 

20 

81 

9-82391 

g 

9-95154 

15 

0.04846 

9.87237 

19 

7 

82 

9-82399 

9.95169 

IS 

0.04831 

9.87230 

7 

18 

i 

0.7 

83 

9.82408 

8 

9.95I85 

16 
15 

0.04815 

9-87223 

7 
7 

17 

2 
3 

1-4 

2.1 

84 

9.82416 

g 

9-95200 

o  .  04800 

9.87216 

16 

4 

2.8 

85 

9.82424 

9-95215 

15 

0.04785 

9.87209 

7 

15 

5 

35 

86 

9-82433 

8 

9-95230 

15 
16 

0.04770 

9-87203 

7 

14 

6 

7 

4.2 
4.9 

87 

9.82441 

9.95246 

0.04754 

9-87196 

13 

8 

5.6 

88 

9-82450 

g 

9.95261 

15 

0.04739 

9.87189 

7 

12 

9 

6.3 

89 

9-82458 

9.95276 

IS 

0.04724 

9.87182 

7 

II 

90 

9.82467 

8 

9.95291 

15 
16 

0.04709 

9.87175 

7 
5 

10 

9i 

9-82475 

9-95307 

0.04693 

9-87169 

09 

6 

92 

9.82484 

g 

9-95322 

15 

0.04678 

9.87162 

7 

08 

i 

0.6     . 

93 

9.82492 

9-95337 

IS 

o  .  04663 

9.87I5S 

7 

07 

2 

1.2 

94 

9.82501 

g 

9-95352 

IS 

_/: 

o  .  04648 

9.87148 

7 

06 

3 

1.8 

2J 

95 

9-82509 

g 

9-95368 

10 

0.04632 

9.87141 

7 

05 

4 
5 

•  4 
3  O 

96 

9-82517 

9 

9-95383 

IS 
IS 

0.04617 

9-87I35 

7 

04 

6 

i:a 

97 

9.82526 

g 

9.95398 

o  .  04602 

9.87128 

03 

7 

4.2 

.      0 

98 

9-82534 

9 

9-95413 

IS 
ift 

0.04587 

9.87121 

7 

02 

8 

4.0 
5-4 

99 

9-82543 

g 

9.95429 

IO 

0.04571 

9.87H4 

fj 

OI 

100 

9.82551 

9-95444 

IS 

0.04556 

9.87107 

t 

00 

Cos 

d. 

Cot 

d.c. 

Tan 

Sin 

d. 

P.  P. 

131° 


48' 


(182) 


42' 


137' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

I 

3.  P. 

00 

9-82551 

9-95444 

0.04556 

9.87107 

g 

100 

01 

02 

03 
04 
05 

o6 

07 
08 
09 

9.82560 
9.82568 
9-82576 
9-82585 
9-82593 
9.82602 

9.82610 
9.82618 
9.82627 

8 
8 
9 
8 
9 
8 

8 

9 
g 

9-95459 
9-95474 
9-95489 

9-95505 
9-95520 
9-95535 
9-95550 
9-95566 
9-95581 

15 
15 
16 

15 
15 
15 
16 
15 

0.04541 
0.04526 
0.04511 

0.04495 
0.04480 
0.04465 
0.04450 
0.04434 
0.04419 

9.87101 
9.87094 
9.87087 
9.87080 
9-87073 
9.87066 

9.87060 
9.87053 
9.87046 

7 
7 
7 
7 
7 
6 

7 
7 

99 
98 
97 
96 
95 
94 
93 
92 
9i 

I 

2 

3 

4 
5 
6 
7 
8 
9 

16 

1.6 

3-2 

4.8 
6.4 
8.0 
9.6 

II.  2 
12.8 
14-4 

10 

9-82635 

9.95596 

0.04404 

9-87039 

90 

ii 

12 
13 
14 

15 
16 

17 
18 
19 

9.82644 
9.82652 
9.82660 
9.82669 
9.82677 
9.82685 
9.82694 
9.82702 
9.82711 

8 
8 
9 
8 
8 
9 
8 

9 
g 

9.95611 
9.95627 
9.95642 

9-95657 
9-95672 
9-95688 

9-95703 
9-95718 
9-95733 

16 
IS 
15 

15 
16 
15 
15 
15 

0.04389 
0.04373 
0.04358 
0.04343 
0.04328 
0.04312 
0.04297 
0.04282 
0.04267 

9-87032 
9-87025 
9.87018 
9.87012 
9-87005 
9.86998 
9-86991 
9.86984 
9.86977 

7 
7 
6 

7 

7 
7 
7 
7 

89 
88 
87 
86 
85 
84 

83 
82 
81 

I 
2 
3 
4 
5 
6 
7 
8 
9 

15 

I.S 

3-0 

fci 

7-5 
9.0 
10.  5 

12.0 
13-5 

20 

9.82719 

g 

9-95748 

16 

0.04252 

9.86970 

80 

21 
22 

23 

24 
25 

26 

27 

28 
29 

9.82727 
9-82736 
9-82744 
9-82752 
9.82761 
9.82769 

9.82777 
9.82786 
9-82794 

9 
8 
8 

9 
8 
8 

9 
8 
g 

9-95764 
9-95779 
9-95794 
9.95809 
9-95825 
9.95840 

9.95855 
9.95870 
9-95886 

15 
15 
15 
16 
15 
15 

15 
16 

15 

0.04236 
0.04221 
o  .  04206 
0.04191 
0.04175 
0.04160 

0.04145 
0.04130 
0.04114 

9-86963 
9.86957 
9-86950 

9.86943 
9-86936 
9.86929 
9.86922 
9.86915 
9.86908 

6 

7 
7 
7 
7 
7 
7 
7 
6 

79 
78 
77 
76 
75 
74 
73 

72 

71 

I 

2 

3 
4 
5 
6 
7 
8 
9 

9 

0.9 
1.8 

11 

4-5 
5-4 
6.3 

7-2 

8.1 

30 

9.82802 

9-95901 

0.04099 

9.86902 

70 

31 
32 
33 

34 
35 
36 

37 
38 
39 

9.82811 
9.82819 
9.82827 
9.82836 
9.82844 
9.82852, 

9.82861 
9.82869 
9.82877 

8 
8 
9 
8 
8 
9 
8 
8 
g 

9.95916 
9-95931 
9-95946 
9.95962 
9-95977 
9-95992 
9.96007 
9-96023 
9.96038 

IS 
IS 
16 

IS 
IS 
IS 
16 
IS 
IS 

o  .  04084 
0.04069 
0.04054 
0.04038 
0.04023 
0.04008 

0.03993 

0.03977 
0.03962 

9-86895 
9.86888 
9.86881 

9.86874 
9.86867 
9.86860 

9-86853 
9.86846 
9-86839 

7 
7 
7 
7 
7 
7 
7 
7 
7 

69 
68 
67 
66 
65 
64 

63 
62 
61 

I 

2 

3 

4 

I 

9 

8 

0.8 
1.6 
2.4 
3-2 
4-0 
4-8 
5-6 
6.4 
7-2 

40 

9.82885 

9-96053 

15 

0.03947 

9.86832 

6 

60 

4i 
42 
43 
44 
45 
46 

47 
48 
49 

9.82894 
9.82902 
9.82910 
9.82919 
9.82927 
9-82935 

9.82944 
9-82952 
9.82960 

8 
8 
9 
8 
8 
9 
8 
8 
8 

9.96068 
9-96083 
9.96099 
9.96114 
9-96129 
9.96144 

9.96160 
9.96I75 
9.96190 

IS 
16 
IS 
IS 

.    J5 
16 

IS 
IS 
IS 

0.03932 
0.03917 
0.03901 

0.03886 
0.03871 
0.03856 
0.03840 
0.03825 
0.03810 

9.86826 
9.86819 
9.86812 
9.86805 
9.86798 
9.86791 
9.86784 
9.86777 
9.86770 

7 
7 
7 
7 
7 
7 
7 
7 
7 

59 
58 
57 
56 
55 
54 
53 

52 

Si 

I 
a 
3 
4 

7 
8 
9 

7 

0.7 
1.4 

2.1 
2.8 
3-5 
4-2 
4-9 
S.6 
6.3 

50 

9.82968 

9-96205 

0.03795 

9-86763 

50 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

] 

3.  P. 

47' 


(183) 


137  < 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

I 

J.  P. 

50 

9.82968 

9.96205 

0.03795 

9-86763 

50 

51 
53 

53 

54 
55 
56 

57 
58 
59 

9.82977 
9.82985 
9-82993 
9.83001 
9.83010 
9.83018 
9.83026 
9-83034 
9-83043 

8 
8 
8 

9 

8 
8 
8 

9 
3 

9.96220 
9.96236 
9-96251 
9.96266 
9.96281 
9.96297 
9.96312 
9-96327 
9.96342 

16 
15 
15 

IS 
16 
15 
15 
15 

0.03780 
0.03764 
0.03749 

0.03734 
0.03719 
0.03703 
0.03688 
0.03673 
0.03658 

9-86756 
9.86749 
9.86742 

9.86735 
9.86728 
9.86721 

9.86714 
9.86707 
9.86700 

7 
7 
7 
7 
7 
7 
7 

7 
g 

49 
48 
47 
46 
45 
44 

43 
42 
41 

i 

2 

3 

4 
5 
6 
7 
8 
9 

16 

1.6 
32 
4-8 
6.4 
8.0 
9.6 

II.  2 
12.8 

14.4 

60 

9-83051 

3 

9-96357 

16 

0.03643 

9.86694 

40 

61 
62 
63 
64 
65 
66 

67 
68 
69 

9.83059 
9-83067 
9-83076 
9-83084 
9-83092 
9.83100 

9-83109 
9-83117 
9-83125 

8 
9 
8 

8 
8 
9 
8 
8 
3 

9.96373 
9.96388 
9-96403 
9.96418 
9.96433 
9.96449 
9-96464 
9.96479 
9.96494 

IS 
15 
IS 

IS 
16 
IS 
15 
IS 
16 

0.03627 
0.03612 
0.03597 
0.03582 
0.03567 
0.03551 
0.03536 
0.03521 
0.03506 

9.86687 
9.86680 
9-86673 
9.86666 
9-86659 
9.86652 

9.86645 
9.86638 
9.86631 

7 
7 
7 
7 
7 
7 
7 
7 
7 

39 
38 
37 
36 
35 
34 
33 
33 
31 

I 

2 

3 

4 
5 
6 
7 
8 
9 

15 

i.S 
3-0 

13 

7-5 
9-o 
10.5 

12.  0 
13-5 

70 

9.83133 

3 

9.96510 

0.03490 

9.86624 

30 

71 
72 
73 
74 
75 
76 

77 
78 
79 

9-83I4I 
9-83I50 
9-83158 
9.83166 
9-83I74 
9.83182 

9-83191 
9.83199 
9.83207 

9 
8 
8 
8 
8 
9 
8 
8 
3 

9-96525 
9-96540 
9.96555 
9.96570 
9.96586 
9.96601 
9.96616 
9-96631 
9.96646 

IS 
IS 
IS 
16 
IS 
IS 
IS 
IS 
16 

0.03475 
0.03460 
0.03445 
0.03430 
0.03414 
0.03399 
0.03384 
0.03369 
0.03354 

9.86617 
9.86610 
9.86603 
9-86596 
9.86589 
9.86582 

9-86575 
9.86568 
9.86561 

7 
7 
7 
7 
7 
7 
7 
7 
7 

39 

28 

37 

26 

35 

34 

23 

22 
21 

I 

2 

3 

4 
5 
6 
7 
8 
9 

9 

o-9 
1.8 

2-7 

3-6 
4-5 
5-4 
6.3 

7-2 

8.1 

80 

9-83215 

3 

9.96662 

0.03338 

9-86554 

20 

81 
82 
83 
84 
85 
86 

87 
88 
89 

9-83223 
9-83232 
9.83240 

9-83248 
9.83256 
9.83264 

9.83272 
9.83281 
9-83289 

9 
8 
8 
8 
8 
8 

9 

8 
3 

9.96677 
9-96692 
9.96707 
9.96722 
9.96738 
9.96753 
9.96768 
9-96783 
9.96798 

IS 
IS 
IS 
16 
IS 
IS 
IS 
15 
16 

0.03323 
0.03308 
0.03293 
0.03278 
0.03262 
0.03247 
0.03232 
0.03217 
0.03202 

9-86547 
9.86540 
9.86533 
9.86526 
9.86518 
9-86511 
9-86504 
9-86497 
9.86490 

7 
7 
7 
8 
7 
7 
7 
7 
7 

19 
18 
17 
16 
15 
14 
13 

12 

ii 

I 

2 

3 

4 
5 
6 
7 
8 
9 

8 

0.8 
1.6 

2-4 
32 

4.0 

4-8 
5.6 
6.4 

7-2 

90 

9-83297 

3 

9.96814 

IS 

0.03186 

9-86483 

7 

10 

9i 

93 

93 
94 
95 
96 

97 
98 
99 

9.83305 
9.83313 
9.83321 

9-83330 
9.83338 
9-83346 

9-83354 
9-83362 
9.83370 

8 

8 
9 
8 
8 
8 
8 
8 
8 

9-96829 
9-96844 
9.96859 

9.96874 
9.96890 
9.96905 
9.96920 
9.96935 
9.96950 

15 
15 
IS 
16 
IS 
IS 
IS 
IS 
16 

0.03171 
0.03156 
0.03141 
0.03126 
0.03110 
0.03095 
0.03080 
0.03065 
0.03050 

9.86476 
9-86469 
9.86462 

9.86455 
9.86448 
9.86441 
9.86434 
9.86427 
9.86420 

7 
7 
7 
7 
7 
7 
7 
7 
7 

09 
08 
07 
06 
05 
04 

03 
02 

01 

I 

2 

3 

4 

7 
8 
9 

7 

0.7 
1-4 

2.1 
2.8 

3-5 

4-2 

il 

6-3 

100 

9.83378 

9.96966 

0.03034 

9-86413 

00 

Cos 

d. 

Cot 

d.c. 

Tan 

Sin 

d. 

I 

>.  P. 

132* 


(184) 


43' 


136' 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

I 

\  P. 

00 

9-83378 

g 

9.96966 

0.03034 

9-86413 

100 

01 

02 

03 
04 
OS 
06 

07 
08 
09 

9-83386 
9-83395 
9-83403 
9.83411 
9-834I9 
9.83427 
9-83435 
9-83443 
9-83451 

9 

8 
8 
8 
8 
8 
8 
8 
g 

9.96981 
9.96996 
9.97011 
9.97026 
9.97042 
9-97057 
9.97072 
9.97087 
9-97102 

15 
15 
15 
16 
IS 
15 
15 
15 
16 

0.03019 
0.03004 
0.02989 
0.02974 
0.02958 
0.02943 
0.02928 
0.02913 
0.02898 

9-86406 
9-86399 
9-86392 
9-86384 
9.86377 
9-86370 
9-86363 
9-86356 
9-86349 

7 
7 
8 

7 
7 
7 
7 
7 

99 
98 
97 
96 
95 
94 
93 

92 

9i 

i 

2 

3 

4 

1 

9 

16 

1.6 

ii 

a 

9-6 

II.  2 
12.8 

14.4 

10 

9-83459 

9.97118 

0.02882 

9-86342 

90 

ii 

12 
13 

U 
15 
16 

17 
18 
19 

9-83468 
9.83476 
9.83484 
9.83492 
9-83500 
9-83508 
9-83516 
9.83524 
9.83532 

8 
8 
8 
8 
8 
8 
8 
8 
g 

9-97I33 
9.97148 
9.97163 
9.97178 
9-97193 
9.97209 

9.97224 
9.97239 
9-97254 

IS 
15 
IS 

IS 
16 
IS 
IS 
IS 

0.02867 
0.02852 
0.02837 
0.02822 
0.02807 
0.02791 
0.02776 
0.02761 
0.02746 

9-86335 
9.86328 
9.86321 

9-86314 
9.86306 
9.86299 
9.86292 
9.86285 
9.86278 

7 
7 
7 
8 
7 
7 
7 
7 

89 
88 
87 
86 
85 
84 

83 
82 

81 

i 

2 
3 
4 
5 
6 
7 
8 
9 

15 

i.  5 
3-0 
4-5 
6.0 
7-5 
9.0 
10.  5 

12.  0 

13-5 

20 

9.83540 

g 

9.97269 

16 

0.02731 

9.86271 

80 

21 
22 

33 
24 
25 

26 

27 

28 

29 

9-83548 
9.83556 
9.83565 

9-83573 
9-83581 
9.83589 

9-83597 
9-83605 
9-83613 

8 
9 
8 

8 
8 
8 
8 
8 
g 

9-97285 
9.97300 
9-97315 
9-97330 
9-97345 
9-9736I 
9-97376 
9-97391 
9.97406 

IS 

IS 
IS 

IS 
16 
IS 
IS 
IS 

0.02715 
0.02700 
0.02685 
0.02670 
0.02655 
0.02639 
o  .  02624 
0.02609 
0.02594 

9.86264 
9-86257 
9.86250 

9.86242 
9-86235 
9.86228 

9.86221 
9.86214 
9.86207 

7 
7 
8 

7 
7 
7 
7 
7 

79 
78 
77 
76 
75 
74 
73 

72 

7i 

i 

2 

3 

4 
5 
6 
7 
8 
9 

9 

0-9 
1.8 
2.7 
3-6 
4-5 

11 

7-2 

8.1 

30 

9.83621 

g 

9.97421 

16 

0.02579 

9.86200 

g 

70 

31 
32 
33 
34 
35 
36 
37 
38 
39 

9-83629 
9-83637 
9-83645 

9.83653 
9.83661 
9-83669 

9.83677 
9-83685 
9-83693 

8 
8 
8 
8 
8 
8 
8 
8 
g 

9-97437 
9-97452 
9.97467 
9.97482 
9-97497 
9-97512 
9-97528 
9-97543 
9-97558 

IS 
IS 
IS 
IS 
IS 
16 

IS 
15 
IS 

0.02563 
0.02548 
0.02533 
0.02518 
0.02503 
0.02488 
0.02472 

0.02457 
0.02442 

9.86192 
9.86185 
9.86178 

9.86171 
9.86164 
9-86157 
9.86150 
9.86142 
9-86135 

7 
7 
7 
7 
7 
7 
8 
7 

69 
68 
67 
66 
65 
64 

63 

62 
61 

i 

2 
3 

4 

7 
8 
9 

8 

0.8 
1.6 
2.4 

3-2 

4-0 
4-8 
5-6 
6.4 
7-2 

40 

9.83701 

g 

9-97573 

0.02427 

9.86128 

60 

4i 
42 
43 
44 
45 
46 

47 
48 
49 

9-83709 
9-837I7 
9-83725 
9-83733 
9-83741 
9-83749 
9-83757 
9.83765 
9-83773 

8 
8 
8 
8 
8 
8 
8 
8 
8 

9.97588 
9.97604 
9.97619 
9-97634 
9.97649 
9.97664 

9.97679 
9-97695 
9.97710 

16 
IS 
IS 
IS 
IS 
IS 
16 
IS 
15 

0.02412 
0.02396 
0.02381 
0.02366 
0.02351 
0.02336 
0.02321 
0.02305 
0.02290 

9.86121 
9.86114 
9.86107 
9-86099 
9.86092 
9.86085 
9.86078 
9.86071 
9.86063 

7 
7 
8 

7 
7 
7 
7 
8 
7 

59 
58 
57 
56 
55 
54 
53 

52 

Si 

I 

2 

3 

4 

7 
8 
9 

7 

0-7 
1-4 

2.1 
2.8 

3-5 
4-2 
4-9 
5-6 
6-3 

50 

9-83781 

9-97725 

0.02275 

9.86056 

60 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P. 

P. 

133< 


46' 


(185) 


43 


136  < 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

p.  p. 

50 

Si 

52 

53 
54 
55 
56 

57 
58 
59 
60 
61 
62 
63 
64 
65 
66 

67 
68 
69 
70 

9.83781 

8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
8 
7 
8 

8 
8 
8 
8 
8 
8 
8 
8 
8 
8 

7 
8 
8 
8 
8 
8 
8 
8 
8 
7 
8 
8 
8 
8 
8 
8 
8 

7 
8 
8 

9-97725 

IS 

15 
16 
15 
15 
IS 
IS 

IS 
16 
IS 
IS 
IS 
IS 
16 

IS 
IS 
IS 
IS 
IS 
16 

IS 
IS 
IS 
IS 

IS 
16 
IS 
IS 
IS 
IS 
IS 
16 
IS 
IS 
IS 
IS 
16 

IS 
IS 
IS 
IS 

IS 
16 
IS 
IS 
IS 
IS 

IS 
16 
IS 

0.02275 

9.86056 

7 
7 
7 
8 

7 
7 
7 

7 
8 
7 
7 

7 
8 
7 
7 
7 
7 
8 
7 
7 
7 
8 
7 
7 

7 
8 
7 
7 
7 
8 

7 

7 
8 
7 
7 
7 
8 

7 
7 
8 

7 
7 
7 
8 

7 
7 
8 

7 
7 
8 

50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 

28 

27 

26 

25 

24 

23 
22 
21 

20 

19 
18 
17 
16 
15 
14 
13 

12 
II 

10 

09 
08 

07 
06 
05 
04 
03 

02 
01 
00 

I 

2 

3 

4 
5 
6 
7 
8 
9 

i 

2 

3 

4 
5 
6 
7 
8 
9 

I 

2 

3 
4 
5 
6 
7 
8 
9 

i 

2 

3 

4 
5 
6 
7 
8 
9 

16 

1.6 

3-2 

4.8 
6.4 
8.0 
9-6 

II.  2 
12.8 
14-4 

15 

i.S 
3-0 
4-5 
6.0 
7-5 
9-0 
10.5 

12.0 

13-5 

8 

0.8 
1.6 

2-4 
3-2 

4.0 

4-8 
5.6 
6.4 
7.2 

7 

0-7 
i-4 

2.1 
2.8 
3-S 

4-2 

4.9 

5-6 
6.3 

9.83789 
9.83797 
9-83805 

9-83813 
9.83821 
9.83829 

9.83837 
9.83845 
9.83853 

9.97740 
9-97755 
9-97771 
9-97786 
9.978oi 
9.97816 

9.97831 
9.97846 
9.97862 

o  .  02260 
0.02245 
0.02229 
0.02214 
0.02199 
0.02184 
0.02169 
0.02154 
0.02138 

9-86049, 
9.86042 
9-86035 
9.86027 
9.86020 
9.86013 
9.86006 
9-85999 
9.85991 

9.83861 

9.97877 

0.02123 

9.85984 

9-83869 
9-83877 
9-83885 
9-83898 
9.83901 
9.83909 
9.839I7 
9.83925 
9-83932 

9.97892 
9.97907 
9-97922 
9-97938 
9-97953 
9.97968 

9.97983 
9.97998 
9.98013 

0.02108 
0.02093 
0.02078 
0.02062 
0.02047 
0.02032 
0.02017 

0.02002 
0.01987 

9-8S977 
9.85970 
9-85962 

9-85955 
9.85948 
9-85941 

9-85934 
9.85926 
9.85919 

9.83940 

9.98029 

O.OI97I 

9-85912 

71 

72 

73 
74 
75 
76 

77 
78 
79 
80 
81 
82 
83 
84 
85 
86 

87 
88 
89 
90 

9i 
92 
93 
94 
95 
96 

97 
98 
99 
100 

9.83948 
9.83956 
9.83964 
9.83972 
9.83980 
9.83988 

9.83996 
9.84004 
9.84012 

9-98044 
9-98059 
9-98074 
9.98089 
9.98104 
9.98120 

9.98135 
9.98150 
9-98165 

O.OI956 
O.OI94I 
O.OI926 
O.OI9II 
0.01896 
0.01880 
0.01865 
0.01850 
0.01835 

9-85905 
9.85897 
9.85890 
9-85883 
9.85876 
9.85868 
9.85861 
9-85854 
9-85847 

9.84020 

9.98180 

O.OI82O 

9.85839 

9.84027 
9-84035 
9-84043 
9.84051 
9.84059 
9.84067 

9.84075 
9-84083 
9.84091 

9.98195 
9.98211 
9.98226 

9.98241 
9.98256 
9.98271 
9.98287 
9.98302 
9-983I7 

O.OI805 
0.01789 
0.01774 
0.01759 
0.01744 
O.OI729 
O.OI7I3 
0.01698 
0.01683 

9-85832 
9-85825 
9-85817 
9.85810 
9.85803 
9.85796 
9.85788 
9-85781 
9.85774 

9-84098 

9-98332 

0.01668 

9-85766 

9.84106 
9.84114 
9.84122 

9-84130 
9-84138 
9.84146 

9-84154 
9.84161 
9.84169 

9-98347 
9-98362 
9.98378 

9.98393 
9-98408 
9-98423 
9.98438 
9.98453 
9.98469 

O.OI653 
0.01638 
0.01622 
O.OI607 
O.OI592 

0.01577 
0.01562 
0.01547 
0.01531 

9-85759 
9-85752 
9-85745 
9-85737 
9.85730 
9-85723 
9.857I5 
9-85708 
9-85701 

9.84177 

9.98484 

0.01516 

9.85693 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P.  P. 

133° 


46  < 


(i  86) 


44' 


135< 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

P.  P. 

00 

OI 

02 
03 
04 
05 
06 

07 
08 
09 
10 
ii 

12 
13 

14 

IS 
16 

17 
18 
i9 
20 

21 
22 
23 
24 
25 
26 

27 
28 
29 

30 

3i 

32 

33 
34 
35 
36 

37 
38 
39 
40 

4i 
42 
43 
44 
45 
46 

47 
48 
49 
50 

9.84177 

8 
8 
8 
8 

7 
8 
8 
8 
8 
7 
8 
8 
8 
8 
8 
7 
8 

8 
8 
8 

7 
8 
8 
8 
8 
7 
8 

8 
8 
7 
8 
8 
8 
7 
8 
8 
8 

7 
8 
8 
8 

7 
8 
8 
8 
7 
8 

8 
7 
g 

9.98484 

IS 
IS 
15 
IS 
16 
IS 
IS 
15 
15 
15 
16 

IS 
IS 
IS 
IS 
IS 
16 

IS 
IS 
IS 
IS 

IS 

16 
IS 
IS 
IS 
IS 

IS 
16 
15 
IS 
IS 
IS 
IS 
16 
IS 
IS 
IS 
IS 
IS 
16 

IS 
IS 
IS 
IS 
IS 
IS 
16 
IS 
IS 

0.01516 

9-85693 

7 
7 
8 
7 

7 
8 

7 

7 
8 
7 
7 
8 
7 
7 
8 
7 
7 
8 
7 
7 
8 

7 
8 
7 

7 
8 
7 
8 
7 
7 
8 

7 
8 

7 

7 
8 
7 
8 
7 
7 
8 

7 
8 
7 
8 
7 
7 
8 
7 
8 

100 

99 
98 
97 
96 
95 
94 
93 

92 

9i 
90 

89 
88 
87 
86 
85 
84 

83 
82 
81 
80 

79 
78 
77 
76 
75 
74 
73 
72 

7i 
70 

69 
68 
67 
66 
65 
64 

63 
62 
61 
60 

59 
58 
57 
56 
55 
54 
53 

52 

5i 
50 

I 

2 

3 

4 
5 
6 
7 
8 
9 

i 

2 

3 
4 
5 
6 
7 
8 
9 

I 

2 

3 

4 
5 
6 
7 
8 
9 

i 

2 

3 

4 
S 
6 
7 
8 
9 

16 

1.6 

3-2 

4-8 
6.4 
8.0 
9.6 

II.  2 
12.8 
14-4 

15 

1-5 
3-0 
4-5 
6.0 
7-5 
9-0 
10.5 

12.0 
13-5 

8 

0.8 
1.6 
2.4 
3-2 

4.0 

4-8 
5-6 
6.4 

7-2 

7 

o.7 
•  4 

.8 
•  5 

.2 

•  9 
5-6 
6.3 

9-84185 
9.84193 
9.84201 

9.84209 
9.84216 
9.84224 

9.84232 
9.84240 
9  84248 

9.98499 
9.98514 
9.98529 

9.98S44 
9-98560 
9.9857S 
9.98590 
9.98605 
9.98620 

0.01501 
0.01486 
0.01471 
0.01456 
0.01440 
0.01425 
0.01410 
0.01395 
0.01380 

9.85686 
9-85679 
9-85671 
9.85664 
9-85657 
9.85649 
9.85642 
9-85635 
9.85627 

9.84255 

9.98635 

0.01365 

9.85620 

9.84263 
9.84271 
9-84279 
9.84287 
9-84295 
9.84302 

9-84310 
9.84318 
9.84326 

9-98651 
9.98666 
9.98681 
9.98696 
9.98711 
9.98726 
9.98742 
9.98757 
9.98772 

0.01349 
0.01334 
0.01319 
0.01304 
0.01289 
0.01274 
0.01258 
0.01243 
0.01228 

9-85613 
9.85605 
9.85598 

9-85591 
9-85583 
9.85576 

9-85569 
9  85561 
9-85554 

9-84334 

9.98787 

0.01213 

9-85547 

9-8434I 
9-84349 
9-84357 
9-8436S 
9-84373 
9.84380 

9-84388 
9.84396 
9.84404 

9.98802 
9.98817 
9.98833 
9.98848 
9-98863 
9.98878 
9.98893 
9-98908 
9.98924 

0.01198 
0.01183 
0.01167 
0.01152 
0.01137 

O.OII22 
O.OII07 
O.OIO92 
O.OIO76 

9-85539 
9.85532 
9-85524 

9.855I7 
9-85510 
9-85502 

9-85495 
9-85487 
9-85480 

9.84411 

9.98939 

o.  01061 

9.85473 

9.84419 
9-84427 
9-84435 
9.84442 
9.84450 
9.84458 
9.84466 
9.84473 
9.84481 

9-98954 
9.98969 
9.98984 
9.98999 
9.990I5 
9.99030 

9.99045 
9.99060 
9.99075 

0.01046 
O.OI03I 
O.OIOI6 
O.OIOOI 

0.00985 
0.00970 

0.00955 
0.00940 
0.00925 

9-85465 
9.85458 
9-85450 

9-85443 
9.85436 
9.85428 

9.85421 
9.854I3 
9-85406 

9.84489 

9.99090 

0.00910 

9-85399 

9.84497 
9.84504 
9.84512 
9.84520 
9-84528 
9.8453S 
9.84543 
9.8455I 
9.84558 

9.99106 
9.99121 
9.99136 

9.99I5I 
9.99166 
9.99181 

9.99196 
9-99212 
9.99227 

0.00894 
0.00879 
0.00864 
0.00849 
0.00834 
0.00819 
0.00804 
0.00788 

0.00773 

9.85391 
9-85384 
9.85376 

9-85369 
9-85361 
9-85354 
9-85347 
9-85339 
9-85332 

9-84566 

9.99242 

0.00758 

9.85324 

Cos 

d. 

Cot      1  d.  c. 

Tan 

Sin 

d. 

P.  P. 

134° 


45  < 


(187) 


44 


Sin 

d. 

Tan 

d.  c. 

Cot 

Cos 

d. 

1 

>.  P. 

50 

9.84566 

g 

9.99242 

0.00758 

9.85324 

50 

5i 

52 

53 

54 
55 
56 

57 
58 
59 

9-84574 
9.84582 
9.84589 

9-84597 
9.84605 
9.84612 
9.84620 
9.84628 
9-84635 

8 

7 
8 

8 

7 
8 

8 

7 
g 

9-99257 
9.99272 
9.99287 

9-99303 
9.99318 
9-99333 
9.99348 
9.99363 
9  99378 

IS 
15 
16 

IS 
IS 
IS 
IS 
IS 
16 

0.00743 
0.00728 
0.00713 
0.00697 
0.00682 
0.00667 
0.00652 
0.00637 
0.00622 

9-853I7' 
9-85309 
9-85302 

9-85294 
9-85287 
9.85279 
9-85272 
9.85265 
9.85257 

8 
7 
8 

7 
8 
7 

7 
8 

49 
48 
47 
46 
45 
44 
43 
42 
41 

I 

2 

3 

4 
5 
6 

16 

1.6 
32 
4-8 
6.4 
8.0 
9.6 

60 

9.84643 

g 

9-99394 

0.00606 

9-85250 

g 

40 

8 

12.8 

6i 
62 
63 
64 
65 
66 

67 
68 
69 

9.84651 
9-84659 
9.84666 

9.84674 
9.84682 
9.84689 
9.84697 
9.84705 
9-84712 

8 
7 
8 

8 
7 
8 

8 

7 
g 

9.99409 
9.99424 
9-99439 
9-99454 
9.99469 
9.99485 
9-99500 
9-99515 
9-99530 

IS 
IS 
IS 

IS 
16 
IS 
IS 
IS 

0.00591 
0.00576 
0.00561 
0.00546 
0.00531 
0.00515 
0.00500 
0.00485 
0.00470 

9.85242 
9.85235 
9-85227 
9.85220 
9.85212 
9-85205 

9.85197 
9-85190 
9.85182 

7 
8 
7 
8 
7 
8 

7 
8 

39 
38 
37 
36 
35 
34 
33 
32 
31 

9 

I 

2 

3 

4 
5 

14.4 

!5 

1-5 
3-0 
4-5 
6.0 
7-5 

70 

9.84720 

9-99545 

0.00455 

9.85175 

g 

30 

6 

9.0 

71 

72 

73 
74 
75 
76 

77 
78 
79 

9.84728 
9.84735 
9.84743 
9.8475I 
9.84758 
9.84766 

9-84773 
9.84781 
9.84789 

7 
8 
8 

7 
8 
7 
8 
8 

9.99560 
9-99576 
9-99591 
9.99606 
9.99621 
9.99636 

9.99651 
9-99666 
9.99682 

16 
IS 
IS 
IS 
IS 
IS 

IS 
16 

0.00440 
0.00424 
0.00409 

0.00394 
0.00379 
0.00364 

0.00349 
0.00334 
0.00318 

9.85167 
9.85160 
9-85I52 
9-85I4S 
9.85137 
9-85130 
9.85122 
9.85H5 
9.85107 

7 
8 
7 
8 
7 
8 

7 
8 

29 

28 

27 

26 

25 
•24 

23 
22 
21 

8 
9 

I 

12.0 

13-5 

8 

0.8 

80 

9.84796 

g 

9.99697 

0.00303 

9.85100 

g 

20 

2 

1.6 

8s 

82 
83 
84 
85 
86 

87 
88 
89 

9.84804 
9.84812 
9.84819 
9.84827 
9-84835 
9.84842 

9.84850 
9-84857 
9.84865 

8 

7 
8 

8 
7 
8 

7 
8 

9.99712 
9.99727 
9.99742 

9-99757 
9-99773 
9-99788 

9-99803 
9.99818 
9.99833 

IS 
IS 
IS 
16 
IS 
IS 
IS 
IS 

0.00288 
0.00273 
0.00258 
0.00243 
0.00227 

O.OO2I2 
0.00197 
0.00182 
O.OOI67 

9-85092 
9-85085 
9.85077 
9.85069 
9.85062 
9.85054 
9.8S047 
9-8S039 
9-85032 

7 
8 
8 

7 
8 
7 
8 

7 
g 

19 
18 
17 
16 
15 
14 
13 

12 

II 

3 
4 
S 
6 
7 
8 
9 

3-2 

4.0 
4-8 
5.6 
6.4 

7-2 

7 

90 

9.84873 

9.99848 

16 

0.00152 

9-85024 

10 

i 

0.7 

9i 
92 
93 
94 
95 
96 

97 
98 
99 

9.84880 
9.84888 
9.84895 
9.84903 
9.84911 
9.84918 
9.84926 
9.84933 
9.84941 

8" 

7 
8 

8 
7 
8 

7 
8 

9.99864 
9.99879 
9.99894 

9-99909 
9-99924 
9-99939 

9-99955 
9.99970 
9-99985 

IS 
IS 

IS 
IS 
IS 
16 

IS 
IS 

O.OOI36 
O.OOI2I 
0.00106 
0.00091 
O.OOO76 
0.0006I 
O.OOO45 
O.OO03O 
O.OOOI5 

9-85017 
9-85009 
9.85001 

9.84994 
9.84986 
9-84979 
9.84971 
9.84964 
9.84956 

8 
8 
7 
8 
7 
8 
7 
8 
7 

09 
08 

07 
06 
05 
04 

03 
02 

OI 

2 

3 

4 
5 
6 
7 
8 
9 

i-4 

2.1 
2.8 

3-5 
4-2 
4-9 
5.6 
6.3 

100 

9.84949 

IO.OOOOO 

o.ooooo 

9.84949 

00 

Cos 

d. 

Cot 

d.  c. 

Tan 

Sin 

d. 

P 

P. 

134C 


45' 


(188) 


TABLE  XXVI.— LOGARITHMIC  VERSED  SINES  AND  EXTERNAL  SECANTS 

Log  vs  =  2  log  a°  +  V    Log  exsec  =  2  log  a°  -f-  E 


Hun- 

0 

0 

Hun- 

1 

• 

dredths 

Vers 

v 

E 

Exsec 

dredths 

Vers 

V 

E 

Exsec 

00 

[nf.  neg. 

6. 
725 

182 
725 

Inf.  neg. 

00 

6.18271 

6. 
714 

182 
780 

6.18278 

02 
04 
06 
08 
IO 
12 
14 

16 
18 

2.78478 
3-38684 
.73903 
.98890 
4.18272 
.34109 
.47498 
.59096 
.69327 

725 
725 
725 
725 
725 
725 
725 
724 
724 

725 
725 
725 
725 
725 

726 
726 
726 

727 

2.78478 
3.38684 
.73903 
.98890 
4.18272 
.34109 
.47498 
.59096 
.69327 

02 
04 
06 
08 
10 
12 

14 
16 
18 

.19991 
.21678 
•23332 
.24956 
6.26549 
.28115 
.29652 
.31163 
.33-461 

713 
713 
712 

712 
711 
711 

711 

710 

709 

782 
785 
787 
789 
791 
794 
797 
799 
801 

.19998 
.21685 
.23339 
.24964 
6.26557 
.28123 

.29661 
.31172 
•33470 

20 

4.78478 

724 

727 

4.78479 

20 

6.34107 

709 

804 

6.34116 

22 
24 
26 
28 
30 
32 
34 
36 
38 

.86757 
.94315 
5.01267 
.07704 
5.13697 
.19302 
.24568 
.29533 
.34229 

724 
724 
724 
724 
724 
724 
723 
723 
723 

727 

728 
729 
729 
730 

731 
731 
732 
733 

.86757 
•94315 
5.01268 
.07705 
5.13697 
.19303 
.24569 
.29534 
.34230 

22 

24 
26 

28 
30 
32 

34 
36 
38 

-35543 
.36955 
.38345 
.39713 
6.41059 
.42385 
.43691 
•44977 
.46246 

708 
708 

707 
707 
706 
706 

70S 
704 
704 

807 
810 
812 

815 
818 
821 
824 
827 
830 

•35553 
.36965 
.38356 

.39724 
6.41070 
•42397 
.43703 
.44989 
•46259 

40 

5.38684 

723 

734 

5.38685 

40 

6.47496 

703 

833 

6.47509 

42 
44 
46 
48 
50 
52 

54 
56 
58 

.42922 
.46962 
.50824 
•54521 
5.58066 
.61473 
.64751 
.67910 
.70958 

723 
722 
722 

722 
722 
722 
721 
721 

721 

735 
735 
736 
737 
739 
740 
740 
742 
743 

.42923 
.46964 
.50825 
•54522 
5.58068 
.6x475 
.64753 
.67912 
.70960 

42 
44 
46 
48 
50 

52 

54 
56 
58 

.48728 
•49943 
.5U4I 
.52322 
6.53488 
.54639 
•55774 
.56895 
.58001 

703 
702 
701 
700 
700 
699 
699 
698 
697 

836 
839 
842 

845 
849 
852 

855 
859 
863 

.48741 
•49957 
•  SUSS 
•52336 
6.53503 
.54654 
•55790 
.56911 
.58018 

60 

5.73902 

721 

745 

5.73904 

60 

6.59093 

697 

866 

6.59110 

62 
64 
66 
68 
70 

72 

74 
76 
78 

.76750 
.79508 
.82181 

.84774 
5.87292 
.89738 
.92118 
•94435 
.96691 

720 

720 

720 

720 

719 
719 
719 
718 
718 

746 
747 
749 
750 
752 
753 
755 
756 
758 

.76753 
•795II 
.82184 

.84777 
5-87295 
.89742 
.92122 
.94438 
-96695 

62 
64 
66 

68 
70 

72 

74 
76 
78 

.60173 
.61238 
.62291 

.63331 
6.64359 
.65375 

.66379 
.67372 
.68353 

696 
695 
694 
694 
693 
692 
692 
691 
690 

870 
873 
877 
88l 
884 
888 
892 
896 
900 

.60190 
.61256 
.62309 
.63350 
6.64378 
•65395 
.66399 
.67392 
.68374 

80 

5-98890 

718 

760 

5.98894 

80 

6.69323 

689 

903 

6.69345 

82 
84 
86 
88 
90 

92 

94 
96 
98 

6.01034 
.03128 
.05171 
.07168 
6.09120 
.11029 
.12897 
.14726 
-16517 

717 
717 
717 
716 
716 
715 
715 
715 
714 

762 
764 
766 

767 
769 
772 
774 
776 
778 

6  .  01039 
.03132 
.05176 

•07173 
6.09125 
•11035 
.12903 
.  14732 
•  16523 

82 
84 
86 
88 
90 
92 
94 
96 
98 

.70383 
.71232 
.72171 
•73100 
6.74019 
.74929 
.75829 
.76718 
.77601 

688 
68? 
686 
686 
685 
684 
683 
682 
681 

907 
911 
915 
919 
924 
928 
932 
936 
941 

.70405 
•71254 
.72194 
.73123 
6.74043 
•74953 
.75854 
.76743 
.77627 

100 

6.18271 

714 

780 

6.18278 

100 

6.78474 

681 

945 

6.78500 

(189) 


TABLE  XXVI.— LOGARITHMIC  VERSED  SINES  AND  EXTERNAL  SECANTS 
Logvs  =  2  logo;0  +  V        Logexsec  =  2logo:0  +  £ 


Hun- 

dredths 

2° 

Hun- 
dredths 

3°          x 

Vers 

V 

E 

Exsec 

Vers 

V  \  E 

Exsec 

00 
02 
04 
06 
08 
10 

12 

14 

16 
18 
20 

22 

24 
26 
28 
30 
32 

34 
36 
38 
40 
42 
44 
46 
48 
So 

52 

54 
56 
58 
60 
62 
64 
66 
68 
70 

72 

74 
76 
78 
80 
82 
84 
86 
88 
90 
92 

94 
96 
98 
100 

6.78474 

6. 
681 
680 
679 
678 

677 
676 
675 
674 
673 
672 

671 
670 
669 
668 
667 
666 
665 
664 
663 
662 

661 
660 
659 
658 

657 
656 
655 
654 
652 
651 
650 

649 
648 
646 
645 
644 
643 
642 
640 
639 
638 

637 
636 
634 

633 
632 
631 
630 
628 
627 
626 

182 
945 
950 
954 
958 

963 
968 
973 
978 
982 
987 
992 
997 

*O02 
006 
Oil 

016 
022 
027 
032 
037 
042 
048 
053 
058 

063 
069 
075 
081 
086 
092 
098 

103 
109 
«5 

121 

127 
133 
139 
145 
151 
157 
163 
169 
176 
182 
189 
195 

201 
208 
215 

221  .. 

6.78501 

00 

02 

04 
06 
08 

10 
12 

14 
16 
18 
20 

22 

24 

26 
28 

30 
32 

34 
36 
38 
40 

42 
44 
46 
48 
50 
52 

54 
56 
58 
60 
62 
64 
66 
68 
TO 

72 

74 
76 
78 
]  80 
82 
84 
86 
88 
90 

92 

94 
96 
98 
100 

7-13687 

6.182 
626 
624 
623 
621 
620 
619 
618 
616 
614 
613 
612 
610 
609 
607 
606 
605 
603 
602 
600 
599 
597 
596 
595 
593 
591 
590 
588 

587 
585 
583 
582 
58l 
579 
577 
575 
574 
572 
571 
569 
567 
566 

564 
562 
56o 
558 
557 
555 
553 
552 
550 
548 

6.183 
221 
228 
234 
241 
248 
255 
261 
268 
275 
283 
290 
296 
303 
3ii 
318 
325 
333 
340 
348 
355 
362 
370 
377 
385 

393 

400 
408 
416 
424 
432 
440 
448 
456 
464 
472 
480 
488 
496 
504 
512 
521 

529 
538 
547 
556 
564 
572 
581 
590 
599 
608 

7.13746 

.79338 
.80194 
.81041 
.81880 
6.82712 
.83535 
.84350 
.85158 
•85959 

.79365 
.80221 
.81069 
.81909 
6.82741 
-83565 
.84381 
.85189 
.85990 

.14264 
•  14837 
•15406 
.15972 
7.I6S34 
.17093 
.17648 
.18199 
.18747 

•  14324 
.14898 
.16468 
•16035 
7.16598 
•I7I57 
.17713 
.  18265 
.18814 

6.86752 

6.86784 

7.19291 

7.19359 

.87538 
.88317 
.89089 

-89854 
6.90612 
•91364 
.92110 
.92849 
.93582 

.87570 
.88350 
.89122 
.89888 
6.90647 
.91400 
.92146 
.92886 
.93619 

.18832 
.20370 
.20904 

•21435 
7-21963 
.22488 
.23010 
.23528 
.24043 

.19901 
.20439 
.20975 
.21507 
7.22035 
.22561 

.23083 
.23603 
.24119 

6.94308 

6.94347 

7.24556 

7.24632 

.95029 
•95744 
.96453 
.97156 
6.97854 
.98546 
.99232 
.99913 
.00589 

.95068 
.95783 
.96493 
.97197 
6.97895 
.98588 

.99275 
•99957 
.00633 

.25065 
.25571 
.26075 
•26575 
7-27073 
.27567 
.28059 
.28549 
.29035 

.251.42 
.25649 
.26154 
.26655 
7-27154 
.27649 
.28142 
.28632 
.29120 

7.01260 

7.01304 

7.29519 

7  •  29605 

.01925 
.02586 
.03241 
.03891 
7.04537 
.05178 
.05814 
.06446 
.07073 

.01971 
.02632 
.03288 

.03939 
7.04585 
.05227 

.05864 
.06496 
.07124 

.30000 
•30478 
•30954 
•31427 
7.31898 
.32366 
.32831 
.33294 
•33755 

.30087 
.30566 
.31043 
.31517 
7.31988 
.32457 
•32924 
.33388 
.33850 

7.07695 

7-07747 

7-34213 

7.34309 

.08314 
.08927 
.09537 
.10142 
7-10743 
.11340 
.11932 
.  12521 
.13106 

.08366 
.08981 
.09591 
.10197 
7.10799 
.11396 
.11790 
.12579 
.13165 

.34669 
.35122 
.35574 
.36022 
7.36469 
•36913 
•37355 
•37794 
.38232 

.34766 
.35220 
.35672 
.36122 
7-36569 
•37014 
•37457 
.37898 
.38337 

7.13687 

7.13746 

7-38667 

7.38773 

(190) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

4° 

Hun- 
dredths 

5° 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

Vers. 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

7-38667 

21  6s 

7.38773 

00 

7.58039 

7.58204 

02 
04 
06 

.39100 
•39531 
.39960 

21.55 
21.45 

21  30 

.39207 
.39639 
.40069 

21.60 
.21.50 
21  35 

02 

04 

06 

.58385 
.58731 

.59074 

17-30 
17.15 
17.15 

.58552 
.58899 
.59244 

17-35 
17-25 
17.20 

08 
IO 

-4P386 
7.40811 

21.25 

.40496 
7.40922 

21.30 

08 

10 

.59417 
7-59758 

17-05 

.59588 
7-59930 

17.10 

12 
14 

16 
18 

.41233 

.41654 

.42072 
.42488 

21.  IO 

2I.O5 
20.90 
20.80 

.41346 

.41767 
.42187 
.42604 

21.  2O 
21.05 
21.00 
20.85 

12 

14 

16 
18 

.60098 
.60436 
.60773 
.61109 

16.90 
16.85 
16.80 

.60271 
.60611 
.60949 
.61287 

17.05 
17.00 

16.90 
16.90 

20 

7.42903 

7-43020 

20 

7.61443 

16  70 

7.61622 

22 
24 
26 
28 
30 
32 

.43315 
.43726 
.44134 

•44541 
7.44946 
•45349 

20.55 
20.40 
20.35 
20.25 
20.15 
20.05 

•43433 
.43845 
.44255 
.44662 
7.45068 
•45472 

2O.6O 
20.50 

20.35 
20.30 

20.20 
20.10 

22 

24 

26 
28 
30 

32 

.61777 
.62108 
.62439 
.62769 
7.63097 
.63424 

16.55 
16.55 
16.50 

16.40 
16.35 
16.25 

.61957 
.62290 
.62622 

.62953 
7-63283 
.63611 

16.65 
16.60 
16.55 
16.50 
16.40 
16.35 

34 
36 
38 

•45750 
.46149 
.46546 

19-95 
19.85 

.45874 
.46275 
.46673 

20.O5 
19.90 

34 
36 
38 

.63749 
.64074 
.64397 

16.25 
16.15 

.63938 
.64264 
.64589 

16.30 
16.25 

40 

7.46942 

7.47070 

40 

7.64719 

7.64912 

42 
44 
46 

•47335 
.47727 
.48118 

19.60 
19-55 
19.40 

.47465 
.47858 
.48249 

19.65 
19-55 
19.50 

42 
44 
46 

.65040 
.65360 
.65678 

16.00 
15.90 
15.85 

.65235 
.65556 
.65876 

16.05 
16.00 
15.90 

48 
50 

52 

.48506 
7.48893 
.49278 

19-35 
19-25 
19.15 

.48639 
7.49027 
.49413 

19.40 
19.30 
19.20 

48 
50 
52 

.65995 
7.66312 
.66627 

15.85 
15-75 
15.70 

.66194 
7.66512 
.66829 

15.90 
15.85 
15-75 

54 
56 
58 

.49661 
.50043 

.50422 

19.10 
18.95 
18  95 

.49797 
.50180 
.50561 

I9-I5 
19.05 
IQ  OO 

54 
56 
58 

.66941 
.67253 
.67565 

15.60 
15.60 
15  55 

.67144 
.67458 
.67771 

15.70 
15.65 
15  60 

60 

7.5o8oi 

18  80 

7.50941 

60 

7.67876 

7.68083 

62 
64 
66 

.5H77 
.51552 
.51926 

18.75 
18.70 
18.55 

.51319 
.51695 
.52070 

18.80 
18.75 
18.65 

62 

64 
66 

.68185 
•68493 
.68800 

15.40 
15-35 
15-35 

.68394 
.68704 
.69013 

15.50 
15  45 
15-35 

68 
70 

72 

.52297 
7.52668 
.53036 

18.55 
18.40 
18.35 

.52443 
7.52814 
.53184 

18-55 
18.50 
18.40 

68 
70 

72 

.69107 
7.69412 
.69716 

15-25 
15.20 
15.15 

.69320 
7.69627 
.69932 

15-35 
15.25 
15.25 

74 
76 
78 

•  53403 
.53769 
•54133 

18.30 
18.20 
18  10 

•53552 
-539I9 
.54284 

18.35 
18.25 
18  20 

74 
76 
78 

.70019 
.70320 
.70621 

15-05 
15-05 

.70237 

.70540 
.70843 

15.15 
15.15 

80 

7-54495 

18  05 

7.54648 

18  10 

80 

7.70921 

14  Q^ 

7.7"44 

82 
84 
86 

.54856 
.55216 
•55574 

17.90 
17.90 
17.80 

.55010 
.55371 
•55730 

18.05 
17-95 
17.90 

82 
84 
86 

.71220 
.71517 
.71814 

14.85 
14.85 
14.80 

.71444 
.71743 
.72042 

14-95 
14-95 
14-85 

88 
90 

92 

•55930 
7.56285 
.56639 

17-75 
17.70 
17.65 

.56088 
7.56444 
.56799 

17.80 
17-75 
17.70 

88 
90 

92 

.72110 
7.72405 
.72698 

14.75 
14.65 
14.65 

.72339 
7.72635 
.72930 

14.80 
14-75 
14-75 

94 
96 
98 

.56991 
•57342 
.57691 

17-55 
17.45 
17  40 

.57153 

•57505 
.57855 

17.60 
17.50 
17  45 

94 
96 
98 

.72991 
.73283 
•73573 

14.60 
14.50 

.73225 
.73518 
.738io 

14.65 
14.60 
14  ^ 

100 

7.58039 

7.58204 

100 

7.73863 

J.  74102 

(191) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

6° 

Hun- 

dredths 

7° 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

00 

7.73863 

7.74102 

00 

7.87238 

7-87563 

02 

.74152 

•74392 

02 

.87486 

.87812 

04 

•74440 

14.40 

.74681 

14-45 

04 

.87732 

12.30 

.88061 

12.45 

06 

.74727 

14-35 
14.25 

•74970 

14-45 
14.35 

06 

.87978 

12.30 
12.30 

.88309 

12.40 
12.35 

08 

.75012 

.75257 

08 

.88224 

.88556 

10 

ia 

7-75297 
.75581 

14.25 
14.20 
14.20 

7-75544 
-75830 

14-35 
14-30 
14.20 

IO 

ia 

7-88469 
.88713 

12.25 

12.20 
12.15 

7.88803 
.89049 

12.35 
12.30 
12.25 

14 

.75865 

.76114 

14 

.88956 

.89294 

16 

.76147 

14.10 

.76398 

14.20 

16 

.89199 

12.15 

.89539 

12.25 

18 

.76428 

14.05 

.76681 

14.15 

18 

.89441 

.89782 

12.15 

20 

7.76708 

7-76963 

20 

7.89682 

7  .  ooo  jo 

22 

.76988 

4' 

•77244 

22 

.89922 

' 

.90268 

' 

24 

.77266 

13.9° 

-77525 

14-05 

24 

.90162 

12.  OO 

.90510 

12.  IO 

26 

•77544 

13.9° 
13-85 

.77804 

13-95 
13.90 

26 

.90402 

11.90 

.90751 

12.05 

28 
30 
33 

.77821 
7.78097 
.78372 

13.80 
13-75 
I3-70 

.78082 
7.78360 
.78637 

13-90 
13.85 
13-75 

28 

30 
32 

.90640 
7.90878 
.91116 

11.90 
II.9O 
11.80 

.90992 

7  .in  _•.<_• 

.91471 

12.  OO 
11-95 

II  95 

34 
36 
38 
40 

.78646 
.78919 
.79192 

13-65 
13  65 
13-55 

.78912 
.79187 
.79462 

13-75 
13-75 
13-65 

TI  fin 

34 
36 
38 
40 

•91352 
.91588 
.91824 

II.80 
II.80 

11.70 

.91710 
.91948 
.92185 

11.90 
11.85 
11.85 

7.79463 

7-79735 

7.92058 

7.92422 

43 
44 
46 

.79734 
.80004 
.80273 

13.50 
13-45 
13.40 

.80007 
.80279 
.80550 

13.60 

13  55 
13  50 

43 
44 
46 

-92293 
.92526 
.92759 

11.65 
11.65 
II.  60 

.02658 
.92893 
.93128 

11.75 
11.75 
11.70 

48 
50 

53 

54 
56 
58 

.80541 
7.80809 
.81075 

.81341 
.81606 
.81870 

13-40 
13.30 
13.30 

13.25 
13-20 

.80820 
7.81089 
.81357 
.81624 
.81891 
.82157 

13-45 
13-40 
13-35 

13-35 
13.30 

48 
50 

53 

54 
56 
58 

.92991 
7.93223 
-93454 
.93684 
.93914 
-94I43 

II.  60 

11-55 

11.50 

11.50 
H-45 

.93362 
7.93596 
.93829 
.94061 
.94293 
.94524 

11.70 
11.65 
II.  60 
II.  60 
11-55 

60 

62 

7-82133 

13-15 

7.82422 

13-20 

60 
62 

7-94372 

11.35 

7.94755 

11.50 

.82396 

.82686 

•94599 

.94985 

64 
66 

68 
70 

73 

.82657 
.82918 

.83179 
7.83438 
-83697 

13.05 
13-05 
13.05 
12.95 
12.95 
12.85 

.82950 
.83212 

.83474 
7.83736 
.83996 

13.20 
13.10 
13.10 
13.10 
13.00 
13  oo 

64 
66 

68 
70 

73 

.94827 
.95054 
.95280 
7.95505 
•95730 

11.40 
H.35 
11.30 
11.25 
11.25 
11.25 

.95214 

•95443 
.95671 
7-95899 
.96126 

11-45 
11-45 
11.40 

11.40 
11-35 
11.30 

74 
76 
78 

.83954 
.84211 
.84468 

12.85 
12.85 

.84256 
.845M 
.84773 

12.90 
12.95 

74 
76 

78 

•95955 
.96178 
.96402 

II.  IS 

II.  20 

.96352 
.96578 
.96803 

11.30 
11.25 

80 

7.84723 

7.85030 

80 

7.  966-M 

7.97028 

82 
84 
86 

.84978 
.85232 
.85485 

12.70 
12.65 
12.65 

.85286 
.85542 
.85797 

12.80 

12.75 
12.75 

82 
84 
86 

.96846 
.97068 
.97289 

II.  IO 

11.05 

II.  OO 

.97252 

.97476 
.97699 

11.20 

11.15 

II.  10 

88 
90 

93 

94 
96 
98 

.85738 
7.85990 
.86241 

.86491 
.86741 
.86990 

12.60 
12.55 
12.50 

12.50 
12.45 

.86052 
7.86306 
.86558 
.86811 
.87062 
.87313 

12.70 
12.60 
12.65 
12.55 
12.55 

88 
90 

93 

94 
96 
98 

-97509 
7.97729 
.97948 
.98167 
.98385 
.98603 

11.00 

10.95 
10.95 

10.90 
10.90 
10  85 

-97921 
7.98143 
.98365 

.98585 
.98806 
.99025 

II.  10 
II.  IO 
II.  OO 

11.05 
10.95 

100 

100 

7.99245 

(192) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

8° 

Hun- 
dredths 

9° 

Diff. 
Vers         .001 

Exsec 

Diff. 
.001 

Diff. 
Vers     !    .001 

Exsec 

Diff. 

.001 

00 

02 
04 
06 
08 

10 
12 

7.98820 

I0.8o 
10.80 
10.80 
10.75 
10.70 
10.70 
10.65 

7-99245 

10.90 
10.90 
10.90 
10.85 
10.85 
10.80 
10.75 

00 

02 
04 
06 
08 
10 
12 

8.09032 

9.60 
9.60 
9.60 
9-55 
9-50 
9-55 
9-50 

8.09570 

9-70 

9  65 
9.60 
9-65 
9-70 
9.60 
965 

.99036 
.99252 
.99468 

.99683 
7.99897 
8.00III 

.99463 
.99681 
.99899 
8.00116 
8.00333 
.00549 

.09224 
.09416 
.09608 

.09799 
8.09989 
.10180 

-09764 
•09959 
.10153 

.10346 
8.10540 
•10732 

14 

16 
18 

.00324 
.00537 
.00749 

10.65 
10.60 

.00764 
.00979 
.01193 

10.75 
10.70 

14 

16 
18 

.  10370 
•10559 
.10748 

9-45 
9-45 
Q  4^ 

.10925 
.11116 
.11308 

9-55 
9.60 

9CC 

20 

8.00961 

8-OI4°7      "I, 

20 

8.10937 

8.II499 

22 
24 
26 

.01172 
.01383 
.01593 

10.55 
10.50 
10.50 

.01621 
.01834 
.02046 

10.65 
10.  60 

10.  60 

22 

24 
26 

.11125 
.11313 
.11500 

9-40 
9-35 
9-35 

.11690 
.11880 
.12070 

9-50 

9-50 
9-45 

28 
30 
32 

.01803 

8.02012 
.02221 

10.  45 
10.45 
10.40 

.02258 
8.02469 
.02680 

10.55 
10.55 
10-55 

28 

30 
32 

.11687 
8.11874 
.12060 

9-35 
9-30 
9-30 

.12259 
8.12448 
.12637 

9-45 
9-45 
9-40 

34 
36 

38 

.02429 
.02637 
.02844 

10.40 
10.35 

.02891 
.03101 
.03310 

10.50 
10.45 

34 
36 

38 

.12246 
.12431 
.12616 

9-25 
9-25 

.12825 
.13013 
.13201 

9-40 
9-40 

9-7C 

40 

8.03051 

8.03519 

40 

8.12801 

9    2O 

8.13388 

9  -JO 

42 
44 
46 

.03257 
.03462 
.03668 

10.25 
10.30 

IO.2O 

.03727 
•03935 
.04143 

10.40 
10.40 
10.35 

42 
44 

46 

.12985 
.13169 
.13352 

9-20 
9-15 
9-15 

.13574 
.13761 
•13947 

9.35 
9.30 

9.25 

48 
50 

52 

.03872 
8.04077 
.04280 

10.25 
IO.I5 
IO.2O 

.04350 
8.04556 
.04762 

10.30 
10.30 

10.  2O 

48 
So 

53 

.13535 
8.13718 
.13900 

9-15 
9.10 
9.10 

.14132 
8.I43I7 
.14502 

9-25 
9-25 
9-25 

54 
56 
58 

.04484 
.04686 
.04889 

10.10 

10.15 

.04968 
.05173 
.05378 

10.25 
10.25 

54 
56 
58 

.14082 
.14263 

-14444 

9-05 
9-05 

.14687 
.14871 
.15054 

9.20 

9-15 

9    2O 

60 

8.05091 

10  05 

8.05582 

10  15 

60 

8.14625 

8.15238 

910 

62 
64 
66 

.05292 

.05493 
•05693 

10.05 

IO.OO 
10.00 

.05785 
.05989 
.06191 

IO.2C 
10.10 

10.15 

62 
64 
66 

.14805 
.14985 
.15165 

9.00 
9.00 
8-95 

.15420 
.15603 
.15785 

9-iS 
9.10 
9.10 

68 
70 

73 

.05893 
8.06093 
.06292 

IO.OO 

9-95 
9-95 

•06394 
8.06595 
.06797 

10.05 

10.10 

10.05 

68 
70 

72 

•  15344 
.8.15523 
.15702 

8-95 
8-95 
8.90 

•15967 
8.16148 
.16330 

9-05 

9.10 
9.00 

74 
76 
78 

.06491 
.06689 
.06886 

9.90 
9-85 

9  GO 

.06998 
.07198 
.07398 

IO.OO 
10.00 

74 
76 
78 

.15880 
.16057 
.16235 

8.85 
8.90 
8  85 

.  16510 
.16691 
.16871 

9-05 
9.00 

8  <K 

80 

8.07084 

9  80 

8.07598 

90S 

80 

8.16412 

8  80 

8.17050 

8  Q^ 

82 
84 
86 

.07280 
.07477 
•07673 

9-85 

9-80 
9-75 

.07797 
•07996 
.08194 

9.95 
9.90 
9.90 

82 
84 
86 

.16588 
.16765 
.16941 

8.85 
8.80 
8-75 

.17229 
.17408 
.17587 

8-95 
8.95 
8.90 

88 
90 

92 

.07868 
8.08063 
.08258 

9-75 
9-75 
9-70 

.08392 
8.08589 
.08786 

9-85 
9-85 
9-85 

88 

90 

92 

.17116 
8.17291 
.17466 

8-75 
8-75 
8.75 

.17765 
8.17943 
.18120 

8.90 
8.85 
8.90 

94 
96 
98 

.08452 
.08646 
.08839 

9.70 
9-65 
9.65 

.08983 
.09179 
•09374 

9-80 
9-75 
o  80 

94 
96 
98 

.17641 
.17815 
.17989 

8.70 
8.70 
8  65 

.18298 
.18474 
.18651 

8.80 
8.85 
8  80 

100 

8.09032 

100 

8.18162 

8.18827 

(193) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

10° 

Hun- 

dredths 

11° 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

8.18162 

0    A- 

8.18827 

8  80 

00 

8.26418 

7   8" 

8.27223 

0     fy, 

02 
04 
06 
08 

.18335 
.18508 
.18680 

.18853 

8.65 
8.60 
8.65 

.19003 
.19178 
.19353 
.19528 

8.75 
8.75 
8.75 

02 
04 
06 
08 

•26575 
.26732 
.26889 

.27045 

7.85 
7.85 
7.80 

.27383 
•27543 
.27703 
.27862 

8.00 
8.00 
7-95 

10 
12 

14 

8.19024 
.19196 
-19367 

8-55 
8.60 

8-55 

8.19703 
.19877 
.20050 

8.75 
8.70 
8.65 

10 
12 

14 

8.27201 
.27357 
.27513 

7.80 

7.80 
7.80 

8.28021 
.28180 

-28339 

7-95 
7-95 
7-95 

16 

.19537 

8.50 

.20224 

8.70 

16 

.27668 

7-75 

.28497 

7.90 

18 
20 

.19708 

8.55 
8.50 

o    ,c 

.20397 

8.65 
8.65 
8  60 

18 
20 

.27823 

7-75 
7-75 

.28655 

7.90 
7-90 

8.19878 

8.20570 

8.27978 

8.28813 

22 

.20047 

.20742 

22 

.28132 

.28970 

7-  5 

24 

.20217 

8.50 

.20914 

8.60 

24 

.28286 

7.70 

.29128 

7.90 

26 

.20386 

8.45 

.21086 

26 

.28440 

7.70 

.29284 

7.80 

8.45 

8.55 

7.70 

7-85 

28 

.20555 

.21257 

28 

•28594 

.29441 

30 
32 

8.20723 
.20891 

8.40 
8.40 
8.40 

8.21428 
.21599 

8.55 
8.55 
8.55 

30 
32 

8.28747 
.28900 

7.65 
7-65 
7-65 

8.29598 
.29754 

7-85 

7.80 
7-75 

34 
36 
38 

.21059 
.21226 
-21393 

8.35 
8.35 
8  15 

.21770 
.21940 

.22110 

8.50 
8.50 

8«e 

34 
36 
38 

.29053 
.29206 
.29358 

7.65 
7.60 

7  60 

.29909 
.30065 
.30220 

7.80 
7-75 

7  80 

40 

8.21560 

8.22279 

8/tc 

40 

8.29510 

7   fio 

8.30376 

42 

.  21726 

•  30 

.22448 

42 

.29662 

.30530 

44 
46 

.21892 
.22058 

8.30 
8.30 
8.30 

.22617 
.22786 

8.45 
8-45 
8.40 

44 
46 

.29813 
.29965 

7-55 
7.60 
7-55 

.30685 
.30839 

7-75 

7-70 
7-70 

48 

.  22224 

.22954 

48 

.30116 

.30993 

50 

8.22389 

8.25 

8.23122 

8.40 

50 

8.30266 

7-5O 

8.3H47 

7.70 

52 

.22554 

8.25 
8.20 

.23290 

8.40 
8.35 

52 

•30417 

7-55 
7-50 

.31300 

7-05 

7.70 

54 
56 
58 

.22718 
.22882 
.23046 

8.20 
8.20 

.23457 
.23624 
.23791 

8.35 

8-35 

8-,o 

54 
56 
58 

.30567 
.30717 
.30866 

7-50 
7-45 

.31454 
.31607 
.31759 

7-65 
7.60 

60 

8.23210 

8.23957 

60 

8.31016 

8.31912 

7   60 

62 
64 
66 

.23373 
.23536 
.23699 

•  15 
8.15 
8.15 
8.10 

.24123 
.24289 
.24455 

8.30 
8.30 
8.25 

62 
64 
66 

.31165 
.31314 
.31462 

7-45 
7-40 
7-45 

.32064 
.32216 
.32368 

7.60 
7.60 

7-55 

68 

.23861 

.  24620 

68 

.31611 

.32519 

70 

8.24023 

8.10 

8.24785 

8.25 

70 

8.31759 

7.40 

8.32671 

7.00 

72 

.24185 

8.10 
8.05 

•24949 

8.25 

72 

.31907 

7.40 
7-35 

.32822 

7-55 

7-50 

74 
76 

.24346 

.24507 

8.05 

.25114 
.25278 

8.20 

74 
76 

.32054 
.32201 

7-35 

.32972 
.33123 

7-55 

78 

.24668 

8.05 
8ne 

.25441 

8.15 

8  20 

78 

.32348 

7-35 

.33273 

80 

8.24829 

8.25605 

8  •,* 

80 

8.32495 

8.33423 

82 
84 
86 

.24989 
.25149 
.25308 

8.00 
7-95 
8  oo 

.25768 
.25931 
.26093 

8.15 
8.10 
8  10 

82 
84 
86 

.32642 
.32788 
.32934 

7-30 
7-30 
7.30 

•33573 
•33722 
.33871 

7-45 
7-45 
7-45 

88 

90 

92 

94 
96 
98 
100 

.25468 
8.25627 
.25785 

.25944 
.26102 
.26260 

7-95 
7.90 
7-95 
7-90 
7.90 
7.90 

.26255 
8.26417 
.26579 
.26740 
.26902 
.27062 

8.10 
8.10 
8.05 
8.10 

8.00 
8.05 

88 
90 
92 

94 
96 
98 
100 

.33080 
8.33226 
•33371 
.335i6 
.33661 
.33806 

7-30 
7-25 
7-25 
7-25 
7-25 
7.20 

.34020 
8.34169 
-343I8 
.34466 
.34614 
.34762 

7-45 
7-45 
7-40 
7-40 
7-40 
7-35 

8  .  26418 

8.27223 

8.33950 

8.34909 

(194) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

12=      ,* 

Hun- 
dredths 

13° 

Vers 

Diff. 

.001 

Exsec 

Diff.| 
.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

8.33950 

8.34909 

00 

8.40875 

6  65 

8.42002 

6  85 

03 
04 
06 

.34094 
.34238 
.34382 

7.20 
7.20 
7.15 

.35057 
.35204 
.35351 

7-35 
7-35 
7-30 

02 
04 
06 

.41008 
.41140 
.41273 

6.60 
6.65 
6.60 

.42139 
.42275 
.42391 

6.80 
6.80 
6.80 

08 
10 
12 

.34525 
8.34668 
.34811 

7-15 
7-15 
7.15 

•35497 
8.35644 
•35790 

7-35 
7-30 
7.30 

08 

10 
12 

.41405 
8.41537 
.41669 

6.60 
6.60 
6.60 

•42547 
8.42683 
.42818 

6.80 
6.75 
6.75 

14 
16 

•34954 
.35096 

7.10 

.35936 
.36082 

7-30 

14 
16 

.41801 
.41933 

6.60 

.42953 
.43088 

6.75 

18 
20 

.35238 

7.10 
7.10 

.36227 

7-25 
7-25 

18 
20 

.42064 

6.  55 
6.55 

6  ^ 

.43223 

6.75 
6.75 
6  70 

8.35380 

8.36372 

8.42195 

8.43358 

22 

24 
26 

•35522 
.35664 
.35805 

7.10 
7-05 

.36517 
.36662 
.36807 

7-25 
7-25 

22 
24 
26 

.42326 
.42457 
.42587 

6.55 
6.50 

.43492 
.43627 
.43761 

6.75 
6.70 

28 
30 
32 

.35946 
8.36087 
.36227 

7-05 
7.00 
7.05 

.36951 
8.37095 
.37239 

7.20 

7.20 

7.20 

28 
30 
32 

.42718 
8.42848 
.42978 

6.50 
6.50 
6.45 

.43895 
8.44028 
.44162 

6.65 
6.70 
6.65 

34 
36 
38 

.36368 
.36508 
.36648 

7.00 
7.00 

ft  Q< 

•37383 
.37526 
.37669 

7.15 
7.15 

34 
36 
38 

•43107 
.43237 
•43366 

6.50 
6.45 

6   A? 

.44295 
.44428 
.4456i 

6.65 
6.65 
6  65 

40 

8.36787 

8.37812 

40 

8.43495 

8.44694 

6  65 

42 
44 
46 

.36927 
.37066 
.37205 

6.95 
6.95 
6.95 

•37955 
.38098 
.38240 

7.15 

7.10 
7.10 

42 
44 
46 

.43624 
•43753 
.43882 

6-45 
6.45 
6.40 

.44827 
•44959 
.45091 

6.60 
6.60 
6.60 

48 
50 

'52 

•37344 
8.37482 
.37620 

6.90 
6.90 
6.95 

.38382 
8.38524 
.38666 

7.10 
7.10 
7.05 

48 
50 
52 

.44010 
8.44138 
.44266 

6.40 
6.  40 
6.40 

.45223 
8.45355 
.45487 

6.60 
6.60 
6.55 

54 
56 
58 
60 
62 
64 
66 

68 
70 

72 

•37759 
.37896 
•38034 

6.85 
6.90 
6.85 
6.90 

6.85 
6.80 
6.85 
6.80 
6.80 
6.80 

.38807 
.38948 
.39089 

7-05 
7-05 
7-05 
7-05 
7.00 
7.00 
7.00 
7.00 
7.00 
6.95 

54 
56 
58 
60 
62 
64 
66 

68 
70 

72 

•44394 
.44522 
.44649 

6.40 
6.35 
6.35 
6.35 
6.35 
6.35 
6.30 

6.35 
6.30 
6.30 

.45618 
.45749 
.45880 

6.55 
6.55 
6.55 
6.55 

6.55 
6.50 
6.50 
6.50 
6.50 
6.50 

8.38171 

8.39230 

8.44776 

8.46011 

.38309 
.38446 
.38582 

.38719 
8.38855 
.38991 

•39371 
.39511 
.39651 
•39791 
8.39931 
.40071 

.44903 
.45030 
-45I57 
.45283 
8.45410 
•45536 

.46142 
.46273 
.46403 

-46533 
8.46663 
.46793 

74 
76 
78 

.39127 
.39263 
•39399 

6.80 
6.80 

671; 

.40210 
•40349 
.40488 

6.95 
6.95 

74 
76 
78 

.  .45662 
.45787 
•45913 

6.25 
6.30 

6   21 

.46923 
.47052 
.47i8i 

6.45 
6.45 
6  41? 

80 

8.39534 

6   7S 

8.40627 

80 

8.46038 

6  21? 

8-47310 

6  45 

82 
84 
86 

.39669 
.39804 
.39938 

6.75 
6.70 
6.75 

.40765 
.40903 
.41042 

6.90 
6.95 
6.85 

82 
84 
86 

.46163 
.46288 
.46413 

6.25 
6.25 
6.25 

•47439 
.47568 
.47696 

6.45 
6.40 
6.45 

88 

90 
92 

.40073 
8.40207 
.40341 

6.70 
6.70 

6.70 

•4II79 
8.4I3I7 
-4I455 

6.90 
6.90 
6.85 

88 
90 
92 

.46538 
8.46662 
.46787 

6.20 

6.25 

6.20 

.47825 
8.47953 
.48081 

6.40 
6.40 
6.40 

94 
96 
98 

.40475 
.40608 
.40742 

6.65 
6.70 
6  65 

.41592 
.41729 
.41866 

6.85 
6.85 
6  80 

94 
96 
98 

.46911 
•47035 
.47158 

6.20 

6.15 
6  20 

.48209 
.48337 
.48464 

6.40 
6-35 
6  35 

100 

8.40875 

8  .  42002 

100 

8.47282 

8.48591 

(195) 


TABLE   XXVI.  —  (Continued) 


Hun- 

dredths 

14° 

Hun- 
dredths 

15° 

Vers] 

Diff. 

.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

00 

8.47282 

6  15 

8.48591 

6  40 

00 

8.53243 

8.54748 

02 

.47405 

.48719 

02 

.53358 

.54867 

5-95 

04 
06 

.47528 
•47651 

•  15 
6.15 
6.15 

.48846 
.48972 

6.35 

6.30 

6.35 

04 
06 

•53473 
.53587 

5-75 
5-70 
5-75 

•54986 
•55105 

5-95 
5-95 

5-95 

08 

•47774 

.49099 

08 

•53702 

.55224 

10 

8.47897 

.15 

8.49226 

•  35 

10 

8.53816 

5-70 

8.55342 

5.90 

12 
14 

.48019 
.48142 

6.15 

.49352 
.49478 

6.30 
6.30 

12 
14 

•53931 
.54045 

5-75 

5-70 

.55461 
•  55579 

5-95 
5.90 

16 
18 

.48264 
.48386 

6.10 

6.10 

.49604 
.49730 

6.30 
6.30 
6  25 

16 
18 

.54159 

.54273 

5-70 
5-70 

.55697 
.55815 

5-90 
5.90 

20 

8.48508 

8.49855 

20 

8.54386 

5-05 

8.55933 

5-9° 

22 

24 
26 

28 
30 
32 

.48629 
.48751 
.48872 

.48993 
8.49114 
.49235 

6.10 
6.05 
6.05 
6.05 
6.05 
6.00 

.49981 
.50105 
.50231 
.50356 
8.50481 
.50606 

6.20 

6.30 
6.25 
6.25 
6.25 
6.  20 

22 

24 
26 

28 

30 
32 

•54500 
.54613 
.54727 
.54840 
8.54953 
.55065 

5-65 
5-70 
5-65 

5-65 
5.6o 
5  65 

.56051 
.56168 
.56285 

.56403 
8.56520 
.56637 

5-9° 
5.85 
5.85 
5.90 
5.85 
5-85 
5  80 

34 
36 

•49355 
.49486 

6.05 

.50730 

.50864 

6.20 

34 
36 

.55178 
.55290 

5.6o 

.56753 

.56870 

5.85 

38 

.49596 

.50979 

6.25 
6  20 

38 

.55403 

5-65 

.56987 

5.85 

40 

8.49716 

8.51103 

6  15 

40 

8.55515 

5-oo 
c  fin 

8.57103 

42 
44 
46 

48 
50 

52 

.49836 
.49956 
•50075 
.50195 
8.50314 
•50433 

6.00 
5-95 
6.00 

5-95 
5-95 
5-95 

.51226 

.51350 
.51474 
.51597 

8.51720 

.51843 

6.20 
6.20 

6.15 
6.15 
6.15 
6.15 

42 
44 
46 
48 
So 

52 

.55627 
•55739 
.55851 
.55962 
8.56074 
.56185 

5-60 
5.6o 
5-55 
5.6o 
5-55 
5-55 

.57219 
•57335 
•57451 

.57567 
8.57683 
•57798 

5.8o 
5-80 
5-80 
5.8o 
5-75 
5.8o 

54 
56 
58 

.50552 
.50671 
.50789 

5-95 
5-90 

.51966 
.52089 

.52211 

6.15 
6.10 

54 
56 
58 

.56296 
.56407 
.56518 

5-55 
5-55 

.57914 
.58029 
.58144 

5-75 
5-75 

60 

8.50908 

8.52333 

6Tr 

60 

8.56629 

8.58259 

62 

.51026 

.52456 

62 

.56740 

.58374 

64 

•5II44 

5-90 

.52578 

6.10 

64 

.56850 

5-50 

.58489 

5-75 

66 
68 

.51262 
.51380 

5-90 
5-90 

.52700 
.52821 

6.10 
6.05 

66 
68 

.56960 
.57070 

5-50 
5.50 

.58603 
.58717 

5-70 
5-70 

70 

72 

8.51498 
•51615 

5-90 
5-85 
5-85 

8.52943 
.53064 

6.05 
6.10 

70 

72 

8.57181 
.57290 

5-55 

5-45 
5-50 

8.58832 
.58946 

5-75 
5.70 

5-70 

74 
76 
78 

.51732 

.51849 
.51966 

5.85 
5-85 

.53186 
.53307 
.53428 

6.05 
6.05 

74 
76 
78 

.57400 
•57510 
.576i9 

5-50 
5-45 

.59o6o 
.59174 
.59288 

5-70 
5-70 

e   fie 

80 

8.52083 

c   Qe 

8.53548 

80 

8.57728 

8.59401 

82 

.52200 

.53669 

82 

.57838 

.59515 

84 
86 

88 
90 

.52316 
.52433 

•52549 
8.52665 

5.8o 
5-85 
S.8o 

5.8o 

.53790 
.53910 
.54030 
8.54150 

6.05 
6.00 
6.00 

6.00 

84 
86 

88 
90 

•57947 
.58056 

.58164 
8.58273 

5-45 

5-45 
5-40 
5-45 

.59628 
•59741 
.59854 
8.59967 

5-65 
5.65 
5-65 
5-65 

92 

-52781 

5.8o 
5-75 

.54270 

6.00 
6  oo 

92 

.58381 

5.40 
5-45 

.60080 

5.65 
5.65 

94 
96      . 

.52896 
.53012 

5.8o 

.54390 

.54509 

5-95 

94 
96 

.58490 
.58598 

5-40 

.60193 
.60305 

5.60 

98 

.53127 

5-75 

.54629 

98 

.58706 

5.40 

.60418 

5-65 
r   fin 

100 

8.53243 

8.54748 

100 

8.58814 

8.60530 

(196) 


TABLE  XXVI.  —  (Continued) 


Hun- 

11 

Hun- 

r 

r° 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

dredths 

Vers 

*. 

Diff. 
.001 

Exsec 

Diff. 
.001 

00 

8.58814 

8.60530 

r    (JO 

00 

8.64043 

er  jo 

8.65984 

02 
04 
06 
08 
10 
12 

14 

16 
18 

.58922 
.59030 
.59137 
.59244 
8.59352 
•59459 
.59566 
.59673 
.59779 

5-40 
5-35 
5-35 
5-40 
5-35 
5-35 
5-35 
5-30 

.60642 
.60754 
.60866 

.60978 
8.61089 
.61201 
.61312 
.61424 
.61535 

5.60 
5.60 
5.60 

5-55 
5.6o 
5-55 
5.6o 
5-55 

02 
04 
06 

08 
IO 
12 

14 

16 
18 

.64145 
.64246 
.64347 
.64448 
8.64549 
.64650 

.64751 
.64851 
.64951 

5-05 
5-05 
5-05 
5.05 
5-05 
5-05 

5.00 
5.00 

.66090 
.66196 
.66301 
.66407 
8.66513 
.66618 

.66723 
.66829 
.66934 

5-30 
5-25 
5-30 
5-30 
5.25 
5-25 
5-30 
5-25 

20 

8.59886 

8.61646 

20 

8.65052 

8.67039 

22 
24 
26 
28 
30 
32 

34 
36 
38 

•59992 
.60099 
.60205 
.60311 
8.60417 
.60523 

.60628 
.60734 
.60839 

5-30 
5-35 
5-30 
5.30 
5-30 
5-30 
5-25 
5-30 
5-25 

.61756 
.61867 
.61978 
.62088 
8.62199 
.62309 
.62419 
.62529 
.62639 

5-55 
5-55 
5-50 

5-55 
5-50 
5-50 
5.50 
5-50 

22 
24 
26 

28 
30 
32 

34 
36 
38 

.65152 
.65252 
.65352 
.65452 
8.65551 
.65651 

.65751 
.65850 
.65949 

S.oo 
5.00 
S.oo 

4-95 
S.oo 
S.oo 

4-95 
4-95 

.67144 
.67248 
.67353 
.67458 
8.67562 
.67666 

.67771 
.67875 
.67979 

5-20 

5.25 
5-25 
5-20 

5-20 

5.25 

5-20 
5-20 

40 

8.60945 

8.62748 

40 

8.66048 

8.68083 

42 
44 
46 
48 
50 

52 

54 
56 
58 

.61050 
-61155 
.61260 

.61364 
8.61469 
.61573 
.61678 
.61782 
.61886 

5-25 

5-25 
5-25 

5-20 

5.25 

5-20 

5.25 

5-20 
5.20 

.62858 
.62968 
.63077 
.63786 
8.63295 
•63404 

.63513 
.63622 
.63730 

5-50 
5-45 
5-45 
5-45 
5-45 
5-45 
5-45 
5-40 

42 
44 
46 
48 
50 

52 

54 
56 
58 

.66147 
.66246 
.66345 

.66444 
8.66542 
.66641 

.66739 
.66837 
.66935 

4-95 
4-95 
4-95 
4.90 
4-95 
4-90 
4-90 
4.90 

.68186 
.68290 
.68393 

.68497 
8.68600 
.68703 
.68807 
.68910 
.69012 

5.20 

5-20 
5-20 

5.15 
5.15 
5.20 

5.15 

S.io 

60 

8.61990 

5-20 

8.63839 

60 

8.67033 

8.69115 

5.15 

62 
64 
66 

68 
70 

72 

74 
76 
78 

.62094 
.62198 
.62301 
.62405 
8.62508 
.62611 
.62714 
.62817 
.62920 

5-20 

5.15 

5.20 

•  5.15 
5.15 

5-15 
5-15 
5-15 

.63947 
.64056 
.64164 
.64272 
8.64380 
.64487 
.64595 
.64703 
.64810 

5-45 
5-40 
5-40 
5.40 
5-35 
5.40 
5-40 
5-35 

62 
64 
66 

68 
70 

72 

74 
76 
78 

.67131 
.67229 
.67327 

•67424 
8.67521 
.67619 
.67716 
.67813 
.67910 

4-90 
4.90 
4-85 
4-85 
4-90 
4-85 
4-85 
4-85 
A  8c 

.69218 
.69321 
•69423 
.69525 
8.69628 
.69730 
.69832 
.69934 
.70036 

5.15 

S.io 
5.10 

5-15 
S.io 
5.10 
S.io 
5.10 

80 

8.63023 

8.64917 

80 

8.68007 

A   8? 

8.70137 

82 
84 
86 

88 
9o 

92 

94 
96 
98 

.63126 
.63228 
.63330 

.63433 
8.63535 
.63637 

.63739 
.63840 
.63942 

S.io 
S.io 
5-15 
S.io 
S.io 
5-10 

5-05 
5.10 

.65024 
.65132 
.65238 

.65345 
8.65452 
.65559 
.65665 
.65771 
.65878 

5-40 
5-30 
5-35 
5-35 
5-35 
5-30 
5-30 
5-35 

82 
84 
86 

88 
90 
92 

94 
96 
98 

.68104 
.68200 
.68297 

•68393 
8.68490 
.68586 
.68682 
.68778 
.68874 

4.80 
4.85 
4.80 

4.85 
4.80 
4.80 
4.80 
4.80 

.70239 
.70340 
.70442 

•70543 
8.70644 
.70745 
.70846 
•70947 
.71048 

5.05 
S.io 
5-05 
5.05 
5.05 
5-05 
5.05 
5-05 

100 

8.64043 

8.65984 

100 

8.68969 

8.71149 

(197) 


TABLE  XXVI.  —  (Continued) 


Hun- 

1 

9° 

Hun- 

1' 

)° 

dredths 

Vers 

Diff. 

.COI 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

8.68969 

A  SO 

8.71149 

00 

8.73625 

8.76058 

02 
04 

.69065 
.69161 

4.80 

.71249 
.71350 

5-05 

02 
04 

.73715 
.73806 

4-55 

.76154 
.76249 

4-7S 

06 

.69256 

4-75 

.71450 

S-oo 

06 

.73896 

4-50 

.76345 

4.80 

08 
IO 

•69351 
8.69447 

4-75 
4.80 

.71551 
8.71651 

5.05 
S.oo 

08 
10 

•73986 
8.74077 

4-50 
4-55 

•76440 
8.76536 

4-75 
4.80 

12 

.69542 

4-75 

•7I75I 

5.00 

12 

.74167 

4-50 

.76631 

4-75 

14 

.69637 

.71851 

14 

.74257 

.76726 

16 

.69732 

4-75 

•7I95I 

5-00 

16 

.74346 

4-45 

.76821 

4-75 

18 

.69827 

4-75 

.72051 

S.oo 

18 

•74436 

4-50 

.76916 

4-75 

20 

8.69921 

8.72150 

20 

8.74526 

8.77011 

22 

.70016 

.72250 

22 

.74616 

.77106 

24 

.70110 

4.70 

.72349 

4-95 

24 

.74705 

4-45 

.77201 

4-75 

26 

.70205 

4-75 

.72449 

S.oo 

26 

•74794 

4-45 

.77296 

4-75 

4.70 

4-95 

4.50 

4.70 

28 

.70299 

.72548 

28 

.74884 

.77390 

30 

8.70393 

4.70 

8.72647 

•  95 

30 

8-74973 

4-45 

8.77485 

4-75 

32 

.7P487 

4.70 

.72746 

•95 

32 

.75062 

4-45 

•77579 

4.70 

34 
36 

.70581 
.70675 

4-70 

.72845 
.72944 

•95 

34 
36 

.75151 
.75240 

4-45 

.77674 
•77768 

4.70 

38 

.70769 

4.70 

A    6? 

.73043 

4-95 

38 

•75329 

4-45 

.77862 

4.70 

40 

8.70862 

8.73142 

40 

8.75417 

8.77956 

42 
44 
46 

.70956 
.71049 
.7H43 

4-65 
4.70 
4.65 

.73240 
•73339 
.73437 

4-95 
4-90 
4.90 

42 
44 
46 

.75506 
•75595 
.75683 

4-45 
4-40 
4-45 

.78050 
.78144 
.78238 

4.70 
4.70 
4.65 

48 
50 

52 

54 
56 
58 

.71236 
8.71329 
.71422 

.71515 

.71608 
.71701 

4-65 
4-65 
4-65 
4.65 
4-65 
A  fin 

•73535 
8.73634 
•73732 
.73830 
•73928 
•74025 

4-95 
4-90 
4-90 
4-90 
4-85 

48 
50 

52 

54 
56 
58 

•75772 
8.75860 
.75948 
.76036 
.76124 
.76212 

4.40 
4.40 
4.40 

4.40 
4.40 

.78331 
8.78425 
.78519 
.78612 
.78706 
.78799 

4.70 
4.70 
4-65 
4-70 
4.65 

A  61? 

60 

8.71793 

A  6? 

8.74123 

60 

8.76300 

8.78892 

A   6"> 

62 
64 
66 

.71886 
.71978 
.72071 

4.60 
4.65 
4.60 

.74221 
.74318 
.74416 

4-85 
4.90 
4-85 

62 
64 
66 

.76387 
.76475 
.76563 

4.40 
4.40 
4-35 

.78985 
.79078 
.79171 

4.65 
4.65 
4.65 

68 
70 

72 

.72163 
8.72255 
.72347 

4.60 
4.60 
4.60 

•74513 
8.74610 
.74707 

4-85 
4-85 
4-85 

68 
70 

72 

.76650 
8.76737 
.76825 

4-35 
4-40 
4-35 

•79264 
8.79357 
•79449 

4.65 
4.60 

4-65 

74 
76 
78 

.72439 
.72531 
.72622 

4.60 
4-55 

A    fio 

.74804 
.74901 
.74998 

4-85 
4-85 

A   R<Z 

74 
76 
78 

.76912 
.76999 
.77086 

4-35 
4-35 

•79542 
.79635 
•79727 

4.65 
4.60 

A  60 

80 

8.72714 

A  60 

8.75095 

A    Oe 

80 

8.77173 

A    -1C 

8.79819 

4  65 

82 
84 
86 

.72806 
.72897 
.72988 

4.55 
4.55 
4.60 

.75192 
.75288 
.75385 

4-80 

4-85 

4.80 

82 
84 
86 

.77260 
.77346 
•77433 

4.30 
4-35 
4-35 

.79912 
.80004 
.80096 

4.60 
4.60 
4.60 

88 

90 
92 

.73080 
8.73171 
.73262 

4.55 
4.55 

4-55 

.75481 
8.75578 
.75674 

4-85 
4.80 
4.80 

88 
90 

92 

•77520 
8.77606 
.77692 

4.30 
4.30 
4-35 

.80188 
8.80280 
.80372 

4.60 
4.60 
4.60 

94 
96 
98 

•73353 
•73443 
•73534 

4-50 
4-55 

•75770 
.75866 
.75962 

4.80 
4.80 

•A   8O 

94 
96 
98 

•77779 
.77865 
•77951 

4-30 
4-30 
4  3° 

.80464 
•80555 
.80647 

4-55 
4.60 
4  55 

100 

8.73625 

8.76058 

100 

8.78037 

8.80738 

(198) 


TABLE   XXVI.  —  (Continued) 


Hun- 

dredths 

20° 

Hun- 
dredths 

21° 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 
.001 

4-05 
4.10 
4.10 
4-05 
4.10 
4-05 
4-05 

4-05 
4.10 
4-05 
4-05 
4.00 
4-05 
4-05 

4-05 
4.00 
4-05 
4.00 
4.00 
4-05 
4.00 
4.00 
4.00 
4.00 
4.00 
4.00 
4.00 

3-95 
4.00 
3-95 
4.00 

3-95 
3-95 
4-00 

3-95 
3-95 
3-95 
3-95 
3-90 
3-95 
3-95 
3-00 
3^95 
3-95 
3-90 
3-90 
3-90 
3-95 
3-90 
3.90 

Exsec 

Diff. 
.001 

00 

02 

04 
06 
08 

IO 
12 

14 

16 
18 
20 

22 

24 
26 
28 

30 

32 

34 
36 
38 
40 

42 
44 
46 
48 
So 

52 

54 
56 
58 
60 
62 
64 
66 

68 
70 

72 

74 
76 
78 
80 
82 
84 
86 

88 
90 
92 

94 
96 
98 
100 

8.78037 

4-30 
4-30 
4-30 
4.25 
4.30 
4.25 
4-30 
4-25 
4-25 
4-25 
4-25 
4.25 
4.25 
4-25 
4.25 
4.25 
4.20 

4-25 
4.20 
4.20 
4.20 

4.25 

4.20 
4.20 

4.15 
4.20 

4.20 
4.20 

4.15 

4.20 

4.15 
4.15 
4.15 
4.15 
4.15 
4.15 

4.10 

4.15 
4.15 
4.15 

4.10 

4-15 
4.10 
4.10 

4-15 
4.10 
4.10 
4.10 
4.10 
4.10 

8.80738 

4.60 

4-55 
4.60 
4-55 
4-55 
4-55 
4-55 
4-55 
4-55 
4.50 

4-55 
4-55 
4-50 
4-50 

4-55 
4-50 
4-50 
4-50 
4-50 
4.50 
4-50 
4-50 
4-50 
4-45 
4-50 
4-45 
4-50 

4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-40 

4-45 
4.40 
4-45 
4.40 
4.40 
4-40 
4.40 
4.40 
4.40 
4-40 
4.40 
4-40 
4-35 

00 

02 
04 
06 

08 
10 
12 

U 
16 
18 
20 

22 
24 
26 
28 

30 

32 

34 
36 
38 
40 

42 
44 
46 

48 
50 

52 

54 
56 
58 
60 
62 
64 
66 

68 
70 

72 

74 
76 
78 
80 
82 
84 
86 

88 
90 
92 

94 
96 
98 
100 

8.82230 

8.85214 

4.40 
4-40 
4-35 
4-35 
4-40 
4-35 
4-35 
4-35 
4-35 
4-35 
4-35 
4-35 
4-30 
4-35 
4-30 
4-35 
4-30 

4-35 
4-30 
4-30 
4-30 
4-25 
4-35 
4-30 
4-30 
4-30 
4-30 

4-25 
4-30 
4-25 
4-30 
4-25 
4-30 
4-25 
4-25 
4-25 
4-25 
4-25 
4-25 
4.20 

4-25 
4-25 
4-25 
4.20 

4-25 
4.20 
4-25 
4.20 
4.20 
4.20 

.78123 
.78209 
.78295 
.78380 
8.78466 
.78551 

.78637 
.78722 
.78807 

.80830 
.80921 
.81013 
.81104 
8.81195 
.81286 

.81377 
.81468 
.8x559 

.82311 
.82393 
.82475 
.82556 
8.82638 
.82719 
.82800 
.82881 
.82963 

.85302 
.85390 
.85477 

.85564 
8.85652 
.85739 
.85826 
.85913 
.86000 

8.78892 

8.81649 

8.83044 

8.86087 

.78977 
.79062 
.79147 
.79232 
8.79317 
.79402 

.79486 
•79571 
.79655 

.81740 
.81831 
.81921 
.82011 
8.82102 
.82192 
.82282 
.82372 
.82462 

.83125 
.83205 
.83286 

.83367 
8.83448 
.83528 

.83609 
.83689 
.83769 

.86174 
.86261 
.86347 

.86434 
8.86520 
.86607 

.86693 
.86780 
.86866 

8.79739 

8.82552 

8.83850 

8.86952 

.79823 
.79908 
•79992 
.80076 
8.80159 
.80243 
.80327 
.80411 
80494 

.82642 
.82732 
.82822 
.82911 
8.83001 
.83090 
.83180 
.83269 
.83358 

.83930 
.84010 
.84090 

.84170 
8.84250 
•84330 
.84410 
.84489 
-84569 

.87038 
.87123 
.87210 
.87296 
8.87382 
.87468 

.87554 
.87639 
.87725 

8.80578 

8.83447 

8.84648 

8.87810 

.80661 
.80744 
.80827 

.80911 
8.80994 
.81077 

.81159 
.81242 
.81325 

.83536 
.83625 
.83714 
.83803 
8.83892 
.83981 
.84069 
.84158 
.84246 

.84728 
.84807 
.84886 
.84966 
8.85045 
.85124 
.85203 
.85282 
.85360 

.87896 
.87981 
.88067 
.88152 
8.88237 
.88322 

.88407 
.88492 
.88577 

8.81408 

8.84335^ 

8.85439 

8.88661 

.81490 
•81573 
.81655 

.81737 
8.81820 
.81902 
.81984 
.82066 
.82148 

.84423 
.84511 
.84599 
.84687 
8.84775 
.84863 

.84951 
.85039 
.85127 

.85518 
.85596 
.85675 

.85754 
8.85832 
.85910 
.85988 
.86067 
.86145 

.88746 
.88831 
.88916 
.89000 
8.89085 
.89169 

•89254 
.89338 
.89422 

8.82230 

8.85214 

8.86223 

8.89506 

(199) 


TABLE  XXVI.—  (Continued) 


Hun- 
dredths 

22° 

Hun- 

dredths 

23° 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

Vdrs  . 

Diff. 
.001 

Exsec 

Diff. 
.001 

00 

8.86223 

8.89506 

00 

8.90034 

8.93631 

02 

.86301 

.89590 

02 

.90109 

3-75 

•93712 

4.05 

04 
06 
08 

.86379 
.86456 

.86534 

3.90 
3-85 
3-90 

.89674 
.89758 
.89842 

4.20 

4.20' 

4.20 

04 
06 

08 

.90183 
•90257 
.90332 

3-70 
3  70 
3-75 

•93793 
.93874 
•93955 

4-05 
4-03 
4-05 

10 
12 

8.86612 
.86689 

3-9° 
3-85 
-3-90 

8.89926 
.90010 

4.20 

4.20 
4.15 

10 
12 

8.90406 
.90480 

3-70 
3-70 
3-70 

8.94035 
.94116 

4.00 
4-C5 
4.05 

14 
16 

.86767 
.86844 

3-85 

.90093 
.90177 

4.20 

14 
16 

.90554 
.90628 

3-70 

•94197 
•94277 

4.00 

18, 
20 

.86922 

3-9° 
3-85 

o  ge 

.90261 

4.20 

4.15 

18 
20 

.90702 

3.70 
3-70 

•94358 

4-05 
4.00 

8.86999 

8.90344 

8.90776 

8.94438 

22 

24 

.87076 
.87153 

3.85 

.90427 
.90511 

4.20 

22 

24 

.90850 
.90923 

3-65 

.94518 
•94599 

4-05 

26 

.87231 

3-9° 

T    Ce 

•90594 

4-I5 

26 

.90997 

3-7° 

.94679 

4.00 

28 

.87308 

.90677 

28 

.91071 

•94759 

30       ' 

8.87385 

3.85 

8.90761 

4.20 

30 

8.91144 

3.65 

8.94839 

4.00 

32 

.87461 

3.80 
3-85 

.90844 

4-15 
4-15 

32 

.91218 

3-70 
3-65 

.94919 

4.00 

4.00 

34 

.87538 

.90927 

34 

.91291 

•94999 

36 
38 

.87615 
.87692 

3-85 
3-85 

->    go 

.91010 
.91093 

4-15 
4-15 

36 
38 

.91365 
.91448 

3.65 
3-65 

•j  ge 

•95079 
.95169 

4.00 
4.00 

40 

8.87768 

-y     0- 

8.9H75 

40 

8.91511 

7  fiC 

8.95238 

42 
44 
46 

48 

.87845 
.87921 
.87998 
.88074 

3-80 

3.85 
3-80 

.91258 
.91341 
•91423 
.91506 

4-15 
4.10 
4-15 

42 
44 
46 
48 

.91584 
.91657 
.91730 

.91803 

3.65 

3-65 
3-65 

.95318 
•95398 
•95478 

•95557 

4.00 
4.00 
3-95 

So 

52 

8.88150 
.88226 

3.80 
3.8o 
3-80 

8.91589 
.91671 

4-15 
4.10 
4.10 

50 

52 

8.91876 
.91949 

3.05 
3-65 
3.6S 

8.95637 
.95716 

4.00 
3-95 
3-95 

54 
56 
58 
60 

.88302 
.88378 
.88454 

3-8o 
3.80 
3-80 
7  80 

•91753 
.91836 
.91918 

4-15 
4.10 
4.10 

54 
56 
58 
60 

.92022 
.92095 
.92167 

3.65 

3-60 
3-65 
-,  gc 

•95795 
.95875 
•95954 

4.00 
3-95 
3-95 

3ne 

8.88530 

8.92000 

8.92240 

8.96033 

62 

.88606 

.  92082 

62 

•92313 

.96112 

64 

.88682 

3.80 

.92165 

4-15 

64 

.92385 

3.6o 

.96192 

4.OO 

66 
68 
70 

72 

.88758 

.88833 
8.88909 
.88984 

3-8o 
3-75 
3-80 
3-75 
3.80 

.92247 
.92328 
8.92410 
.92492 

4.10 
4-05 
4.10 
4.10 
4.10 

66 

68 
70 

72 

.92457 
.92530 
8  .  92602 
.92674 

3-6o 
3-65 

3-60 
3.6o 
3.6o 

.96271 

.96350 
8.96428 
.96507 

3-95 
3-95 
3-90 
3-95 
3-95 

74 
76 
78 

.89060 
.89135 
.89210 

3  75 
3-75 

.92574 
.92656 
.92737 

4.10 
4-05 

74 
76 
78 

.92746 
.92818 
.92891 

3.6o 
3-65 

.96586 
.96665 
.96744 

3-95 
3-95 

80 

8.89286 

8.92819 

80 

8.92962 

<3  6O 

8.96822 

•2    QtT 

82 
84 
86 

.89361 
.89436 
.89511 

3-75 
3-75 
3-75 

.92900 
.92982 
•93063 

4.10 
4-05 
4.10 

82 
84 
86 

.93034 
.93io6 
.93178 

3.6o 
3-6o 
3-60 

.96901 
.96979 
.97058 

3-9° 
3-95 
3-90 

88 
90 

92 

.89586 
8.89661 
.89735 

3-75 

3-70 
3  75 

.93145 
8.93226 
.93307 

4-05 
4-05 
4.05 

88 
9o 

92 

.93250 
8.93321 
-93393 

3-55 
3-60 
3.60 

.97136 
8.97215 
.97293 

3-95 
3-90 
3-9° 

94 
96 
98 

.89810 
.89885 
.89960 

3-75 
3-75 

•93388 
.93469 
•93550 

4-05 
4-05 

94 
96 
98 

.93465 
.93536 
.93607 

3-55 
3-55 
•t  60 

•97371 
•97450 
.97528 

3-  95 
3.90 
3  9° 

100 

8.90034 

8.93631 

100 

8.93679 

8.97606 

(200) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

24° 

Hun- 

dredths 

25° 

Vers 

Diflf. 
.001 

Exsec 

Diflf. 

.001 

Vers 

Diflf. 
.001 

Exsec 

Diflf. 
.001 

00 

8.93679 

8.97606 

00 

8.97170 

9-0*443 

02 

•93750 

.97684 

02 

•97239 

.01518 

04 

.93821 

3-55 

.97762 

3-9° 

04 

•97307 

3-40 

•01594 

3  80 

06 

.93892 

3-55 

.97840 

3-9° 

06 

•97375 

3.40 

.01669 

3-75 

08 

.93964 

•97918 

08 

•97443 

.01744 

10 
12 

8.94035 
.94106 

3-55 
3-55 

8-97995 
•98073 

3  85 
3-90 

10 
12 

8.97512 
.97580 

3-45 
3-40 

9.01819 
.01895 

3-75 
3-80 

3-55 

3-9° 

3-40 

3-75 

14 
16 
18 

•94177 
•94247 
.94318 

3-50 
3-55 

.98151 
.98229 
.98306 

3.90 
3.85 
•3  go 

14 

16 
18 

.97648 
.97716 
.97784 

3-40 
3-40 

.01970 
.02045 
.02120 

3-75 
3-75 

20 

8.94389 

8.98384 

•i   fie 

20 

8.97851 

9-02195 

22 

.94460 

.98461 

22 

.97919 

.02270 

24 
26 

•94530 
.94601 

3-50 
3.55 

.98539 
.98616 

3.90 

3.85 

7  Re 

24 
26 

97987 
.98055 

3-40 
3-40 

•02345 
.02419 

3-75 
3-70 

28 
30 

.94671 
8.94742 

3-55 

.98693 
8.98771 

3-90 

28 

30 

.98122 
8.98190 

3-40 

.02494 
9.02569 

3-75 
3-75 

32 

.94812 

3-50 

.98848 

3  85 

32 

•98257 

3-35 

.02644 

3-75 

34 
36 

.94882 
•94953 

3-55 

.98925 
.99002 

3-85 

34 
36 

.98325 
.98392 

3-35 

.02718 
.02793 

3-75 

38 
40 

.95023 

3-50 
3-50 

.99079 

3-85 
3.85 

•j    Or 

38 
40 

.98459 

3-35 

3-40 

.02867 

3-70 
3-75 

8.95093 

8.99156 

8.98527 

9.02942 

42 
44 
46 
48 
50 

52 

54 
56 

.95163 
•95233 
.95303 
•95373 
8.95443 
•95513 
.95582 
.95652 

3.50 
3-50 
3-50 
3-50 
3-50 
3-45 
3.50 

.99233 
•99310 
.99387 
.99464 
8.99541 
.99617 
.99694 
•99771 

3-85 
3-85 

3-85 

3-85 
3.8o 
3-85 
3-85 

42 
44 
46 

48 
50 

52 

54 
56 

.98594 
.98661 
.98728 

.98795 
8.98862 
.98929 
.98996 
•99063 

3-35 
3-35 
3-35 
3-35 
3-35 
3  35 
3-35 

.03016 
.03091 
.03165 
•03239 
9.03314 
.03388 
.03462 
.03536 

3-70 

3-75 
3-70 
3-70 
3-75 
3-70 
3-70 
3-70 

58 

•95722 

3-5O 

.99847 

•1    Or 

58 

.  99130 

3-35 

.  03610 

3-70 

60 
62 
64 
66 

8-95791 

3-50 

3-45 
3-50 

8.99924 

3-80 
3-80 

3-85 

60 
62 
64 
66 

8.99197 

3.30 
3-35 
3  35 

9-03684 

3-70 
3-70 
3-70 

.95861 
•95930 
.96000 

9.00000 
'  .  00076 
•00153 

.99263 
•99330 
•99397 

.03758 
.03832 
.03906 

68 
70 

72 

74 

.96069 
8.96138 
.96207 
.96277 

3-45 
3-45 
3-45 
3-50 

.00229 
9.00305 
.00382 

.00458 

3.8o 
3.8o 
3-85 
3-80 

68 
70 

72 

74 

.99463 
8.99530 
•99596 
.99663 

3-30 
3-35 
3  30 
3-35 

.03980 
9.04054 
.04127 

.04201 

3-70 
3-70 
3-65 
3-70 

76 
78 
80 
82 

.96346 
.96415 

3-45 
3-45 
3-45 
3-45 

•00534 
.00610 

3.8o 
3-80 
3-80 
3.8o 

76 
78 
80 
82 

.99729 
•99795 

3-30 
3-30 
3-30 
3-35 

.04275 
.04348 

3.70 
3.65 
3-70 

3-65 

8.96484 

9.00686 

8.99861 

9.  04422 

.96553 

.00762 

•99928 

.  04495 

84 
86 

88 

.96621 
.96690 

.96759 

3-40 
3-45 
3-45 

.00838 
.00913 
•00989 

3-8o 
3-75 
3-80 

84 
86 

88 

•99994 
9.00060 

.00126 

3-30 
3-30 

3-30 

.04569 
.04642 

.04715 

3-70 
3.65 
3-65 

90 

92 

94 
96 

8.96828 
.96896 

.96965 
.97033 

3-45 
3.40 
3-45 
3-40 

9.01065 
.01141 
.01216 
.01292 

3-8o 
3.8o 
3-75 
3.8o 

90 

92 

94 
96 

9.00192 
.00258 
.00323 
.00389 

3-30 
3-30 
3-25 
3-30 

9.04789 
.04862 

•04935 
.05008 

3-70 
3-65 
3-65 
3-65 

98 
100 

.97102 

3-45 

3-40 

.01367 

3-75 
3-80 

98 
100 

•00455 

3-30 
3-30 

.05082 

3-70 
3-65 

8.97170 

9-01443 

9.00521 

9.05155 

(201) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

26° 

Htm- 
dredths 

27° 

Vers 

Dift. 
.001 

Exsec 

Diff. 

.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 
02 
04 
06 
08 
10 

J     12 

9.00521 

3-25 
3-30 
3-25 
3-30 

3-25 
3-30 
3-25 

9.05155 

3.65 
3-65 
3-65 
3-60 

3-65 
3-65 
3.65 

00 

02 

04 
06 

08 

10 
12 

9.03740 

3-15 
3-15 
3-15 
3-15 
3-15 
3-15 
3-15 

9-08752 

3-55 
3-55 
3-50 
3-55 
3-55 
3-50 
3-55 

.00586 
.00652 
.00717 

.00783 
9.00848 
.00914 

.  05228 

.05301 
.05374 
.05446 
9.05519 
.05592 

.03803 
.03866 
•03929 
.03992 
9.04055 
.04118 

.08823 
.08894 
.08964 
.09035 
9.09106 
.09176 

14 

16 
18 
20 

.00979 
.01044 
.01109 

3-25 
3-25 
3-30 

.05665 

.05738 

.05810 

3-65 
3.6o 
3-65 
i  fio 

14 

16 
18 
20 

.04181 

.04244 
.04306 

3-15 
3.10 
3-15 

•09247 
.09318 
.09388 

3-55 
3-50 
3-55 

9-OII75 

9.05883 

9-04369 

9-09459 

22 

24 

.01240 
.01305 

3-25 

.05955 
.06028 

3.65 

22 

24 

.04432 

.04494 

3.10 

.09529 
•09599 

3-50 

26 

.01370 

3-25 

.06101 

3.65 

26 

•04557 

3-15 

.09670 

3-55 

28 

30 

32 

.01435 
9  .  01500 
.01565 

3-25 
3-25 
3-25 
3.20 

.06173 
9.06245 
.06318 

3-6o 
3-60 
3-65 
3.60 

28 
30 
32 

..04619 
9.04682 
.04744 

3-10 

3-15 
3-10 
3-15 

.09740 
9.09810 
.09881 

3-50 
3-50 
3-55 
3-50 

34 
36 
38 

.01629 
.01694 
.01759 

3-25 
3-25 

.06390 

.06462 
.06535 

3.6o 
3-65 
i  go 

34 
36 
38 

.04807 
.04869 
.04931 

3-10 
3-10 

.09951 

.IO02I 
.lOOgi 

3-50 
3-50 

40 

9.01824 

9.06607 

3  fin 

40 

9-04993 

9.IOI6I 

42 

.01888 

.06679 

42 

.05055 

.10231 

44 
46 

.01953 
.02017 

3-25 
3-20 

3.25 

.06751 
.06823 

3.60 

3.60 
3.60 

44 
46 

.05118 
.05180 

3-15 
3-10 
3-10 

.  I030I 
.10371 

3-50 
3-50 
3-50 

48 

.02082 

.06895 

48 

.05242 

.10441 

50 

52 

9.02146 
.02210 

3-20 
3-20 

3.25 

9.06968 
.07039 

3.65 
3.55 
3.60 

50 

52 

9.05304 
.05366 

3-io 
3-10 
3-05 

9-I05II 
.  I058I 

3-50 
3-50 
3-45 

54 
56 
58 
60 

.02275 
•02339 
.02403 

3.20 

3-20 
3-20 

.07111 

.07183 
.07254 

3.60 
3.55 
3.60 

-,  60 

54 
56 
58 
60 

.05427 
.05489 
.05551 

3-10 
3-10 
3.10 

3  IO 

.IO650 
.  10720 
.10790 

3-50 
3-50 
3-50 
•i  415 

9-02467 

9.07326 

9-05613 

9.10860 

62 
64 
66 

68 

.02531 
.02596 
.02660 

.02723 

3.25 

3-20 

3.15 

.07398 
.07469 
.07541 
.07613 

3-55 
3-60 
3-60 

62 
64 
66 

68 

.05675 
.05736 
.05798 
.05859 

3-05 
3-10 
3-05 

.10929 
.10999 
.11068 
.11138 

3-50 
3-45 
3-50 

70 

72 

74 
76 
78 

9.02787 
.02851 

.02915 
.02979 
.03043 

3-20 

3.20 

3-20 
3-20 
3-20 

9.07684 
.07756 
.07827 
.07898 
.07970 

3-55 
3.6o 
3-55 

3-55 
3-60 

70 

72 

74 
76 
78 

9-05921 
.05982 

.06044 
.06105 
.06166 

3-io 
3-05 
3-10 

3-05 
3-05 

9.II207 
.11277 

.11346 
.11415 

.11485 

3-45 
3-50 
3-45 
3-45 
3-50 

80 

9.03106 

9  .  08041 

80 

9.06228 

•2     O^ 

9-II554 

3  45 

82 
84 
86 

.03170 
-03233 
•03297 

3.15 

3-20 

3.15 

.08112 
.08184 
.08255 

3-60 
3-55 
3-55 

82 
84 
86 

.06289 
.06350 
.06411 

3-05 
3-05 
3-05 

.11623 
.11692 
.11762 

3  45 
3-50 
3-45 

88 
90 

92 

.03360 
9.03424 
.03487 

3-20 

3.15 

3.15 

.08326 
9.08397 
.08468 

3-55 
3-55 
3-55 

88 
.90 
92 

.06472 
9.06533 
.06594 

3-05 
3-05 
3-05 

.11831 
9.II900 
.11969 

3-45 
3-45 
3-45 

94 
96 
98 

.03550 
.03614 
.03677 

3-20 

3.15 

.08539 

.08610 

.08681 

3-55 
3-55 

94 
96 
98 

.06655 
.06716 
.06777 

3-05 
3-05 

•7     O1? 

.12038 
.12107 
.12176 

3-45 
3-45 
3  45 

100 

9-03740 

9.08752 

100 

9.06838 

9-12245 

(202) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

28° 

Hun- 

dredths 

29° 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9.06838 

3  05 

9-12245 

3.40 

00 

9-09823 

2-95 

9-15641 

3  35 

02 
04 
06 

.06899 
.06960 
.  07020 

3-05 
3-00 
3-05 

.12313 
.12382 
.12451 

3-45 
3-45 
3-45 

02 
04 
.06 

.09882  • 
.09940 
.09999 

2.90 
2.95 
2.90 

.15708 
•15775 
.15842 

3-35 
3-35 
3-35 

08 
IO 
12 

.07081 
9.07141 
07202 

3.00 
3-05 
3-05 

.  12520 
9.12588 
12657 

3-40 
3  45 
3-45 

08 

10 
12 

.10057 
9  10115 
.10174 

2.90 
2  95 
2.90 

.15909 
9.15976 
.  16043 

3-35 
3  35 
3-30 

14 
16 
18 

.07263 
.07323 
-07383 

3.00 
3.00 
3  05 

.12726 

.12794 
.12863 

3-40 
3-45 
3  4° 

14 

16 
18 

.  10232 

.  10291 
.10349 

2.95 
2.90 

2  90 

.16109 
.16176 
.  16243 

3-35 
3-35 
3  3° 

20 

9.07444 

3  oo 

9.I293I 

3  45 

20 

9.10407 

2  90 

9-16309 

3  35 

22 
24 
26 

-07504 
.07564 
.07625 

3.00 
3-05 
3.00 

.13000 
.13068 
.13137 

3-40 
3-45 
3-40 

22 

24 
26 

.10465 
.10523 
.10581 

2.90 
2.90 
2.90 

.16376 
.16443 
.16509 

3-35 
3-30 
3-35 

28 

30 
32 

.07685 
9-07745 
.07805 

3.00 
3.00 
3.00 

.13205 
9.13273 
.13341 

3.40 
3-40 
3-45 

28 

30 
32 

.10639 
9.10697 
•10755 

2.90 
2.90 
2.90 

.16576 
9.16642 
.16709 

3-30 
3-35- 
3-30 

34 
36 
38 

.07865 
-07925 
.07985 

3-00 
3.00 
3  oo 

.13410 
.13478 
.13546 

3-40 
3-40 
3  4° 

34 
36 
38 

.10813 
.10871 
.10929 

2.90 
2.90 
2  QO 

•  16775 
.16842 
.16908 

3-35 
3-30 

40 

9.08045 

3  oo 

9-13614 

3  4° 

40 

9-10987 

2  90 

9.16974 

3  35 

42 
44 
46 

.08105 
.08165 
.08225 

3.00 
3-00 
2-95 

.13682 
.13750 
.13818 

3-40 
3-40 

3-40 

42 
44 
46 

.11045 

.11102 
.IIl6o 

2.85 
2.90 

2.90 

.17041 
.17107 
.17173 

3-30 
3-30 
3-30 

48 
50 
52 

.08284 
9-08344 
.08404 

3.00 
3.00 
2.95 

.13886 
9-13954 
.  14022 

3-40 
3-40 
3-40 

48 
So 
52 

.11218 
9.II275 
•II333 

2.85 
2.90 
2.85 

.17239 
9-I7306 
.17372 

3-35 
3-30 
3-30 

54 
56 
58 

.08463 
.08523 
.08583 

3.00 
3.00 

2  <X 

.14090 
.14158 
.  14226 

3-40 
3-40 
3  35 

54 
56 
58 

.11390 
.11448 
.11505 

2.90 
2.85 

2  QO 

.17438 
.17504 
.17570 

3-30 
3-30 

60 

9.08642 

2  95 

9.14293 

3  4O 

60 

9-II563 

2  85 

9-17636 

62 
64 
66 

.08701 
.08761 
.08820 

3.00 
2.95 
3.00 

.14361 
.14429 
.14496 

3-40 
3-35 
3-40 

62 
64 
66 

.11620 
.11677 

•II735 

2.85 
2.85 
2.85 

.17702 
.17768 
.17834 

3-30 
3-30 
3-30 

68 
70 

72 

.08880 
9.08939 
.08998 

2.95 
2.95 
2.95 

.14564 
9.14632 
.14699 

3-40 
3-35 
3-40 

68 
70 

72 

.11792 
9-11849 
.11906 

2.85 
2.85 
2.  85 

.17900 
9.17966 
.  18031 

3-30 
3.25 
3-30 

74 
76 
78 

.09057 
.09116 
.09176 

2.95 
3.00 
2.95 

.14767 
.14834 
.14902 

3-35 
3-40 
3-35 

74 
76 
78 

.11963 

.  12020 

.12077 

2.85 
2.85 

2  85 

.18097 
.18163 
.  18229 

3-30 
3-30 
3  25 

80 

9-09235 

2  95 

9.14969 

3  35 

80 

9.12134 

2  85 

9-18294 

82 
84 
86 

.09294 
.09353 
.09412 

2-95 
2.95 
2.90 

.15036 
.15104 
.15171 

3-40 
3-35 
3-35 

82 
84 
86 

.12191 
.  12248 
.12305 

2.85 
2.85 
2.85 

.18360 
.18426 
.18491 

3-30 
3-25 
3-30 

88 
90 
92 

.09470 
9.09529 
.09588 

2.95 
2.95 
2.95 

.15238 
9.15305 
•15373 

3-35 
3-40 
3  35 

88 
90 

92 

.12362 
9.12419 
.12476 

2.85 
2.85 
2.80 

.18557 
9.18622 
.18688 

3-25 
3-30 
3-25 

94 
96 
98 

.09647 
.09706 
.09764 

2.95 
2.90 
2.95 

.15440 
.15507 
.15574 

3-35 
3-35 
3-35 

94 
96 

98 

.12532 
.12589 
.12646 

2.85 
2.85 
2.80 

.18753 
.18818 
.18884 

3-25 
3-30 
3  25 

100 

9-09823 

9-15641 

100 

9.12702 

9.I8949 

(203) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

30° 

Hun- 

dredths 

31° 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

9.12702 

2  85 

9.18949 

3  25 

00 

9-15483 

2  70 

9.22176 

02 

04 
06 

.12759 
.12815 
.12872 

2.8o' 
2.85 
2.80 

.19014 
.19080 
•I9I45 

3-30 
3-25 
3-25 

02 

04 
06 

•15537 
•15592 
•  15647 

2-75 
2.75 

2.70 

.22240 
.22304 
.22367 

3-20 

3.15 
3.20 

08 

10 
12 

.12928 
9-12985 
.13041 

2.85 
2.80 
2.80 

.19210 
9.19275 
•I934I 

3-25 
3-30 
3-25 

08 

10 
12 

.15701 
9.I5756 
.15810 

2.75 
2.70 
2.75 

.22431 
9-22495 
.22558 

3-20 
3  IS 
3.20 

14 

16 

18 

.13097 
.13154 
.  13210 

2.80 
2.80 

2  80 

.19406 
•I947I 
.19536 

3-25 
3  25 
3  25 

14 

16 
18 

.15865 
.15919 
•15973 

2.70 
2.70 
2  75 

.22622 
.22685 
.22749 

3  15 
3  20 

20 

9.13266 

2  80 

9.19601 

3  25 

20 

9.16028 

2.70 

9.22812 

3  20 

22 

24 
26 

.13322 
.13378 
•13434 

2.80 

2.80 
2.80 

.19666 
•I973I 
.19796 

3-25 
3-25 
3-25 

22 

24 
26 

.16082 
.  16136 
.16190 

2.70 
2.70 

2.70 

.  22876 
.22939 
.23003 

3-15 

3-20 

3-15 

28 
30 
32 

.13490 
9-I3546 
.13602 

2.80 

2.80 

2.80 

.19861 
9.19926 
.19990 

3  25 

3-20 

3-25 

28 
30 
32 

.16244 
9.16299 
.16353 

2.75 

2.70 
2.70 

.23066 
9.23129 
.23193 

3-15 
3-20 
3.15 

34 
36 
38 

.13658 
•13714 
.  13770 

2.80 
2.80 

2.80 

.20055 

.  2OI2O 
.20185 

3-25 
3-25 
3.20 

34 
36 
38 

.16407 
.16461 
.16515 

2.70 
2.70 
2.70 

.23256 
•23319 
•23383 

3-15 

3-20 

3  15 

40 

9.13826 

2  80 

9.20249 

3  25 

40 

9.16569 

2.70 

9.23446 

3  15 

42 
44 
46 

.13882 
•13937 
.13993 

2.75 

2.80 
2.80 

.20314 
.20379 
.20443 

3-25 
3-20 

3.25 

42 
44 
46 

.16623 
.16676 
.16730 

2.65 

2.70 
2.70 

.23509 
•23572 
.23635 

3-15 
3-iS 
3-15 

48 
50 

52 

.14049 
9.14104 
.14160 

2.75 

2.80 
2.80 

.20508 
9.20572 
.20637 

3.20 
3.25 

3.20 

48 
So 

52 

.  16784 
9.16838 
.16892 

2.70 
2.70 
2.65 

.23698 
9-23761 
.23824 

3.15 
3-15 
3-15 

54 
56 
58 

.14216 
.14271 
.14327 

2.75 
2.80 
2  75 

.2O70I 
.20766 
.20830 

3.25 

3.20 
3  25 

54 
56 
58 

.  i6945 
.16999 
.17053 

2.70 
2.70 
2.65 

.23887 
.23950 
.24013 

3  IS 
3-15 
3  IS 

60 

9.14382 

2  75 

9.20895 

3  20 

60 

9.17106 

2  70 

9.24076 

3  IS 

62 
64 
66 

.14437 
.14493 
.14548 

2.80 
2.75 
2.75 

.20959 
.2IO23 
.21088 

3.20 
3-25 
3.20 

62 
64 
66 

.  17160 
-17213 
.17267 

2.65 

2.70 

2.65 

•24139 
.  24202 
.24265 

3-iS 
3-iS 
3-iS 

68 
70 

72 

.14603 
9.14659 

.14714 

2.80 
2.75 
2.75 

.21152 
9.2I2I6 
.21280 

3-20 

3.20 

3.25 

68 
70 

72 

.17320 
9-17374 
.17427 

2.70 
2.65 
2.65 

.24328 
9.24390 
j24453 

3.10 
3-15 
3-iS 

74 
76 
78 

.14769 
.14824 
.14879 

2.75 
2.75 
2  75 

.21345 
.21409 
•21473 

3-20 
3-20 
3  20 

74 
76 
78 

.17480 
.17534 
.17587 

2.70 
2.65 
2.65 

.24516 
.24578 
.24641 

3.10 
3-15 
3.I5 

80 

9-14934 

9-21537 

80 

9.17640 

2  65 

9.24704 

3  1° 

82 
84 
86 

.14989 
.15044 
.15099 

2.75 
2.75 
2-75 

.2I6OI 
.21665 
.21729 

3-20 
3-20 

3.20 

82 
84 
86 

.17693 
•  17747 
.17800 

2.70 

2.65 
2.65 

.24766 
.24829 
24891 

3-15 
3.10 
3-IS 

88 
90 
92 

.15154 
9.15209 
.15264 

2.75 
2.75 
2.75 

.21793 
9-21857 
.21921 

3-20 
3-20 

3-20 

88 
90 

92 

.17853 
9-17906 
.17959 

2.65 
2.65 
2.65 

•24954 
9-25017 
•25079 

3-lS 
3-10 
3.10 

94 
96 
98 

.15319 
.15373 
.  15428 

2.70 
2.75 
2  75 

.21985 
.22049 

.22112 

3-20 

3.15 

3.20 

94 
96 
98 

.  18012 
.18065 
.18118 

2.65 
2:65 
2.65 

.25141 
.25204 
.25266 

3-15 
3.10 
3-15 

100 

9.15483 

9.22176 

100 

9.18171 

9.25329 

(204) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

32° 

Hun- 
dredths 

33° 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

9.18171 

2  60 

9-25329 

3  10 

00 

9.20771 

2.60 

9.28412 

3.05 

02 
04 
06 

.  18223 
.  18276 
.18329 

2.65 

2.65 

2.65 

•25391 
.25453 
.25515 

3  10 
3.10 
3-15 

02 

04 
06 

.20823 
.20874 
.20925 

2  55 
2.55 
2.55 

•28473 
.28534 
.28595 

3-05 
3-05 
3-05 

08 
IO 
12 

.18382 
9.I8435 
.18487 

2.65 

2.60 
2.65 

.25578 
9.25640 

.25702 

3.10 
3.10 
3.10 

08 

IO 
12 

.20976 
9.21027 
.21078 

2.55 
2.55 
2.55 

.28656 
9.28717 
.28778 

3-05 
3-05 
3-05 

14 

16 
18 

.18540 
.18592 
.18645 

2.60 
2.65 

2  6S 

•25764 
.25826 
.25889 

3.10 
3-15 
3  10 

14 

16 

18 

.21129 
.21180 
.21231 

2.55 
2.55 
2.55 

.28839 
.28900 
.28961 

3-05 
3-05 
3.00 

20 

9.18698 

2  60 

9-25951 

3  10 

20 

9.21282 

2.50 

9.29021 

3.05 

22 
24 
26 

.18750 
.18803 
.18855 

2.65 

2.60 
2.60 

.26013 
.26075 
.26137 

3.10 
3.10 
3-io 

22 
24 
26 

.21332 
.21383 
.21434 

2.55 
2.55 
2-55 

.29082 
•29143 
.29203 

3-05 
3.00 
3-05 

28 
30 
32 

.18907 
9.18960 
.19012 

2.65 
2.60 
2.60 

.26199 
9.26261 
.26323 

3.10 
3.10 
3-05 

28 
30 
32 

.21485 
9-21535 
.21586 

2.50 
2-55 
2.55 

.29264 
9.29325 
.29385 

3-05 
3.00 
3-05 

34 
36 
38 

.19064 
.19117 
.19169 

2.65 
2.60 

2  60 

.26384 
.26446 
.  26508 

3.10 
3  10 

34 
36 
38 

.21637 
.21687 
.21738 

2.50 
2.55 
2.50 

.29446 
.29507 
.29567 

3.<?5 
3.00 
3-05 

40 

9.19221 

2  60 

9.26570 

3.10 

40 

9.21788 

2.55 

9.29628 

3.00 

42 
44 
46 

.19273 
.19325 
•19377 

2.60 
2.60 

2.65 

.26632 
.26694 
.26755 

3-10 
3-05 
3.10 

42 
44 
46 

.21839 
.21889 
.21940 

2.50 
2.55 
2.50 

.29688 
.29749 
.29809 

3-05 
3.00 
3-05 

48 
50 
52 

.19430 
9.19482 
.19534 

2.60 
2.60 
2.60 

.26817 
9.26879 
.26940 

3.10 
3-05 
3-io 

48 
50 

52 

.21990 
9.22041 
.22091 

2.55 

2.50 
2.50 

.29870 
9-29930 
29990 

3.00 
3.00 
3-05 

54 
56 

.19586 
.19637 

2.55 
2  60 

.27002 
.27064 

3-10 
3-05 

54 
56 

.22141 
.  22192 

2.55 
2.50 

.30051 
.30111 

3.00 
3.00 

58 

.19689 

2  60 

.27125 

3  10 

58 

.22242 

2.50 

.30171 

3-05 

60 

9.I974I 

2  60 

9.27187 

3  °5 

60 

9.22292 

2  SO 

9.30232 

3.00 

62 
64 
66 

•19793 
.19845 
.19897 

2.60 
2.60 
2.55 

.27248 
.27310 
.27371 

3.10 
3-05 
3.10 

62 
64 
66 

.22342 
.22392 
.22442 

2.50 
2.50 

2.55 

.30292 
.30352 
.30412 

3.00 
3.00 
3-05 

68 

.19948 

2.60 

.27433 

3.05 

68 

.22493 

2.  SO 

•30473 

3.00 

70 

9.20000 

2  60 

9-27494 

3.05 

70 

9-22543 

2.50 

9-30533 

3.00 

72 

.20052 

2.55 

.27555 

3.10 

72 

.22593 

2.50 

.30593 

3.00 

74 
76 
78 

.20103 
.20155 
.20206 

2.55 
2.55 
2  60 

.27617 
.27678 
.27739 

3-05 
3-05 
3  10 

74 
76 
78 

.22643 
.22693 
.22743 

2.50 
2.50 
2  SO 

.30653 
.30713 
.30773 

3.00 
.    3-00 
3.00 

80 

9.20258 

2  55 

9.27801 

3  °5 

80 

9-22793 

2  SO 

9.30833 

3.00 

82 
84 
86 

.20309 
.20361 
.20412 

2.60 

2.55 
2.60 

.27862 
.27923 
.27984 

3-05 
3-05 
3.10 

82 
84 
86 

.22843 
.22892 
.22942 

2.45 

2.50 
2.50 

.30893 
.30953 
.31013 

3.00 
3.00 
3.00 

88 

.  20464 

2.55 

.28046 

3.05 

88 

.22992 

2.50 

.31073 

3.00 

90 

92 

9-20515 
.20566 

2.55 
2.60 

9.28107 
.28168 

3-05 

3-05 

90 
92 

9-23042 
.23091 

2.45 
2.50 

9-3II33 
.3H93 

3.00 
3.00 

94 
96 

.20618 
.20669 

2.55 
2.55 

.  28229 
.28290 

3-05 
3-05 

94 
96 

.23141 
.23191 

2.50 
2.45 

.31253 
.31313 

3-00 
3.00 

98 

.20720 

2.55 

.28351 

3.05 

98 

.23240 

2.50 

.31373 

3.00 

100 

9.20771 

9.28412 

100 

9-23290 

9-31433 

(205) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

34° 

Hun- 

dredths 

35° 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

V4rs 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

9.23290 

9-31433 

00 

9-25731 

9-34395 

02 

.23340 

.31492 

02 

•25779 

•34454 

04 

.23389 

2.45 

.31552 

3.00 

04 

.25827 

2.40 

•34512 

2.90 

06 
08 

.23439 
.23488 

2.50 
2.45 

.31612 
.31672 

3.00 
3-00 

06 
08 

-25875 
•25923 

2.40 
2.40 

•34571 
.34630 

2-95 
2-95 

10 

9-23538 

2.50 

9.3I73I 

2.95 

10 

9-25971 

2.40 

9.34688 

2.90 

12 

.23587 

2.45 

.31791 

3-oo 

12 

26019 

2.40 

•34747 

2-95 

14 

.23636 

.31851 

14 

.26067 

•34805 

16 

.23686 

2.50 

.31910 

2.95 

16 

.26115 

2.40 

.34864 

2-95 

18 

.23735 

2-45 

.31970 

3.00 

18 

.26163 

2.40 

•34922 

2.90 

20 

9.23784 

9.32030 

20 

9.26211 

9.34981 

22 

.23834 

.32089 

2.95 

22 

.26258 

2.35 

.35039 

24 

.23883 

2.45 

.32149 

3.00 

24 

.26306 

2.40 

•35098 

2.95 

26 

.23932 

2.45 

.32208 

2-95 

26 

•26354 

2.40 

.35156 

2.90 

28 

.23981 

.32268 

28 

.  26402 

.35215 

30 

9.24030 

2.45 

9.32327 

2.95 

30 

9-26449 

2.35 

9-35273 

2.90 

32 

•24079 

2-45 

.32387 

3-oo 

32 

•26497 

2.40 

•35331 

2.90 

34 
36 

.24129 
.24178 

2.45 

.32446 
.32506 

3-00 

34 
36 

.26545 
.26592 

2.35 

•35390 
-35448 

2.90 

38 

.24227 

2.45 

.32565 

2-95 

38 

.26640 

2.40 

.35506 

2.90 

40 

9.24276 

9.32624 

40 

9.26687 

9.35565 

2  00 

42 

.24325 

.32684 

42 

.26735 

.35623 

44 

.24374 

2.45 

.32743 

2-95 

44 

.26782 

2.35 

.35681 

2.90 

46 

.24422 

2.40 

.32802 

2.95 

46 

.26830 

2.40 

•35739 

2.9O 

48 

.24471 

.32861 

48 

.26877 

•35798 

50 

52 

9.24520 
.24569 

2.45 
2.45 
2-45 

9-32921 
.32980 

3-oo 
2-95 
2.95 

50 

52 

9.26924 
.26972 

2.35 

2.40 
2.35 

9-35856 
.35914 

2.90 
2.90 
2.90 

54 

.24618 

.33039 

54 

.27019 

•35972 

56 

.24666 

2.40 

•33098 

2.95 

56 

.27066 

2.35 

.36030 

2.90 

58 

.24715 

2.45 

.33158 

3.00 

58 

.27114 

2.40 

.36088 

2.90 

2  QO 

60 

9.24764 

9.33217 

60 

9.27161 

9.36146 

62 

.24813 

.33276 

62 

.27208 

.36204 

64 

.24861 

2.40 

•33335 

2.95 

64   ' 

.27255 

2.35 

.36262 

2.90 

66 

.24910 

2.45 
2.40 

•33394 

2.95 
2-95 

66 

.27302 

2.35 
2.35 

.36320 

2.90 
2.90 

68 

24958 

-33453 

68 

.27349 

.36378 

70 

9.25007 

2.45 

9-33512 

2.95 

70 

9.27396 

2.35 

9-36436 

2.90 

72 

.25055 

2.40 

•33571 

2.95 

72 

.27444 

.36494 

2.90 

2.45 

2.95 

2.35 

2.9O 

74 
76 
78 

.25104 
.25152 
.  25201 

2.40 
2.45 

.33630 
.33689 
.33748 

2-95 
2.95 

74 
76 
78 

.27491 
.27538 
.27585 

2.35 
2.35 

.36552 
.36610 
.36668 

2.90 
2.90 
2  QO 

80 

9.25249 

9.33807 

80 

9.27632 

9.36726 

2  QO 

82 
84 
86 

.25297 
.25346 
•25394 

2-45 
2.40 
2.40 

.33866 
.33925 
.33984 

2.95 
2-95 
2.90 

82 
84 
86 

.27678 
.27725 
.27772 

2-35 
2.35 
2.35 

•36784 
.36842 
.36900 

2.90 
2.90 

2.85 

88 

90 

92 

.25442 
9.25491 
.25539 

2.45 
2.40 
2.40 

34042 
9.34101 
.34i6o 

2.95 
2.95 
2.95 

88 
90 
92 

.27819 
9.27866 
.27913 

2-35 
2.35 
2.30 

.36957 
9.370I5 
•37073 

2.90 
2.90 
2.90 

94 
96 
98 

•25587 
.25635 
.25683 

2.40 
2.40 

.34219 
.34277 
.34336 

2.90 
2-95 

94 
96 
98 

•27959 
.28006 
.28053 

2.35 
2.35 

.37131 
.37188 
.37246 

2.85 
2.90 

2  QO 

100 

9.2573I 

9-34395 

100 

9.28099 

9-37304 

(206) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

36° 

Hun- 
dredths 

37° 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

9-28099 

9-37304 

00 

9.30398 

9.40163 

02 
04 

06 

.28146 
.28193 
.28239 

2.35 
2.35 
2.30 
2.35 

.37361 
•37419 
•37477 

2.90 
2.90 
2.85 

02 

04 
06 

.30444 
•30489 
•30534 

2.25 
2.25 
2.25 

.40220 
•40277 
•40334 

2.85 
2.85 
2.80 

08 

10 
12 

14 

16 

.28286 
9.28332 
•28379 
.28425 
.28472 

2.30 
2.35 
2.30 

2.35 

•37534 
9-37592 
.37649 
.37707 
.37764 

2.90 
2.85 

2.90 

2.85 

08 

10 
12 

14 

16 

..30579 
9-30624 
.30670 

•30715 
.30760 

2.25 
2.30 
2.25 

2.25 

•40390 
9-40447 
•40503 
.40560 
.40617 

2.85 
2.80 
2.85 
2.85 

18 

.28518 

2.30 

.37822 

2.90 

18 

.30805 

2.25 

.40673 

2  Re 

20 

22 

24 
26 

28 

9-28565 

2.30 
2.30 
2.35 
2.30 

9.37879 

2.90 

2.85 
2.90 
2.85 

20 

22 

24 
26 

28 

9.30850 

2.25 

2.25 
2.25 
2.25 

9.40730 

2.80 

2.85 
2.80 
2.85 

.28611 
.28657 
.28704 
.28750 

•37937 
•37994 
.38052 
.38109 

.30895 
.30940 
•30985 
.31030 

.40786 
•40843 
.40899 
•40956 

30 
32 

9.28796 
.28842 

2.30 
2.30 
2.35 

9-38167 
.38224 

2.90 
2.85 
2.85 

30 
32 

9-31075 
.31120 

2.25 
2.25 
2.25 

9.41012 
.41069 

2.8o 
2.85 
2.80 

34 
36 
38 

.28889 
.28935 
.28981 

2.30 
2.30 

.38281 
.38339 
.38396 

2.90 
2.85 

2  8C 

34 
36 
38 

.31165 
.31210 
-31254 

2.25 

2.20 

.41125 
.41182 
.41238 

2.85 
2.80 

40 

9-29027 

9.38453 

40 

9-31299 

9-41294 

2  Re 

42 
44 
46 

•29073 
.29119 
.29165 

2.30 
2.30 

•38511 
.38568 
.38625 

2.85 
2.85 
2  Re 

42 
44 
46 

-31344 
•31389 
•31433 

2.25 
2.20 

.41351 

.41407 
.41464 

2.80 
2.85 
2  80 

48 
50 

.29211 
9.29257 

2.30 

.38682 
9-38739 

2.85 

48 
50 

.31478 
9-3I523 

2.25 

.41520 
9-4I576 

2.80 

52 

54 
56 

•29303 
.29349 
.29395 

2.30 
2.30 
2.30 

.38797 
•38854 
.389" 

2.90 
2.85 
2.85 

52 

54 
56 

-31567 
.31612 
.31657 

2.25 
2.25 

.41632 
.41689 
.41745 

2.85 
2.80 

58 

.29441 

2.30 

•38968 

2.85 

58 

.31701 

2.  2O 

.41801 

2Ro 

60 

9-29487 

2.30 

9-39025 

•  05 

2  Of 

60 

9-3I746 

9-41857 

2  Re 

62 
64 

.29533 
.29578 

2.25 

.  .39082 
.39139 

2.8S 

62 
64 

.31790 
.31835 

2.25 

.41914 
.41970 

2.8o 

66 

.29624 

2.30 

.39196 

2.85 

66 

•31879 

.42026 

68 
70 

.29670 
9-29716 

2.30 

.39253 
9-39310 

2.85 

68 
70 

•31924 
9.31968 

2.  2O 

.42082 
9-42138 

2.80 

72 

.29761 

2.25 
2.30 

.39367 

2.85 
2.85 

72 

.32013 

2.25 
2.20 

.42194 

2.8o 

74 
76 

.29807 
•29853 

2.30 

•39424 
.39481 

2.85 

74 
76 

•32057 
.32101 

2.  2O 

.42250 
•42307 

2.85 

78 

.29898 

2.25 

•  39538 

2.85 
2  Re 

78 

.32146 

2.25 

.42363 

2  80 

80 

9.29944 

9-39595 

80 

9-32190 

9.42419 

2  80 

82 
84 
86 

.29989 
•30035 
.30080 

2.25 

2.30 
2.25 

•39652 
•39709 
•39766 

•  °5 
2.8S 
2.85 

82 
84 
86 

.32234 
.32278 
•32323 

2.20 
2.25 

•42475 
.42531 
.42587 

2.80 

2.80 

2  80 

88 
90 

92 

.30126 
9.30171 
.30217 

2.30 
2.25 
2.30 
2.25 

•39823 
9.39880 
-39936 

2.85 

2.85 
2.80 
2.85 

88 
90 

92 

.32367 
9-32411 
.32455 

2.20 
2.  2O 
2.20 

.42643 
9-42699 
•42755 

2.80 

2.80 

2.75 

94 
96 
98 

.30262 
.30308 
.30353 

2.30 
2.25 

•39993 
.40050 
.40107 

2.85 
2.85 

94 
96 
98 

.32499 
•32543 
.32587 

2.  2O 

2.  2O 

.42810 
.42866 
.42922 

2.80 
2.80 

2  80 

100 

9.30398 

9.40163 

100 

9-32631 

9.42978 

(207) 


TABLE  XXVI.  —  (Continued} 


Hun- 
dredths 

38° 

Hun- 

dredths 

39° 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

9-32631 

9.42978 

2   So 

00 

9.34802 

9-45752 

02 
04 

•  32675 
.32719 

2.20 

•43034 
.43090 

2.80 

02 
04 

.34845 
.34888 

2.15 

•45807 
.45862 

2.75 

06 

•32763 

2.20 

.43146 

2.80 

06 

•34930 

2.15 

•45917 

2.75 
2-75 

08 

.32807 

.43202 

08 

•34973 

•45972 

10 
12 

9-32851 
•32895 

2.20 
2.  2O 

9.43257 
•43313 

2.75 
2.80 
2.80 

10 

12 

9-350x6 
.35058 

2.15 
2.IO 
2.15 

9.46027 
.46082 

2-75 
2-75 
2.75 

14 

16 

.32939 
.32983 

2.20 

.43369 
.43425 

2.80 

14 

16 

.35101 
.35144 

2.15 

.46137 
.46192 

2.75 

18 

.33027 

.43480 

2.75 

2  80 

18 

.35186 

.46247 

20 

9.33070 

9.43536 

20 

9.35229 

9-46302 

22 

•33II4 

' 

•43592 

22 

.35272 

•46357 

24 
26 

.33158 
.33202 

2.  2O 
2.15 

.43647 
.43703 

2.75 
2.80 

2.80 

24 
26 

.35314 
•35357 

2.15 

2.10 

.46412 
.46467. 

2.75 
2-75 
2.75 

28 
30 
32 

•33245 
9.33289 
•33333 

2.20 
2.20 
2.15 

-43759 
9.43814 
.43870 

2.75 
2.80 
2.80 

28 
30 
32 

•35399 
9-35442 
.35484 

2.15 
2.IO 
2.10 

.46522 
9.46576 
.46631 

2.70 
2.75 
2.75 

34 
36 
38 

•33376 
•33420 
.33463 

2.20 
2.15 

-43926 
•43981 
.44037 

2.75 
2.80 

34 
36 
38 

•  35526 
.35569 
.356ii 

2.15 

2.10 

.46686 
.46741 
.46796 

2.75 
2.75 
2  75 

40 

9.33507 

9.44092 

2  80 

40 

9.35654 

9.46851 

2  7O 

42 
44 
46 

•33550 
•33594 
.33637 

2.20 

2.15 

2.  2O 

.44148 
•44203 
•44259 

2.75 
2.80 
2-75 

42 

44 
46 

.35696 
•35738 
.35780 

2.IO 
2.IO 
2.15 

.46905 
.46960 
.47015 

2.75 
2.75 
2.75 

48 
So 

52 

.33681 
9-33724 
-33768 

2.15 

2.20 
2.15 

.44314 
9-44370 
.44425 

2.80 
2.75 
2.80 

48 
SO 

52 

.35823 
9.35865 
.35907 

2.10 
2.10 
2.IO 

.47070 
9-47124 
•47179 

2.70 
2.75 
2.75 

54 
56 
58 

•  338n 
.33854 
.33898 

2.15 

2.  2O 

.44481 
.44536 
•44592 

2.75 
2.80 

54 
56 
58 

•35949 
•35991 
•36034 

2.10 
2.15 

•47234 

.47288 
-47343 

2.70 
2.75 
2  75 

60 

9-33941 

9.44647 

60 

9.36076 

9-47398 

62 
64 
66 

•33984 
.34028 
.34071 

2.20 
2.15 
2.15 

.44702 
.44758 
.44813 

2-75 
2.80 
2.75 
2.75 

62 
64 
66 

.36118 
.36160 
.36202 

2.IO 
2.IO 
2.IO 

.47452 
•47507 
.47562 

2.75 
2-75 

2.70 

68 
70 

72 

.34114 
9-34157 
.34200 

2.15 
2.15 
2.  2O 

.44868 
9.44924 
•44979 

2.80 
2.75 
2  75 

68 
70 

72 

.36244 
9.36286 
.36328 

2.10 
2.10 
2.IO 

.47616 
9.47671 
.47725 

2.75 
2.70 
2.75 

74 
76 
78 

•34244 
•34287 
•34330 

2.15 
2.15 

.45034 

.45090 
•45145 

2.80 
2.75 

74 
76 
78 

.36370 
.36412 
.36454 

2.10 
2.10 

.47780 
.47834 
.47889 

2.70 
2.75 
2  75 

80 

9-34373 

2  15 

9.45200 

80 

9.36496 

9-47944 

2.70 

82 
84 
86 

.34416 
•34459 
•34502 

2.15 
2.15 
2.15 

.45255 
•453II 
•45366 

2.80 
2-75 
2.75 

82 
84 
86 

.36538 
.36579 
.36621 

2.05 

2.IO 
2.10 

.47998 
.48053 
.48107 

2.75 

2.70 
2.70 

88 
90 

92 

•34545 
9-34588 
.34631 

2.15 
2-15 

2.15 

•45421 
9.45476 
•45481 

2.75 
2.75 
2  75 

88 
90 
92 

.36663 
9-36705 
.36747 

2.IO 
2.10 
2.O5 

.48161 
9.48216 
.48270 

2.75 
2.70 
2.75 

94 
96 
98 

•34674 
.34716 
•34759 

2.10 
2.15 
2  15 

.45586 
.45642 
.45697 

2.80 
2.75 

94 
96 
98 

.36788 
.36830 
.36872 

2.10 
2.10 

.48325 
.48379 
.48433 

2.70 
2.70 
2.75 

100 

9.34802 

9-45752 

100 

9.36913 

9.48488 

(208) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

40° 

Hun- 
dredths 

41° 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

9  36913 

9.48488 

00 

9.38968 

9.51190 

2  6=; 

02 

.36955 

.48542 

02 

•39009 

.51243 

04 

.36997 

2.IO 

.48597 

2.75 

04 

.39049 

.51297 

2.70 

06 

.37038 

2.05 

.48651 

2.70 

06 

.39090 

2.05 

.51351 

2.70 

08 

.37080 

-48705 

08 

.39130 

.51405 

10 
12 

9-37I2I 
.37163 

2.05 

2.IO 

9.48760 
.48814 

2-75 
2.70 

IO 
12 

9.39I7I 
.39211 

2.05 

2.00 

9  51459 
.51512 

2.70 
2.65 

2.05 

2.70 

2.70 

14 

16 

.37204 
.37246 

2.10 

.48868 
.48922 

2.70 

14 

16 

.39251 
.39292 

2.05 

.51566 
.51619 

2.65 

18 

.37287 

2.05 

.48977 

2.75 

18 

•39332 

.51673 

2.70 

20 

9.37329 

•49031 

20 

9.39372 

9.51727 

22 
24 
26 

-37370 
•37412 
•37453 

2.10 

2.05 
2.05 

.49085 
.49149 
.49194 

2.70 
2.75 
2.70 

22 

24 
26 

.39413 
•39453 
•39493 

2.00 
2.OO 
2.05 

.51780 
.51834 
.51887 

2.70 
2.65 
2.70 

28 
30 
32 

•37494 
9.37536 
•37577 

2.10 

2.05 
2.05 

.49248 
9-49302 
.49356 

2.70 
2.70 
2.70 

28 
30 
32 

•39534 
9-39574 
.39614 

2.00 
2.OO 
2.00 

.51941 
9-51995 
.52048 

2.70 
2.65 
2.70 

34 
36 
38 

.37618 
.37659 
•37701 

2.05 

2.10 

•49410 
.49465 
.49519 

2.75 
2.70 

34 
36 
38 

.39654 
.39694 
•39735 

2.OO 
2.05 

.52102 
.52155 
.52209 

2.65 

2.70 

40 

9-37742 

9-49573 

40 

9-39775 

9.52262 

42 
44 

.37783 
.37824 

2.05 

-49627 
.49681 

2.70 

42 
44 

.39815 
.39855 

2.OO 

.52316 
.52369 

2.65 

46 

.37865 

2.05 
2.O5 

•49735 

2.70 
2.70 

46 

.39895 

2.OO 
2.OO 

.52423 

2.70 
2.65 

48 

.37906 

.49789 

48 

•39935 

.52476 

50 

52 

9-37948 
.37989 

2.05 
2.05 

9-49843 
.49897 

2.70 
2.70 
2.70 

50 

52 

9-39975 
.40015 

2.OO 
2.0O 
2.OO 

9-52529 
.52583 

2.05 
2.70 
2.65 

54 

.38030 

-49951 

54 

.40055 

.52636 

56 
58 

.38071 
.38112 

2.05 
2.05 

.50005 
.50059 

2.70 
2.70 

56 
58 

.40095 
•40135 

2.OO 
2.OO 

.52690 
•52743 

2.70 
2.65 

60 

9.38153 

9-50II3 

60 

9-40175 

9.52796 

2  70 

62 

.38194 

.50167 

62 

.40215 

' 

.52850 

64 
66 

.38235 
.38276 

2.05 
2.05 

.50221 
.50275 

2.70 
2.70 

64 
66 

.40255 
.40294 

2.00 

1-95 

.52903 
.52956 

2.05 

2.65 

68 

72 

•38317 
9  38357 
.38398 

2.00 

2.05 

.50329 
9.50383 
-50437 

2.70 
2.70 

68 
70 
72 

•40334 
9-40374 
.40414 

2.OO 
2.OO 

•53010 
9.53063 

2.65 
2.65 

2.05 

2.70 

2.00 

2.70 

74 
76 
78 

38439 
.38480 
.38521 

2.05 

2.05 

.50491 
•50544 
.50598 

2.65 

2.70 

74 
76 
78 

•40454 
.40493 
.40533 

1-95 

2.OO 

.53170 
.53223 
.53276 

2.65 
2.65 

80 

9-38562 

9.50652 

80 

9-40573 

9-53330 

2  65 

82 

.38602 

.50706 

82 

.40613 

.53383 

84 
86 

.38643 
.38684 

2.05 

2.05 
2.OO 

.50760 
.50814 

2.70 
2.70 
2.65 

84 
86 

.40652 
.40692 

i-95 

2.00 
I  0,5 

.53436 
.53489 

2.05 

2.65 
2.65 

88 
90 

92 

-38724 
9  38765 
.38806 

2.05 
2.05 

2.00 

.50867 
9.50921 
•50975 

2.70 
2.70 
2.70 

88 
90 
92 

.40731 
9.40771 
.40811 

2.00 
2.0O 
1-95 

•53542 
9.53596 
.53649 

2.70 
2.65 
2.65 

94 
96 
98 

.38846 
.38887 
.38928 

2.05 
2.05 

.51029 
.51083 
.51136 

2.70 
2.65 

94 
96 
98 

.40850 
.40890 
.40929 

2.00 

1-95 

•53702 
•53755 
.53808 

2.65 
2.65 

2  65 

100 

9.38968 

9.5H90 

100 

9-40969 

9-5386I 

(209) 


TABLE  XXVI.  —  (Continued} 


Hun- 

42 

Hun- 

43 

* 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

9.40969 

9.5386i 

00 

9-42918 

9-56505 

•7    fic 

02 
04 
06 

.41008 
.41048 
.41087 

2.00 

i-95 

.53915 
-53968 
.54021 

2.65 
2.65 

02 
04 
06 

.42957 
.42995 
.43033 

1-95 

90 
90 

.56558 
.56611 
.56663 

2.65 
2.60 

2.65 

•95 

2.65 

08 
IO 
12 

.41127 
9.41166 
.41205 

1-95 
1-95 

2.00 

.54074 
9-54127 
.54180 

2.65 
2.65 

2  60 

08 
10 
12 

-43072 
9.43110 
•43149 

90 
95 
90 

.56716 
9-56768 
.56821 

2.60 
2.65 
2.60 

14 

16 

18 

.41245 
.41284 
.41323 

1-95 
1-95 

-54232 
.54286 
•54339 

2.70 
2.65 

14 
16 
18 

.43187 
.43225 
.43264 

.90 
•  95 

.56873 
.56926 
.56979 

2.65 
2.65 

2  60 

20 

9  41363 

I  0^ 

9-54392 

,  fie 

20 

9-43302 

.90 

9.57031 

2   6% 

22 
24 
26 

.41402 
.41441 
.41480 

1-95 
1.95 

2.00 

-54445 
-54498 
•54551 

2.65 
2.65 
2.65 

22 
24 
26 

-43340 
.43378 
•43417 

•9° 
.90 
-95 
.90 

.57084 
.57136 
.57189 

2.60 
2.65 
2.60 

28 
30 
32 

.41520 
9-4IS59 
.41598 

1-95 
1-95 
1-95 

.54604 
9-54657 
•54710 

2.65 
2.65 

2  65 

28 
30 
32 

•43455 
9-43493 
-43531 

.90 
•  90 
Qo 

.57241 
9-57294 
.57346 

2.65 
2.60 
2.65 

34 
36 
38 

•41637 
.41676 
.41715 

1-95 
1-95 

2  OO 

.54763 
.54816 
.54869 

2.65 
2.65 

34 
36 
38 

.43569 
.43608 
.43646 

•  95 
•  90 

•57399 
-57451 
•57503 

2.60 
2.60 
2  6  "5 

40 

9-41755 

i  95 

9.54922 

,  Cf 

40 

9.43684 

.90 

9.57556 

2  60 

42 
44 
46 

-41794 
•41833 
.41872 

1.95 
1-95 
1-95 

-54975 
.55028 
.55081 

2.65 
2.65 
2.65 

42 
44 
46 

•43722 
.4376o 
•43798 

.90 

•  90 
.90 
•9° 

.57608 
.57661 
•57713 

2.65 
2.60 
2.65 

48 
So 
52 

.41911 
9-4I950 
.41989 

1-95 
1-95 
1-95 

.55134 

9-55I87 
.55240 

2.65 
2.65 
2.60 

48 
So 

52 

.43836 
9.43874 
-43912 

.90 
.90 
•90 

•57766 
9-578I8 
.57870 

2.60 
2.60 

2.65 

54 
56 

.42028 
.42067 

1-95 

.55292 
•55345 

2.65 

54 
56 

•43950 
.43988 

.90 

•57923 
•57975 

2.60 

2  60 

58 

.42106 

1.90 

.55398 

2.65 

y  fir 

58 

.44026 

-90 

.58027 

2.65 

60 

9.42144 

1-95 

9-55451 

60 

9.44064 

9.58080 

2.60 

62 

.42183 

1-95 

.55505 

9  fio 

62 

.44102 

.58132 

2  60 

64 
66 

.42222 
.42261 

1.95 
1.95 

•55557 
•55609 

2.60 
2.65 

64 
66 

.44140 
.44177 

-85 
90 

.58184 
.58237 

2.65 

2.60 

68 
70 

72 

.42300 
9-42339 
.42377 

1-95 
1.90 
1-95 

.55662 
9-55715 
.55768 

2.65 
2.65 

2.60 

68 
70 

72 

.44215 
9-44253 
.44291 

.90 
.90 
.90 

.58289 
9-5834I 
.58394 

2.60 
2.65 

2.60 

74 
76 
78 

.42416 
.42455 
.42494 

i-95 
1-95 
1.90 

.55820 
.55873 
.55926 

2.65 
2.65 

2  AC 

74 
76 
78 

.44329 
.44366 
.44404 

-85 
.90 

.58446 
.58498 
.58550 

2.60 
2.60 
2.65 

80 

9-42532 

1.95 

9-55979 

y  f,n 

80 

9.44442 

9-58603 

2.60 

82 
84 

•42571 
.42610 

1-95 

I   QO 

.56031 
.56084 

2.65 

82 
84 

.44480 
.44517 

.85 

.58655 
:58?07 

2.60 

2  60 

86 

.42648 

1.95 

.56137 

2.65 

2  60 

86 

.44555 

•  90 
9° 

.58759 

2.65 

88 

90 

.42687 
9.42725 

1.90 
i  90 

.56189 
9.56242 

2.65 

88 
90 

•44593 
9-44630 

.85 

.58812 
9.58864 

2.60 
2  60 

92 

.42764 

1.  95 

.56295 

2.05 
2.60 

92 

.44668 

•  90 
.85 

.58916 

2.60 

94 
96 
98 

.42803 
.42841 
.42880 

1.90 
1-95 
1.90 

.56347 
.56400 
.56453 

2.65 
2.65 

«  fin 

94 
96 
98 

.44705 
•44743 
.44781 

.90 
.90 

Ur 

.58968 
.59020 
.59073 

2.60 

2.65 

2  60 

100 

9.42918 

9.56505 

100 

9.44818 

9.59125 

(210) 


TABLE  XXVI.  —  (Continued} 


Hun- 

44 

Hun- 

45 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

00 

9.44818 

9.59125 

00 

9-46671 

9.61722 

02 

04 

.44856 
.44893 

1.90 
-85 

•59177 
.59229 

2.60 

02 
04 

.46708 
.46744 

.05 

80 

.61774 
.61826 

2.60 

06 

•44931 

.90 
85 

.59281 

2.60 

2  60 

06 

.46781 

85 
80 

.61878 

2.60 
2  55 

08 
IO 

.44968 
9-45005 

-85 

•59333 
9.59385 

2.60 

08 

10 

.46817 
9.46854 

85 

.61929 
9.61981 

2.60 

12 

.45043 

.90 
85 

.59437 

2.6O 
2  65 

12 

.46890 

80 
85 

.62033 

2.60 

2  60 

14 

.45080 

•59490 

14 

•46927 

.62085 

16 
18 

.45"8 
-45155 

.90 
.85 

•59542 
.59594 

2.6O 
2.60 
9   fid 

16 
18 

.46963 
.47000 

.80 
.85 
So 

.62136 
.62188 

2.55 
2.60 
2  fin 

20 

9-45192 

9.59646 

2  60 

20 

9.47036 

80 

9.62240 

22 
24 
26 

.45230 
-45267 
.45304 

.90 

.85 
.85 
QO 

.59698 
•59750 
.59802 

2.60 
2.6O 
2  60 

22 

24 
26 

.47072 
.47109 
•47145 

.85 
.80 
85 

.62291 
.62343 
.62395 

2.6o 
2.60 
2  55 

28 
30 
32 

•45342 
9-45379 
.45416 

.85 
.85 
.85 

.59854 
9.59906 
.59958 

2.60 
2.60 
2.60 

28 
30 
32 

.47182 
9.47218 
.47254 

.80 
.80 
.85 

.62446 
9.62498 
.62550 

2.60 
2.60 
2.55 

34 
36 
38 

•45453 
•45490 
.45528 

-85 
.90 

«c 

.60010 
.60062 
.60114 

2.60 
2.60 
2  60 

34 
36 
38 

.47291 
.47327 
.47363 

.80 
.80 
80 

.62601 
.62653 
.62705 

2.60 
2.60 

40 

9-45565 

Qc 

9.60166 

2  60 

40 

9-47399 

Se 

9.62756 

2  60 

42 
44 
46 

.45602 
.45639 
.45676 

.85 
.85 
85 

.60218 
.60270 
.60322 

2.60 
2.60 
2  60 

42 
44 
46 

.47436 
-47472 
.47508 

.80 
.80 
.80 

.62808 
.62859 
.62911 

2.55 

2.60 
2.60 

48 
50 
52 

.45713 
9-45750 
•45787 

.85 
.85 
85 

.60374 
9.60426 
.60478 

2.60 
2.60 
2  60 

48 
So 

52 

•47544 
9.47580 
.47616 

.80 
.80 
85 

.62963 
9.63014 
.63066 

2.55 
2.60 
2-55 

54 
56 
58 

.45824 
.45861 
.45898 

.85 
.85 

.60530 
.60582 
.60634 

2.60 
2.60 

2    fid 

54 
56 
58 

.47653 
•47689 
•47725 

.80 
.80 

So 

•63117 
.63169 
.  63220 

2.60 
2.55 

2    fio 

60 

9-45935 

Of 

9.60686 

2  60 

60 

9.47761 

80 

9-63272 

62 
64 
66 

•45972 
.46009 
.46046 

-85 
.85 
.85 

.60738 
.60790 
.60841 

2.60 

2.55 

2.60 

62 
64 
66 

•47797 
.47833 
.47869 

.80 
.80 
.80 

•63323 
.63375 
•63427 

2.60 
2.60 
2.55 

68 
70 

72 

.46083 
9.46120 
.46157 

.85 
•  85 
•  85 

.60893 
9-60945 
.60997 

2.60 
2.60 
2.60 

68 
70 

72 

•47905 
9-47941 
•47977 

.80 
.80 
.80 

.63478 
9-63530 
.63581 

2.60 

2.55 

2.60 

74 
76 
78 

.46194 
.46230 
.46267 

.80 
•  85 

Qe 

.61049 
.61101 
.61153 

2.60 
2.60 

74 
76 
78 

.48013 
.48049 
.48085 

.80 
.80 
80 

.63633 
.63684 
-63736 

2.55 
2.60 

80 

9.46304 

X- 

9.61204 

2  60 

80 

9.48121 

9.63787 

2  60 

82 
84 
86 

•46341 
.46378 
.46414 

.85 
.80 
85 

.61256 
.61308 
.61360 

2.60 
2.60 
2  60 

82 
84 
86 

.48156 
.48192 
.48228 

.80 
.80 
80 

.63839 
.63890 
•  63941 

2.55 
2.55 

2  60 

88 
90 

92 

.46451 
9.46488 
•46524 

.85 
.80 
•  85 

.61412 
9.61464 
.61515 

2.60 
2.55 
2.60 

88 
90 
92' 

.48264 
9.48300 
.48336 

.80 
.80 
•  75 

.63993 
9.64044 
.64096 

2.55 
2.60 
2.55 

94 
96 
98 

.46561 
.46598 
.46634 

.85 
.80 

.61567 
.61619 
.61671 

2.60 
2.60 

94 
96 
98 

.48371 
.48407 
.48443 

.80 
.80 
80 

.64147 
•64199 
.64250 

2.60 
2.55 

100 

9.46671 

9.61722 

100 

9.48479 

9-64301 

(211) 


TABLE  XXVI.  —  (Continued) 


Hun- 

46 

Hun- 

4 

r 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

9-48479 

9.64301 

2  60 

00 

9.50243 

9.66865 

02 
04 
06 
08 
10 
12 

14 

16 
18 

•48514 
.48550 
.48586 
.48621 
9-48657 
.48693 
.48728 
.48764 
.48799 

.80 
.80 
•  75 

.80 
.80 
•  75 
.80 
-75 
80 

.64353 
.64404 
.64456 

.64507 
9-64558 
.64610 
.64661 
.64713 
-   .64764 

2.55 
2.60 
2.55 

2-55 
2.60 
2.55 
2.60 
2.55 

02 
04 

06 
08 

10 
12 

14 

16 
18 

.50278 
-50313 
•50347 
.50382 
9.50417 
•50452 

.50487 
.50521 
.50556 

1-75 
1-75 
1.70 

1-75 
1-75 
1-75 

1.70 
1-75 

.66916 
.66967 
.67018 
.67069 
9.67120 
.67171 
.  67222 
.67273 
.67325 

2.55 
2.55 
2.55 
2.55 
2.55 
2-55 

2.55 
2.60 

20 

9.48835 

9-64815 

?  fin 

20 

9.50591 

9.67376 

22 
24 
26 

28 
30 

32 

34 
36 
38 

.48870 
.48906 
.48941 

.48977 
9.49012 
.49048 
.49083 
.49119 
.49154 

.80 
-75 
.80 

-75 
.80 
-75 
.80 
•  75 

.64867 
.64918 
.64969 
.  65021 
9-65072 
.65123 

.65175 
.  65226 
.65277 

2.55 

2.55 

2.60 

2.55 
2.55 

2.60 

2.55 
2.55 

22 
24 
26 
28 
30 

32 

34 
36 
38 

.50625 
.50660 
•50695 
.50729 
9.50764 
•50799 

.50833 
.50868 
.50902 

1-75 
1.  75 

1.70 

1-75 
1-75 

1.70 

1-75 

1.70 

.67427 
.67478 
-67529 
.67580 
9-67631 
.67682 

.67733 
.67784 
-67835 

2.55 
2.55 
2.55 
2.55 
2.55 
2.55 
2.55 
2.55 

40 

9.49189 

80 

9-65328 

2  60 

40 

9-50937 

9.67886 

42 
44 
46 

48 
50 

52 

54 
56 
58 

.49225 
.49260 
.49295 

•49331 
9.49366 
•49401 

•49437 
•49472 
•49507 

•  75 

-75 
.80 

•  75 
.75 
.80 

•  75 
•  75 

.65380 
.65431 
.65482 

.65534 
9.65585 
.65636 

.65687 
•65739 
.65790 

2.55 
2.55 
2.60 

2.55 
2.55 
2.55 
2.60 
2.55 

42 
44 
46 
48 
50 

52 

54 
56 
58 

.50971 
.51006 
.51040 
•51075 
9-5II09 
•51144 
.5H78 
.51213 
.51247 

1.75 
1.70 
1-75 
1.70 
1.75 
1.70 

1-75 
1.70 

.67937 
.67988 
.68039 
.68090 
9.68141 
.68192 

.68243 
.68294 
.68345 

2.55 
2.55 
2-55 
2.55 
2.55 
2.55 
2.55 
2-55 

60 

9-49542 

9-65841 

60 

9-51281 

9.68396 

62 
64 
66 

68 
70 

72 

74 
76 
78 

.49577 
.49613 
.49648 

.49683 
9-49718 
.49753 
.49788 
.49823 
.49858 

.80 
-75 
•  75 
•  75 
-75 
•  75 
•  75 
.75 

.65892 
•65944 
•65995 
.66046 
9.66097 
.66148 
.66200 
.66251 
.66302 

2.60 
2.55 
2.55 
2.55 
2.55 
2.60 

2.55 
2.55 

62 
64 
66 

68 
70 

72 

74 
76 
78 

.51316 
.51350 
.51384 
.51419 
9-51453 
.51487 
.51522 
.51556 
.51590 

1.70 
1.70 
1-75 
1.70 
1.70 
1-75 
1.70 
1.70 

-68447 
.68498 
•68549 
.68600 
9.68651 
.68702 

.68753 
.68804 
.68855 

2.55 
2.55 
2.55 
2.55 
2.55 
2.55 
2.55 
2.55 

80 

9.49893 

•75 

9-66353 

80 

9.51624 

9-68905 

82 
84 
86 

88 
90 

92 

94 
96 
98 

.49928 
.49963 
.49998 

.50033 
9.50068 
.50103 
.50138 
.50173 
.50208 

•  75 
•  75 
•  75 
.75 
•  75 
•  75 
-75 
.75 

.66404 
.66455 
.66507 
.66558 
9.66609 
.66660 

.66711 
.66762 
.66813 

2.55 
2.55 
2.55 
2.55 
,2.55 
2.55 
2.55 
2.  55 

2  60 

82 
84 
86 

88 
90 
92 

94 
96 
98 

.51659 
.51693 
.51727 
.51761 
,9-51795 
.51829 

.51863 
.51898 
.51932 

1.70 
1.70 
1.70 
1.70 
1.70 
1.70 
1.70 
1.70 

.68956 
.69007 
.69058 
.69109 
9.69160 
.69201 
.69262 
.69313 
.69364 

2.55 
2.55 
2-55 
2.55 
2.55 
2.55 
2.55 
2.55 
2  55 

100 

9.50243 

9.66865 

100 

9-51966 

9.69415 

(212) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

48° 

Hun- 
dredths 

49° 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

9.51966 

9.694I5 

00 

9-53648 

9.7I954 

02 

.52000 

-69465 

02 

.53682 

.72005 

04 

.52034 

1.70 

.69516 

2.55 

04 

•53715 

1.65 

•72055 

2.50 

06 

.52068 

1.70 

.69567 

2.55 

06 

•53748 

1.65 

.72106 

2.55 

08 

.52102 

1.70 

.69618 

2.55 

08 

.53781 

1.65 

•72157 

2-55 

10 

9.52136 

1.70 

9.69669 

2.55 

IO 

9-53815 

1.70 

9.72208 

2-55 

12 

.52170 

1.70 

.69720 

2-55 

12 

-53848 

1.65 

.72258 

2.50 

1.70 

2-55 

1.65 

2.55 

14 

.52204 

.69771 

14 

.53881 

•72309 

16 
18 

.52238 
.52271 

1.70 
1.65 

.69822 
.69872 

2.55 
2.50 

16 
18 

•53914 
•53947 

1.65 
1.65 
i  6? 

.72360 
.72410 

2.55 
2.50 

20 

9.52305 

9-69923 

20 

9.53980 

9.72461 

22 

.52339 

.69974 

22 

-54013 

.72512 

24 

.52373 

1.70 

.70025 

2-55 

24 

.54046 

1.  65 

.72562 

2.50 

26 

.52407 

1.70 

.70076 

2.55 

26 

.54080 

1.70 

.72613 

2.55 

28 

.52441 

1.70 

.70127 

i* 

28 

•54II3 

1.65 

.72664 

2.55 

30 
32 

9.52475 
.52508 

1.70 
1.65 
1.70 

9.70177 
.70228 

2.50 

2.55 
2-55 

30 
32 

9.54146 
-54I79 

1.65 
1.65 
1.65 

9.72714 
.72765 

2.50 
2-55 
2-55 

34 

.52542 

.70279 

34 

.54212 

.72816 

36 

.52576 

1.70 

•70330 

2.55 

36 

.54245 

1.65 

.72866 

2.50 

38 

.52610 

1.70 
i  6=; 

.70381 

2.55 

38 

.54278 

1.65 

.  72917 

2.55 

40 

9-52643 

9-7043I 

40 

9-543II 

i  6s 

9.72968 

42 

.52677 

.70482 

42 

-54344 

.73018 

44 
46 
48 

.52711 
•52745 
.52778 

1.70 
1.70 
1.65 

-70533 
•70584 
•70635 

2.55 
2.55 
2-55 

44 
46 

48 

•54377 
.54409 
•54442 

1.65 

i.  60 
1.65 

.73069 
•73120 

.73170 

2.  55 
2.55 
2.50 

50 
52 

9.52812 
.52846 

1.70 
1.70 
1.65 

9-70685 
.70736 

2.50 
2.55 
2.  55 

So 

52 

9-54475 
.54508 

1.65 
1.65 
1.65 

9-73221 
•73271 

2.55 

2.50 
2.50 

54 

-52879 

-70787 

54 

•54541 

73321 

56 

.52913 

1.70 

.70838 

2.55 

56 

-54574 

1.65 

•73372 

2-55 

58 

.52946 

1.65 

.70889 

2.55 

58 

.54607 

1.65 
T  fin 

.73423 

2.55 

60 

9.52980 

9.70939 

60 

9-54639 

T  fie 

9-73474 

2-55 

62 
64 

.53014 
.53047 

1.65 

.70990 
.71041 

2.55 

62 
64 

.54672 
•54705 

1.  05 

1.65 

•73524 
•73575 

2.50 
2-55 

66 

.53081 

1.70 
1.65 

.71092 

2.55 
2.50 

66 

.54738 

1.65 
1.65 

.  73626 

2.55 
2.50 

68 
70 

72 

-53II4 
9.53I48 
.53i8i 

1.70 
1.65 
1.70 

.71142 
9-7II93 
.71244 

2.55 
2.55 
2-55 

68 
70 

72 

•54771 
9-54803 
.54836 

1.  60 
1.65 
1.65 

.73676 
9-73727 
•73778 

2.55 
2-55 
2.50 

74 
76 
78 

•53215 
.53248 
.53282 

1.65 
1.70 

.71295 
.71345 
.71396 

2.50 
2.55 

74 
76 
78 

.54869 
-54901 
-54934 

i.  60 
1.65 

.73828 
.73879 
.73929 

2.55 
2.50 

80 

9.53315 

1-5 

9-71447 

80 

9-54967 

T   fin 

9.73980 

82 
84 

•53348 
.53382 

1.70 

.71498 
.71548 

2.50 

82 
84 

•54999 
.55032 

1.65 

.74031 
.74081 

2.55 
2.50 

86 

•53415 

1.65 

•71599 

2.55 

86 

.55065 

1.65 

.74132 

2.55 

1.70 

2-55 

i.  60 

2.50 

88 
90 
92 

.53449 
9.53482 
•53515 

1.65 
1.65 

.71650 
9.71700 
•7I75I 

2.50 
2.55 

88 
90 
92 

.55097 
9-55I30 
.55162 

i.  6s 
i.  60 

.74182 
9.74233 
.74284 

2.55 
2.55 

1.70 

2.5S 

1.65 

2.50 

94 
96 
98 

•53549 
.53582 
.53615 

1.65 
i.  65 

.71802 
.71853 
•71903 

2.55 

2.50 

94 
96 
98 

•55195 
.55228 
.55260 

1.65 
i.  60 

•74334 
.74385 
•74435 

2.55 
2.50 

100 

9.53648 

9.7I954 

100 

9-55293 

9.74486 

(213) 


TABLE  XXVI.  —  (Continued') 


Hun- 
dredths 

60° 

Hun- 

dredths 

51° 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

Vets 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9.55293 

i  60 

9-74486 

00 

9.56900 

T  fin 

9-77013 

02 

•55325 

.74536 

02 

-56932 

•77063 

2.50 

04 

•55358 

1.05 

.74587 

2.55 

04 

.56963 

I  60 

.77H4 

2.55 

06 

-55390 

1.65 

.74638 

2.55 
2.50 

06 

.56995 

1.  60 

.77164 

2.50 
2  55 

08 

10 
12 

•55423 
9-55455 
.55487 

i.  60 
i.  60 
1.65 

.74688 
9-74739 
.74789 

2.55 
2.50 
2.55 

08 
10 

12 

.57027 
9.57059 
.57090 

1.  60 

1.55 
i.  60 

•77215 
9.77265 
-773I6 

2.50 
2.55 
2.50 

14 
16 
18 

•55520 
.55552 
.55585 

i.  60 
1.65 
i  60 

.74840 
.74890 
-  74941 

2.50 
2-55 

14 
16 
18 

.57122 

.57154 
.57185 

i.  60 
1-55 
T  fin 

•77366 

.77417 
•  77467 

2.55 
2.50 

20 

9.55617 

I  60 

9-74992 

20 

9-57217 

I  60 

9-77518 

22 

.55649 

•  75042 

22 

.57249 

.77568 

24 

.55682 

1.05 

.75093 

2.55 

24 

.57280 

I  60 

.77619 

2.55 

26 

.55714 

i.  60 

•75143 

2.50 
2.55 

26 

•57312 

1-55 

.77669 

2.50 
2.55 

28 

.55746 

•75194 

28 

•57343 

I  60 

.77720 

30 

9-55779 

1.65 

9-75244 

2.50 

30 

9-57375 

I  60 

9-77770 

2.50 

32 

.55811 

.75295 

2-55 

32 

•57407 

.77821 

2.55 

34 

.55843 

•75345 

34 

.57438 

I  60 

.77871 

36 
38 

.55875 
.55908 

1.65 
i  60 

.75396 
•75447 

2.55 
2.55 

36 
38 

•57470 
•57501 

1.55 
I  60 

.77922 
-77972 

2.55 
2.50 

40 

9-55940 

I  60 

9-75497 

40 

9-57533 

9-78023 

42 
44 
46 
48 
So 

52 

•55972 
.56004 
.56036 

.56069 
9.56101 
•56133 

i.  60 
i.  60 
1.65 
i.  60 
i.  60 
i.  60 

•75548 
•75598 
.75649 

.75699 
9-75750 
.75800 

2.50 
2.55 
2.50 

2.55 
2.50 
2.55 

42 
44 
46 
48 
So 

52 

.57564 
.57596 
.57627 

.57659 
9.57690 
•57721 

1.  60 
1-55 
1.  60 
1.55 
1-55 
1.  60 

.78073 
.78124 
.78174 
.78225 
9-78275 
.78326 

2.55 
2.50 
2.55 
2.50 
2.55 
2  50 

54 

.56165 

.75851 

54 

•57753 

.78376 

56 
58 

.56197 
.56229 

i.  60 
i.  60 
i  60 

•75901 
.75952 

2.50 
2.55 

56 
58 

.57784 
.57816 

1.  60 

.78427 
.78477 

2.55 
2.50 

60 

9.56261 

I  60 

9.76002 

60 

9-57847 

9.78527 

62 

.56293 

.76053 

62 

.57878 

i  60 

.78578 

64 
66 

68 
70 

72 

.56325 
.56357 
.56390 
9.56422 
.56454 

i.  60 
1.65 
i.  60 
i.  60 

.76103 
.76144 
.76204 
9.76255 
.76306 

2.50 
2.55 
2.50 

2.55 
2.55 

64 

66 

68 
70 

72 

•57910 
•57941 
•57972 
9-58004 
.58035 

1-55 

1.55 
i.  60 
1.55 

.78628 
.78679 
.78729 
9.78780 
.78830 

2.50 
2.55 
2.50 

2.55 
2.50 

74 
76 

.56485 
.56517 

i.  60 

.76356 
.76407 

2.55 

74 
76 

.58066 
.58097 

1.55 
I  60 

.78881 
.78931 

2.50 

78 

.56549 

i.  60 

i  60 

.76457 

2.50 

78 

.58129 

.78982 

2.55 

80 

9-56581 

i  60 

9.76508 

80 

9.58160 

9.79032 

82 
84 
86 

.56613 
.56645 
.56677 

i.  60 
i.  60 
i  60 

.76558 
.76609 
.76659 

2.55 
2.50 
2  55 

82 
84 
86 

.58191 
.58222 
.58253 

1.55 
1.55 
1  60 

.79083 
•79133 
.79184 

2.50 
2.55 
2.50 

88 
90 

92 

.56709 
9.56741 
.56773 

i.  60 
i.  60 

.76710 
9.76760 
.76811 

2.50 
2.55 

88 
90 
92 

.58285 
9-58316 
.58347 

1.55 
1.55 

•79234 
9.79285 
•79335 

2.55 
2.50 

94 
96 
98 

.56804 
.56836 
.56868 

1-55 
i.  60 
i.  60 
I  60 

.76861 
.76912 
.76962 

2.50 

2.55 
2.50 

94 
96 
98 

.58378 
.58409 
.58440 

1-55 
1.55 
1.55 

•79386 
.79436 
.79487 

2.55 

2.50 
2.55 

2  50 

100 

9-56900 

9-77013 

100 

9.58471 

9-79537 

(214) 


TABLE  XXVI.  —  (Continued) 


Hun- 

5J 

5° 

Hun- 

I 

1° 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9-S847I 

9-79537 

00 

9.60008 

9.82062 

02 
04 

.58502 
.58534 

.60 

•79588 
.79638 

2.50 

02 
04 

.60039 
.60069 

•  So 

.82113 
.82163 

2.50 

06 

.58565 

.55 

.79689 

2.55 

06 

.60100 

•  55 

.82214 

2.55 

08 

.58596 

-79739 

08 

.  60130 

.82264 

zo 

9.58627 

•  55 

9-79790 

2.55 

10 

9  .  60160 

•  SO 

9-82315 

2.55 

12 

.58658 

.55 

•79840 

2.50 

12 

.60191 

•  55 

•82365 

2.50 

14 

.58689 

.79891 

14 

.  60221 

.82416 

16 

.58720 

•  55 

•79941 

2.50 

16 

.60251 

•  50 

.82466 

2.SO 

18 

.58751 

•  55 

.79992 

2.55 

18 

.60282 

•  55 

•82517 

2.55 

20 

9-58782 

9.80042 

2  SS 

20 

9.60312 

9.82568 

22 

.58812 

.80093 

22 

.60342 

.82618 

24 
26 

.58843 
•58874 

•  55 
•  55 
•  55 

.80143 
.80194 

2.5O 
2.55 
2.50 

24 
26 

.60372 
.60403 

•  50 
•  55 
•  So 

.82669 
.82719 

2.55 
2.50 
2.  55 

28 

.58905 

.80244 

28 

•60433 

.82770 

30 
32 

9.58936 
.58967 

•  55 
•  55 

9-80295 
•80345 

2.55 

2.50 

30 
32 

9.60463 
.60493 

•  50 
•  50 

9.82820 
.82871 

2.50 
2.55 

34 
36 
38 

.58998 
.59029 
.59059 

•  55 
•  50 

.80395 
.80446 
.80496 

2.55 
2.50 

34 
36 
38 

•60523 
•60554 
.60584 

•  55 
•  50 

.82921 
.82972 
.83022 

2.55 

2.50 

40 

9.59090 

9-80547 

40 

9.60614 

9-83073 

42 
44 
46 

•59I2I 
.59152 
.59183 

•  55 
•  55 

•  50 

•80597 
.80648 
.80698 

2.55 
2.50 
2.55 

42 
44 
46 

.60644 
.60674 
.60704 

-50 
•  50 
•  50 

•83123 
•83174 
•83225 

2-55 
2.55 
2.50 

48 
50 
52 

.59213 
9-59244 
.59275 

•  55 
•  55 
•55 

.80749 
9-80799 
.80850 

2.50 
2.55 
2.50 

48 
50 
52 

•60734 
9.60764 
•60795 

•  50 
•  55 
•  So 

•83275 
9-83326 
.83376 

2.55 
2.50 
2.55 

54 
56 
58 

.59306 
.59336 
.59367 

•  50 
•  55 

.80900 
.80950 
.81001 

2.50 
2.55 
2  55 

54 
56 
58 

.60825 
.60855 
.60885 

•  50 
•  50 

•83427 
.83477 
.83528 

2.50 
2-55 

60 

9-59398 

50 

9.81052 

2  SO 

60 

9-60915 

50 

9-83579 

2   ^0 

62 
64 
66 

.59428 
•59459 
•59490 

•  55 
•  55 
•  50 

.81102 
.81153 
.81203 

2.55 
2.50 
2.55 

62 
64 
66 

.60945 
.60975 
.61005 

•  50 
•  50 
•  50 

.83629 
.83680 
.83730 

2.55 
2.50 
2.55 

68 
70 

73 

.59520 
9-59551 
.59581 

•  55 
•  50 
•  55 

.81254 
9-81304 
.81355 

2.50 
2.55 
2.50 

68 
70 

72 

•61035 
9.61065 
.61095 

•  50 
•  SO 

•  45 

.83781 
9-83831 
.83882 

2.50 

2.55 
2-55 

74 
76 
78 

.59612 
.59643 
.59673 

•  55 

•  50 

tre 

.81405 
.81456 
•81507 

2.55 
2-55 

2  SO 

74 
76 
78 

.61124 
.61154 
.61184 

•  So 
•  50 

"»O 

.83933 
.83983 
.84034 

2.50 
2.  55 

80 

9-59704 

5° 

9-81557 

2  55 

80 

9.61214 

So 

9.84084 

2   ec 

82 
84 
86 

•59734 
.59765 
.59795 

•  55 
•  50 
•  55 

.81608 
.81658 
.81709 

2.50 
2-55 
2.50 

82 
84 
86 

.61244 
.61274 
.61304 

•  So 
•  So 
•So 

.84135 
.84186 
.84236 

2.55 
2.50 
2.55 

88 
90 
92 

.59826 
9-59856 
-59887 

•  50 
•  55 
•  50 

.81759 
9.81810 
.81860 

2.55 
2.50 
2.55 

88 
90 

92 

.61334 
9-61363 
.61393 

•  45 
•  50 
.50 

.84287 
9-84337 
.84388 

2.50 

2.55 
2.55 

94 
96 
98 

.59917 
•59948 
•59978 

•  55 
•  50 
SO 

.81911 
.81961 
.82012 

2.50 
2.55 

2  SO 

94 
96 
98 

.61423 
.61453 
.61483 

•  50 
•  So 

.84439 
.84489 
.84540 

2.50 
2-55 

100 

9.60008 

9.82062 

100 

9.61512 

9.84590 

(215) 


TABLE  XXVI.  —  (Continued) 


Hun- 

54 

Hun- 

55 

0 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

9.61512 

9-84590 

00 

9.62984 

9  87125 

02 

.61542 

.84641 

02 

-63013 

.87176 

04 

.61572 

So 

.84692 

2.55 

04 

.63042 

45 

.87227 

2-55 

06 

.61602 

So 

.84742 

2.50 

06 

-63071 

.     45 

.87277 

2.50 

08 

10 

.61631 
9.61661 

So 

.84793 
9.84844 

2.55 

08 

IO 

.63101 
9-63130 

45 

•87328 
9-87379 

2.55 

12 

.61691 

So 

.84894 

2.50 

12 

•63159 

45 

•87430 

2-55 

14 

16 

.61720 
.61750 

So 

.84945 
.84996 

2.55 

14 

16 

.63188 
•63217 

45 

.87480 
.87531 

2.55 

18 

.61780 

So 

.85046 

2.50 

18 

.63246 

45 

.87582 

2.55 
2  55 

20 

9.61809 

9.85097 

20 

9-63275 

9-87633 

22 

24 

.61839 
.61868 

45 

.85147 
.85198 

2.55 

22 

24 

•63304 
.63333 

-45 

.87684 
-87735 

2.55 

26 

.61898 

50 
50 

.85249 

2.55 
2.50 

26 

.63362 

-45 
•  45 

.87785 

2.50 
2-55 

28 
30 

.61928 
9.61957 

45 

•85299 
9-85350 

2.55 

28 
30 

.63391 
9-63420 

-45 

.  87846 
9.87887 

2.55 

32 

.61987 

•  5° 
45 

.85401 

2.55 
2.50 

32 

.63448 

•  40 
•45 

.87938 

2.55 

34 
36 
38 

.62016 
.62046 
.62075 

•  50 

45 

•85451 
.85502 
•85553 

2.55 
2-55 

34 
36 
38 

.63477 
.63506 
.63535 

-45 
•  45 

.87989 
.88040 
.88090 

2.55 
2.50 
2  *;<; 

40 

9.62105 

9-85603 

40 

9-63564 

45 

9.88141 

2  55 

42 
44 
46 

.62134 
.62164 
.62193 

•  50 
•  45 
.50 

.85654 
.85705 
.85755 

2.55 
2.50 
2.55 

42 
44 
46 

.63593 
.63622 
.63651 

-45 
•  45 
•  40 

.88192 
.88243 
.88294 

2.55 
2.55 
2.55 

48 
50 

52 

.62223 
9.62252 
.62282 

•  45 
•  50 
45 

.85806 
9-85857 
.85907 

2.55 
2.50 
2-55 

48 
50 
52 

.63679 
9-63708 
.63737 

•  45 
-45 
•45 

.88345 
9-88395 
.88446 

2.50 
2.55 
2.55 

54 
56 
58 

.62311 
.62340 
.62370 

•  45 
•  50 
45 

.85958 
.86009 
.86060 

2.55 
2.55 

2  SO 

54 
56 
58 

.63766 
.63795 
.63823 

-45 
.40 
45 

.88497 
.88548 
.88599 

2.55 
2.55 
2.55 

60 

9.62399 

9.86110 

60 

9-63852 

45 

9.88650 

2  55 

62 
64 
66 

.62429 
.62458 
.62487 

•  45 
•  45 
.50 

.86161 
.86212 
.86262 

2.55 
2.50 
2.55 

62 
64 
66 

.63881 
.63910 
.63938 

•  45 
-40 
•  45 

.88701 
.88752 
.88803 

2.55 
2.55 
2.55 

68 
70 

72 

.62517 
9-62546 
.62575 

•  45 
•  45 
•  45 

.86313 
9-86364 
.86415 

2.55 
2.55 
2.50 

68 
70 

72 

.63967 
9.63996 
.64025 

•  45 
•  45 
•  40 

.88854 
9.88904 
.88955 

2.50 
2.55 
2-55 

74 
76 
78 

.62604 
.62634 
.62663 

•  50 
•  45 

45 

.86465 
.86516 
.86567 

2.55 
2.55 
2  50 

74 
76 
78 

.64053 
.64082 
.64111 

•  45 
•  45 
.40 

.89006 
.89057 
.89108 

2.55 
2.55 
2.55 

80 

9.62692 

9.86617 

80 

9-64139 

45 

9.89159 

2.55 

82 
84 
86 

.62722 
.62751 
.  62780 

.45 
•  45 
•  45 

.86668 
.86719 
.86770 

2.55 
2.55 
2.50 

82 
84 
86 

.64168 
.64197 
.64225 

•  45 
.40 
•45 

.89210 
.89261 
.89312 

2.55 
2.55 
2.55 

88 

.62809 

.86820 

88 

.64254 

.89363 

2  55 

90 
92 

9.62838 
.62868 

•  50 
•  45 

9.86871 
.86922 

2-55 
2.55 

90 
92 

9.64282 
.64301 

•  45 
.40 

9.89414 
-89455 

3.55 
2.55 

94 
96 
98 

.62897 
.62926 
.62955 

•  45 
•  45 
45 

.86973 
.87023 
.87074 

2.50 
2.55 
2-55 

94 
96 
98 

.64339 
.64368 
-64396 

•  45 
.40 
•  45 

.89516 
.89567 
.89618 

2.55 
2.55 
2-55 

100 

9  62984 

9.87125 

100 

9.64425 

9.89669 

(216) 


TABLE   XXVI.  —  (Continued} 


Hun- 

• 

>° 

Hun- 

fi 

7° 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9.64425 

9.89669 

00 

9-65836 

9.92225 

02 

.64453 

.89720 

02 

.65863 

.92276 

04 

.64482 

-45 

.89771 

2.55 

04 

.65891 

.40 

.92327 

2.55 

06 

.64510 

•  40 

.89822 

2.55 

06 

.65919 

.40 

.92379 

08 

•64539 

.89873 

08 

.65947 

.92430 

10 

9-64567 

•  40 

9.89924 

2.55 

10 

9-65975 

.40 

9.92481 

2.55 

12 

-64596 

•  45 

.89975 

2.55 

12 

.66003 

.40 

.92532 

2.55 

14 

.64624 

.90026 

14 

.66031 

.92584 

16 

.64653 

•  45 

.90077 

2.55 

16 

.66059 

•  4° 

.92635 

18 

.64681 

.40 

.90128 

2.55 

18 

.66086 

•  35 

.92686 

2.55 

2  60 

20 

9.64709 

9.90179 

20 

9.66114 

9.92738 

22 

.64738 

.90230 

22 

.66142 

.92789 

34 
26 

.64766 
.64794 

•  40 
.40 
•  45 

.90281 
.90332 

2-55 
2.55 
2.55 

24 
26 

.66170 
.66198 

.40 
.40 
•  35 

.92840 
.92892 

2.55 
2.60 

2.55 

28 
30 
32 

.64823 
9.64851 
.64880 

•  40 
.40 

.90383 
9-90434 
•90485 

2.55 
2.55 

28 

30 
32 

.66225 
9.66253 
.66281 

.40 

.40 

.92943 
9.92994 
.93046 

2.55 

2.60 
2  55 

34 
36 
38 

.64908 
•64936 
.64964 

.40 
.40 

.90536 
.90587 
.90638 

2.55 
2.55 

34 
36 
38 

.66309 
.66336 

.66364 

•  35 

.40 

.93097 
-93I49 
.93200 

2.60 
2.55 
2  55 

40 

9-64993 

9.90689 

2  60 

40 

9-66392 

9-93251 

2  60 

42 
44 
46 

.65021 
.65049 
.65077 

.40 
.40 
•  45 

.90741 
.90792 
.90843 

2.55 
2.55 
2.55 

42 
44 
46 

.66419 
.66447 
.66475 

.40 
.40 
•  35 

.93303 
•93354 
.93405 

2.55 
2.55 
2.60 

48 
So 
52 

.65106 
9.65134 
.65162 

.40 
.40 
•  4° 

.90894 
9.90945 
.90996 

2.55 
2.55 
2.55 

48 
50 
52 

.66502 
9-66530 
.66558 

.40 
.40 
•  35 

•93457 
9-93508 
.93560 

2.55 
2.6o 
2.55 

54 
56 

.65190 
.65218 

.40 

.91047 
.91098 

2.55 

54 
56 

.66585 
.66613 

.40 

.936ii 
.93663 

2.60 

58 

.65247 

.91149 

2.55 

2  60 

58 

.66640 

•35 

.93714 

2  60 

60 

9-65275 

40 

9.91201 

60 

9.66668 

9-93766 

2  55 

62 
64 
66 

•65303 
•65331 
.65359 

-40 
.40 
.40 

.91252 
•91303 
•91354 

2.55 
2.55 
2.55 

62 
64 
66 

.66696 
•66723 
.66751 

•  35 
.40 
•  35 

.93817 
.93869 
.93920 

2.6o 
2.55 
2.55 

68 
70 

72 

.65387 
9.65415 
.65444 

.40 
•  45 

.40 

.91405 
9.91456 
.91508 

2.55 

2.60 
2.55 

68 
70 

72 

.66778 
9.66806 
.66833 

.40 
•  35 
.40 

•93971 
9.94023 
.94074 

2.60 
2.55 
2.60 

74 
76 

•65472 
.65500 

.40 

•91559 
.91610 

2.55 

74 
76 

.66861 
.66888 

-35 

.94126 
•94177 

2.55 

78 

.65528 

.91661 

2.55 

78 

.66916 

.40 

.94229 

2  60 

80 

9.65556 

40 

9.91712 

2  60 

80 

9.66943 

9.94281 

2  55 

82 

.65584 

.91764 

82 

.66971 

•94332 

2.60 

84 

.65612 

•91815 

84 

.66998 

.94384 

2.55 

86 

.65640 

.40 

.91866 

2-55 

86 

.67026 

•  35 

•94435 

2.60 

88 
90 

.65668 
9-65696 

.     .40 

.91917 
9.91968 

2-55 

2  60 

88 
90 

.67053 
9.67080 

•  35 

.94487 
9-94538 

2.55 

2  6O 

92 

.65724 

•  40 

.  92020 

2-55 

92 

.67108 

•  35 

•94590 

2.55 

94 
96 
98 

.65752 
.65780 
.65808 

.40 
.40 
40 

.92071 
.92122 
.92173 

2.55 
2.55 

2  60 

94 
96 
98 

.67135 
.67163 
.67190 

•  40 
•  35 

.94641 
.94693 
•94745 

2.60 
2.60* 
2  55 

100 

9-65836 

9  .  92225 

100 

9.67217 

9.94796 

(217) 


TABLE  XXVI.  —  (Continued) 


Hun- 

5 

8° 

Hun- 

5 

9° 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

9.67217 

9.94796 

2  60 

00 

9-68571 

9.97387 

2  fin 

02 
04 

•67245 
.67272 

•  35 

.94848 
.94900 

2.60 

02 

04 

•68598 
.68624 

•  30 

-97439 
-97491 

2.60 

06 

.67299 

•  35 

40 

•94951 

2.55 
2  60 

06 

.68651 

•  35 
35 

•97543 

2  60 

08 

.67327 

•95003 

08 

.68678 

•97595 

10 

9-67354 

•  35 

9-95054 

2.55 

10 

9-68705 

•  35 

9.97647 

2.6o 

12 

.67381 

•  35 

.95106 

2  60 

12 

.68731 

-30 

.97699 

2  fin 

14 

.67408 

.95158 

14 

•68758 

•97751 

16 
18 

•67436 
.67463 

•  40 
•  35 

•95209 
.95261 

2-55 

2.60 

2  60 

16 
18 

.68785 
.68811 

-35 
-30 

.97803 
.97855 

2.60 
2.60 

2   fir 

20 

9.67490 

9-95313 

20 

9.68838 

9.97908 

2  60 

22 
24 

•67517 
.67545 

•  40 

.95364 
.95416 

2.60 

22 
24 

.68865 
.68892 

-35 

.97960 
.98012 

2.60 

26 

.67572 

•  35 
•  35 

•95468 

2.60 

2.60 

26 

.68918 

-30 
•35 

..98064 

2.6O 

2  60 

28 

•67599 

•95520 

28 

.68945 

.98116 

30 
32 

9.67626 
•67653 

•35 

•  35 

•  4° 

9-95571 
•95623 

2.55 
2.60 
2.60 

30 
32 

9.68971 
.68998 

•  30 
•  35 
35 

9.98168 
.98220 

2.60 
2.60 
2  65 

34 

.67681 

.95675 

34 

.69025 

.98273 

36 

.67708 

•  35 

.95726 

2.55 

36 

.69051 

-30 

.98325 

2.60 

38 

•67735 

•  35 

•95778 

2  fin 

38 

.69078 

•  35 

.98377 

2.60 

40 

9.67762 

9-95830 

2  60 

40 

9-69104 

•  3O 

9-98429 

42 

.67789 

.95882 

42 

.69131 

.98481 

2  65 

44 

.67816 

•  35 

•95934 

44 

.69158 

•  35 

.98534 

2  60 

46 

•67843 

•  35 
•  35 

•95985 

2.55 
2  60 

46 

.69184 

•  30 
35 

.98586 

2.60 

48 

.67870 

•96037 

48 

.69211 

.98638 

2  60 

So 

52 

9.67897 
•67925 

•  35 

•  40 
•  35 

9.96089 
.96141 

2.60 
2  60 

50 
52 

9.69237 
.69264 

•  3O 
-35 
30 

9.98690 
.98743 

2.65 
2.60 

54 

.67952 

.96193 

54 

.69290 

.98795 

2  60 

56 
58 

•67979 
.68006 

•  35 

•  35 

.96244 
.96296 

2-55 
2.60 
2  60 

56 
58 

-69317 
.69343 

•35 

-30 

.98847 
.98899 

2.60 
2.65 

60 

9.68033 

9.96348 

•2  fin 

60 

9.69370 

9.98952 

2  60 

62 
64 
66 

.68060 
.68087 
.68114 

•  35 
•  35 
•  35 

.96400 
-96452 
•96504 

2.60 
2.60 
2  60 

62 
64 
66 

-69396 
.69423 
.69449 

-35 
-30 
35 

.99004 
.99056 
.99109 

2.60 
2.65 
2.60 

68 

.68141 

.96556 

68 

.69476 

.99161 

2  60 

70 

72 

9.68168 
.68195 

•  35 
•35 
•  35 

9.96607 
.96659 

2.55 
2.60 
2  60 

70 

72 

9-69502 
.69528 

•  30 
-30 
35 

9.99213 
.99266 

2.65 
2.60 

74 
76 
78 

.68222 
.68248 
.68275 

•  30 
35 

.96711 
•96763 
.96815 

2.60 
2.60 
2  60 

74 
76 
78 

.69555 
.69581 
.69608 

-30 
•  35 

•99318 
•99371 
•99423 

2.65 
2.60 
2.60 

80 

9.68302 

9.96867 

2  60 

80 

9-69634 

9-99475 

2.65 

82 

.68329 

.96919 

82 

.69660 

.99528 

2  60 

84 
86 

.68356 
.68383 

35 
35 
35 

.96971 
•97023 

2.60 
2  60 

84 
86 

.69687 
.69713 

35 
30 
30 

.99580 
.99633 

2.65 
2.60 

88 

90 

92 

.68410 
9-68437 
.68463 

35 
30 
35 

•97075 
9.97127 
•97179 

2.60 
2.60 
2  60 

88 

90 

92 

-69739 
9.69766 
.69792 

35 
30 
30 

.99685 
9-99738 
.99790 

2.6S 
2.60 
2.65 

94 
96 
98 

.68490 
.68517 
•68544 

35 
35 

.97231 
•97283 
.97335 

2.60 
2.60 
2  60 

94 
96 
98 

.69818 
.69844 
.69871 

30 
35 

.99843 
.99895 
•99947 

2.60 
2.60 
2  65 

100 

9-68571 

9.97387 

100 

9.69897 

o.ooooo 

(218) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

60° 

Hun- 
dredths 

61° 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9.69897 

o.ooooo 

%  £.- 

00 

9.71197 

0.02640 

2  6s 

02 
04 
06 

.69923 
.69949 
.69976 

1.30 
1-35 
1.30 

.00053 
.00105 
.00158 

2.60 

2.65 

2.60 

02 

04 

06 

.71223 
.71248 
.71274 

1.25 
1.30 
1.30 

.02693 
.02746 
.02799 

2.65 
2.65 
2.65 

08 

.70002 

.00210 

08 

.71300 

.02852 

10 
12 

9.70028 
.70054 

1.30 
1-30 
1-35 

0.00263 
.00315 

2.65 
2.60 
2.65 

IO 
12 

9.71325 
.71351 

1.25 
1.30 
1.30 

0.02905 
.02958 

2.65 
2.65 

2.70 

14 

16 
18 

.70081 
.70107 
.70133 

1.30 
1.30 

.00368 

.00420 
.00473 

2.60 

2.65 

2  6? 

14 

16 
18 

.71377 

.71402 
.71428 

1.25 
1-30 

.03012 
.03065 
.03118 

2.65 
2.65 

2  6"? 

20 

9.70159 

0.00526 

2  fin 

20 

9.71454 

0.03171 

2  6^ 

22 
24 
26 
28 
30 
32 

.70185 
.70211 
.  -70237 
.70264 
9.70290 
.70316 

1.30 
1.30 
1-35 
1.30 
1.30 
1.30 

.00578 
.00631 
.00684 
.00736 
0.00789 
.00842 

2.65 
2.65 
2.60 

2.65 
2.65 
2.65 

22 
24 
26 
28 

30 

32 

-71479 
.71505 
.71530 
.71556 
9-71582 
.71607 

1.30 
1.25 
1.30 
1.30 
I  25 
1.30 

.03224 
.03278 
.03331 

.03384 
0.03437 
.03491 

2.70 
2.65 
2.65 
2.65 
2.70 
2.65 

34 
36 
38 

•70342 
.70368 
.70394 

1.30 
1.30 

.00894 
.00947 
.01000 

2.65 
2.65 

2  60 

34 
36 
38 

.71633 
.71658 
.71684 

1.25 
1.30 

.03544 
.03597 
.03651 

2.65 
2.65 
2  61; 

40 

9.70420 

0.01052 

"2  fix 

40 

9.71709 

0.03704 

2  fir 

42 

.70446 

.01105 

42 

•71735 

-03757 

44 
46 

.70472 
.70498 

1.30 
1.30 

.01158 

.01211 

2.65 
2.65 

44 
46 

.71760 
.71786 

1.25 
1.30 

.03811 
.03864 

2.70 
2.65 

48 
So 

52 

.70524 
9.70550 
•70576 

1.30 
1.30 

.01263 
O.OI3I6 
.01369 

2.65 
2.65 

48 
So 

52 

.71811 
9.7I837 
.71862 

1.30 
1.25 

.03917 
0.03971 
.04024 

2.70 

2.65 

54 
56 
58 

.70602 
.70628 
•70654 

1.30 
1.30 

.  01422 

•01475 
.01528 

2.65 
2.65 

«  fin 

54 
56 
58 

.71888 
.71913 
.71939 

1.25 
1.30 

.04078 
.04131 
.04184 

2.65 
2.65 

60 

62 
64 
66 

68 
70 

72 

9.70680 

1.30 
1.30 
1.30 
1.30 
1.30 
1.25 
1.30 

0.01580 

2.65 
2.65 

2.65 
2.65. 
2.65' 
2.65 
2.65 

60 

62 
64 
66 

68 
70 

72 

9.71964 

1.25 
1.30 
1.25 
1.30 
1.25 

1.25 

1.30 

1.25 

0.04238 

2.65 
2.70 
2.65 
2.70 

2.65 
2.70 
2.65 

.70706 
.70732 
.70758 

.70784 
9.70810 
.70835 

.01633 
.01686 
•01739 
.01792 
0.01845 
.01898 

.71990 
.72015 
.72041 

.72066 
9.72091 
.72117 

.04291 
.04345 
.04398 
.04452 
0.04505 
.04559 

74 
76 

.70861 
.70887 

1.30 

.01951 
.02004 

2.65 

74 
76 

.72142 
.72167 

1.25 

.04612 
.04666 

2.70 

78 

.70913 

1.30 

.02056 

2.60 
9  fie 

78 

.72193 

1.30 

.04720 

2.70 
2  fit 

80 
82 
84 

9.70939 

1.30 
1.30 

0.02109 

2.65 
2.65 

80 
82 
84 

9.72218 

1.25 

1.25 
1.30 

0.04773 

2.70 
2.65 

-70965 
.70991 

.02162 
.02215 

.72243 
.72269 

.04827 
.04880 

86 

.71016 

1.25 
1.30 

.02268 

2.65 
2.65 

86 

•72294 

1.25 
1.25 

.04934 

2.70 
2.70 

88 
90 

.71042 
9.71068 

1.30 

.02321 

0.02374 

2.65 

88 
9o 

.72319 

9.72345 

1.30 

.04988 
0.05041 

2.6S 

92 

71094 

1.30 
1.30 

,02427 

2.65 
2.65 

92 

.72370 

1.25 
1.25 

-05095 

2.70 
2.70 

94 
96 
98 

.71120 
•7II45 
.71171 

1.25 
1.30 

.02480 
.02534 
.02587 

2.70 
2.65 

2  6t 

94 
96 
98 

•72395 
.72420 
•72446 

1.25 

1.30 

.05149 
.05202 
.05256 

2.65 

2.70 

100 

9.71197 

o  .  02640 

100 

9.72771 

0.05310 

(219) 


TABLE  XXVI.  —  (Continued) 


Hun- 

e: 

1° 

Hun- 

• 

I" 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

9.72471 

0.05310 

00 

9.73720 

0.08015 

02 

04 

.72496 
.72521 

-25 

-05364 
•05417 

2.65 

02 

04 

•73745 
.73769 

.20 

.08070 
.08124 

2.75 
2.70 

06 
08 

•72547 
.72572 

-30 
•  25 

•05471 
.05525 

2.70 
2.70 

06 
08 

•73794 
•73819 

.25 
•  25 

.08179 
.08233 

2.75 

2.70 

10 

9.72597 

.25 

0.05579 

2.70 

IO 

9-73844 

.25 

0.08288 

2-75 

12 

14 

.72622 
.72647 

.25 
•  25 

.05633 
.05686 

2.70 
2.65 

12 

14 

.73868 
.73893 

.20 
-25 

•08343 
•08397 

2.75 
2.70 

16 

.72672 

•25 

.05740 

2.70 

16 

.73918 

.25 

.08452 

2.75 

18 

.72698 

•  30 

•05794 

2.70 

18 

•73942 

.20 

.08506 

2.70 

20 

9.72723 

0.05848 

20 

9.73967 

0.08561 

22 

.72748 

.05902 

22 

•73992 

.08616 

2.75 

24 

.72773 

•  25 

.05956 

2.70 

24 

.74016 

.20 

.08670 

2.70 

26 

.72798 

•25 

.06010 

2.70 

26 

•74031 

•25 

.08715 

2.75 

28 

.72823 

.06064 

28 

.74065 

.08780 

2-75 

30 

9.72848 

.25 

o.  06118 

2.70 

30 

9.74090 

-25 

0.08835 

2.75 

32 

•72873 

.25 

.06172 

2.70 

32 

•74II5 

.25 

.08889 

2.70 

34 
36 

.72898 
•72923 

•25 

.06226 
.06280 

2.70 

34 
36 

•74139 
.74164 

.25 

.08944 
.08999 

2.75 

38 

.72948 

.25 

•06334 

2.70 

38 

.74188 

.09054 

2-75 

40 

9-72973 

0.06388 

40 

9-74213 

0.09108 

42 
44 

.72999 
•73024 

.25 

.06442 
.06496 

2.70 

42 
44 

•74237 
.74262 

.25 

.09163 
.09218 

2.75 

46 

48 

•73049 
•73074 

.25 
•25 

.06550 
.06604 

2.70 
2.70 

46 
48 

.74286 
•743II 

.20 
•25 

•09273 
.09328 

2-75 
2.75 

So 

9-73099 

.25 

0.06658 

2.70 

50 

9-74335 

0.09383 

2.75 

52 

.73123 

.06712 

2.70 

52 

.74360 

•25 

.09438 

2.75 

54 

.73148 

.06766 

54 

.74384 

•09493 

56 

•73173 

.25 

.06820 

2.70 

56 

.74409 

.25 

-09548 

2.75 

58 

.73198 

•25 

.06874 

2.70 

58 

•74433 

.09602 

2.70 

60 

9  73223 

0.06929 

60 

9.74458 

0.09657 

62 

.73248 

.06983 

62 

.74482 

.09712 

64 
66 
68 

•73273 
.73298 

.73323 

.25 
.25 
.25 

•07037 
.07091 

.07146 

2.70 
2.70 
2.75 

64 
66 

68 

•74507 
-74531 
•74556 

.25 

.20 
•25 

.09767 
.09823 
.09878 

2.75 
2.80 
2-75 

70 

9-73348 

.25 

0.07200 

2.70 

70 

9-74580 

0.09933 

2.75 

72 

•73373 

.25 

•07254 

2.70 

72 

.74604 

.20 

.09988 

2.75 

74 

•73398 

.07308 

74 

.74629 

.10043 

76 

•73422 

.07363 

2.70 

76 

.74653 

.10098 

2-75 

78 

•73447 

.25 

.07417 

2.70 

78 

.74678 

•25 

.  IOI53 

2.75 

80 

9-73472 

0.07471 

80 

9.74702 

0.10208 

82 

•73497 

.07526 

82 

.74726 

.  10263 

84 

•73522 

.25 

.07580 

2.70 

84 

-74751 

-25 

.  I03I9 

2.80 

86 

•73547 

.25 

.07634 

2.70 

86 

•74775 

•  10374 

2.75 

.20 

2-75 

.20 

2.75 

88 

•73571 

.07689 

88 

•74799 

.10429 

90 

9.73596 

.25 

0.07743 

2.70 

9o 

9.74824 

-25 

o  .  10484 

2.75 

92 

.73621 

.25 

.07798 

2-75 

92 

.74848 

.10540 

2.80 

94 

.73646 

.07852 

94 

.74872 

.10595 

96 

.73671 

.25 

.07906 

2.70 

96 

.74896 

.10650 

2.75 

98 

.73695 

.07961 

2.75 

98 

•74921 

-25 

.  10705 

2.75 

2  80 

100 

9-73720 

0.08015 

100 

9-74945 

0.10761 

(220) 


TABLE  XXVI.  —  (Continued) 


Hun- 

64 

° 

Hun- 

6£ 

»° 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

00 

9-74945 

0.10761 

00 

9.76146 

0.13551 

2  8s 

02 

.74969 

.10816 

02 

.76170 

.13608 

04 
06 

•74993 
.75018 

-25 
.20 

.  10871 
.  10927 

2.75 

2.80 

2.75 

04 
06 

•76194 
.76218 

.20 
.15 

.13664 
.13720 

2.80 

2.80 
2.85 

08 

.75042 

.10982 

08 

.76241 

•13777 

zo 

9.75066 

0.11038 

10 

9-76265 

0.13833 

2.80 

12 

.75090 

.25 

.11093 

2.75 

2.80 

12 

.76289 

.20 
.20 

.13890 

2.85 
2.80 

14 
16 
18 

•75II5 
•75139 
.75163 

.20 
.20 

.11149 
.11204 
.11260 

2.75 
2.80 

14 

16 
18 

•76313 
.76336 
.76360 

-15 

.20 

.13946 
.14003 
.14059 

2.85 
2.80 

2  Of 

20 

9-75I87 

0.11315 

2  80 

20 

9.76384 

0.14116 

2  80 

22 

•7521  I 

.11371 

22 

.76408 

.  14172 

24 

26 

•75235 
.75260 

.25 

.11426 
.11482 

2-75 

2.80 

24 
26 

.76431 
.76455 

.15 

.20 

.  14229 
.14285 

2.85 
2.80 
2  8s 

28 
30 
32 

.75284 
9.75308 
•75332 

.20 
.20 
.20 

.11537 
O.H593 
.11649 

2.80 
2.80 

2.75 

28 
30 
32 

.76479 
9.76502 
.76526 

-IS 

.20 
.20 

.14342 
0.14398 
.14455 

2.80 
2.85 
2.85 

34 
36 
38 

•75356 
.75380 
.75404 

.20 
.20 
2O 

.11704 
.11760 
.11816 

2.80 
2.80 

34 
36 
38 

•76550 
.76573 
.76597 

.15 

.20 

.14512 
.14568 
.14625 

2.80 
2.85 

2  8S 

40 

9.75428 

20 

0.11871 

2  80 

40 

9.76620 

0.14682 

2  80 

42 
44 
46 

•75452 
•75476 
•75500 

.20 
.20 
.20 

.11927 
.11983 
.12039 

2.80 
2.80 
2.75 

42 
44 
46 

.76644 
.76668 
.76691 

.20 

.15 

.20 

.14738 
.14795 
.14852 

2.85 
2.85 
2.85 

48 
50 

.75524 
9-75549 

.25 

.12094 
0.12150 

2.80 
2  80 

48 
50 

•76715 
9.76738 

•  IS 

.14909 
0.14966 

2.85 

20n 

52 

•75573 

.20 

.12206 

2.80 

52 

.76762 

.15 

.  15022 

2.85 

54 
56 
58 

•75597 
.75621 
.75645 

.20 
.20 
2O 

.  12262 
.12318 
-  12373 

2.80 
2.75 

2  80 

54 
56 
58 

•76785 
.76809 
-76833 

.20 
.20 

.15079 
.15136 
.15193 

2.85 
2.85 

60 

9.75669 

15 

0.12429 

2  80 

60 

9-76856 

0.15250 

2  8s 

62 

64 
66 

•75692 
•757i6 
•75740 

.20 
.20 
.20 

.  12485 
.  12541 
•12597 

2.80 
2.80 
2.80 

62 
64 
66 

.76880 
.76903 
.76927 

•  15 
.20 

.15 

.15307 
.15364 
.15421 

2.85 
2.85 
2.85 

68 
70 

.75764 
9-75788 

.20 

.12653 

0.12709 

2.80 
2  80 

68 
70 

-76950 
9.76974 

.20 

.  15478 
0.15535 

2.85 
i  Re 

72 

.75812 

.20 

.12765 

2.80 

72 

.76997 

.20 

.15592 

2.85 

2.85 

74 
76 
78 

.75836 
.75860 
-75884 

.20 
.20 
.20 

.  12821 
.12877 
•  12933 

2.80 
2.80 
2  80 

74 
76 
78 

.77021 

.77044 
.77068 

•  IS 

.20 
15 

.15649 
.15706 
.15764 

2.85 
2.90 

2  85 

80 

9.75908 

.20 

0.12989 

2  85 

80 

9.77091 

0.15821 

82 
84 
86 

•75932 
•75956 
.75980 

.20 
.20 
-IS 

.  13046 
.  13102 
.13158 

2.80 
2.80 
2.80 

82 
84 
86 

•77II4 
.77138 
.77161 

.20 

.15 
.20 

.15878 
.15935 
•15992 

2.85 
2.85 
2.85 

88 
90 

92 

.76003 
9.76027 
.76051 

.20 
.20 
.20 

.13214 
0.13270 
.13326 

2.80 
2.80 
2.85 

88 
9o 

92 

•77185 
9.77208 
•77231 

•  IS 
.15 
.20 

.16049 
0.16107 
.16164 

2.90 
2.85 
2.85 

94 
96 
98 

-76075 
.76099 
.76123 

.20 
.20 
.15 

.13383 
•13439 
•  13495 

2.80 
2.80 
2.80 

94 
96 
98 

•77255 
•77278 
•77301 

.15 
•  15 

.  16221 
.16279 
.16336 

2.90 
2.85 

2  8* 

100 

9.76146 

o.  13551 

100 

9  77325 

o  16393 

(221) 


TABLE  XXVI.  —  (Continued) 


Hun- 

| 

i° 

Hun- 

6' 

r° 

1 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff.  1 
.001  1 

00 

9-77325 

0.16393 

00 

9.78481 

0.19293 

oa 
04 

•77348 
•77371 

i.iS 

.  16451 
.  16508 

2.85 

02 
04 

.78504 
-78527 

I.iS 

•19352 
.19410 

2-90  1 

06 

•77395 

i  15 

.16566 

2.90 

2  85 

06 

.78550 

I.IO 

.19469 

2-95  1 
2.95  1 

08 

.77418 

.16623 

08 

.78572 

.  19528 

10 

9-77441 

I.iS 

0.16681 

2.90 

10 

9-78595 

i.iS 

0.19587 

95  1 

xa 

.77465 

.16738 

2.85 

12 

.78618 

i  -15 

.19645 

.90  1 

14 
z6 
18 

.77488 
•77SI  i 
•77534 

I.IS 
I.IS 

.  16796 
.16853 
.16911 

2.85 
2.90 

14 

16 
18 

.78641 
.78664 
.78687 

I.iS 
I.iS 

•  19704 
•19763 
.  19822 

95  1 

.95  1 

20 

9-77558 

0.16969 

2  8? 

20 

9.78710 

0.19881 

2  00  1 

aa 
24 
26 

.77581 
.77604 
.77627 

I.IS 
I.IS 
1.  20 

.17026 
.17084 
.17142 

2.90 
2.90 
2.85 

22 
24 
26 

.78732 
.78755 
.78778 

I.iS 
I.iS 
1.15 

•19939 
.19998 
.20057 

2-95  1 
2-95  1 
2-95  1 

28 
30 
32 

.77651 
9.77674 
.77697 

I.IO 

I.iS 
1.15 

.17199 
0.17257 
.17315 

2.90 
2.90 
2.85 

28 

30 

32 

.78801 
9-78823 
.78846 

I.IO 

i-iS 
I.iS 

.20116 
0.20175 
.20234 

2-95  1 
2-95  1 
2-95  1 

34 
36 
38 

.77720 
•77744 
.77767 

1.20 

1.15 

•17372 
•17430 
.17488 

2.90 
2.90 

34 
36 
38 

.78869 
.78892 
.78915 

I.iS 
I.IS 

.20293 
.20352 
.  20412 

295 

3-00  1 
2  Q5  1 

40 

9-77790 

O.I7S46 

40 

9-78937 

I  15 

0.20471 

2  05  1 

42 
44 

.77813 
.77836 

I.iS 

.17604 
.17662 

2.90 

42 
44 

.78960 
.78983 

I.IS 

.20530 
.20589 

s 

46 

•77859 

1.15 

.17720 

2.9O 

46 

.79005 

I  15 

.20648 

•  yo  i 

48 
50 

.77882 
9.77906 

1.20 

.17778 
0.17836 

2.90 

48 
50 

.79028 
9.7905I 

I.IS 

.20708 
0.20767 

52 

.77929 

I.IS 

.17894 

2  90 

52 

•79073 

I  15 

.20826 

°i 

54 
56 
58 

•77952 
•77975 
.77998 

1  C/l  C/l  t 

•17952 
.  18010 
.18068 

2.90 
2.90 

54 
56 
58 

.79096 
•79II9 
.79141 

i.iS 

I.IO 

i  IS 

.20885 
.20945 
.21004 

300 

3- 

60 

9.78021 

0.18126 

60 

9.79164 

I  IS 

0.21064 

2  95  1 

62 
64 
66 

.78044 
.78067 
.78090 

I.IS 
I.IS 
I.iS 

.18184 
.18242 
.18300 

2.90 
2.90 
2.90 

62 
64 
66 

.79187 
.79209 
.79232 

I.IS 
I.IS 
I.IS 

.21123 
.21183 
.21242 

3-00  1 
2-95  1 
3  oo  1 

68 
70 

72 

.78113 
9.78I36 
.78159 

I.IS 
I.IS 
I.IS 

.18358 
0.18417 
.18475 

2.95 
2.90 
2.90 

68 
70 

72 

.79255 
9.79277 
.79300 

I.IO 

I.iS 

I.IO 

.21302 
0.21361 
.21421 

2-95 
3-00  1 
2-95  1 

74 
76 
78 

.78182 
.78205 
.78228 

I.iS 
I.IS 

.18533 
.18592 
.18650 

2.95 
2.90 

74 
76 
78 

•79322 
•79345 
.79368 

I.iS 
1.15 

I.IO 

.21480 
.21540 
.21600 

3.00  1 
3-00  1 
2-95  1 

80 

9.78251 

I  15 

0.18708 

80 

9-79390 

i.iS 

0.21659 

3.00  1 

82 

.78274 

.18767 

82 

•79413 

.21719 

84 
86 

.78297 
.78320 

I.IS 
I.IS 
1.15 

.18825 
.18883 

2.90 
2.90 
2.95 

84 
86 

•79435 
•79458 

I.iS 

I.IO 

.21779 
.21839 

3-00  1 
2-95  1 

88 

90 

92 

•78343 
9-78366 
.78389 

I.IS 
I.IS 
1.15 

.18942 
0.19000 
.19059 

2.90 
2.95 
2.90 

88 
90 

92 

.79480 
9-79503 
.79525 

I.iS 

I.IO 

1.15 

.21898 
0.21958 
.22018 

3-00  1 
3-00  1 
3-00  1 

94 
96 
98 

.78412 
.78435 
.78458 

i  IS 
I.IS 

.19117 
.19176 
.19234 

2.95 
2.90 
2  95 

94 
96 
98 

.79548 
•79570 
•79593 

I.IO 

I.iS 

I.IO 

.  22078 
.22138 
.  22198 

il 

100 

9  78481 

o  19293 

100 

9.79615 

o  .  22258 

(222) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

68° 

Hun- 

dredths 

69° 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9-796I5 

0.22258 

00 

9-80729 

0.25296 

02 

.79638 

.22318 

02 

.80751 

•25357 

04 

06 

.79660 
.79683 

i.  IS 

.22378 
.22438 

3.00 
3-00 

04 
06 

.80773 
.80795 

I.IO 

•25419 
.25480 

3.10 
3-OS 

08 

•79705 

.22498 

08 

.80817 

•25542 

IO 

9.79728 

i.  IS 

0.22558 

3-00 

IO 

9-80839 

I.IO 

0.25604 

3.10 

12 

.79750 

I.IO 

.22618 

3-00 

12 

.80861 

I.IO 

.25666 

3.10 

I.IO 

3.00 

I.IO 

3.05 

14 

•79772 

.22678 

14 

.80883 

.25727 

16 

•79795 

i.  IS 

.22739 

3-05 

16 

.80905 

.25789 

3.10 

18 

.79817 

.22799 

3-oo 

18 

.80927 

.25851 

3-10 

20 

9.79840 

0.22859 

20 

9.80949 

0.25913 

22 

24 
26 

.79862 
.79884 
•79907 

I.IO 

i.  IS 

.  22920 
.22980 
.23041 

3-00 
3-OS 

22 

24 
26 

.80971 
.80993 
.81015 

I.IO 
I.IO 

-25975 
.26037 
.26099 

3.10 
3-10 

28 

.79929 

.23101 

28 

.81037 

.26161 

30 
32 

9-79952 
•79974 

i.  IS 

I.IO 
I.IO 

0.23161 
.23222 

3-oo 
3-OS 
3  oo 

30 
32 

9-81059 
.81080 

i.  05 

I.IO 

0.26223 
.26285 

3.10 
3.10 
3-io 

34 
36 

.79996 
.80019 

i.  IS 

.23282 
.23343 

3-OS 

34 
36 

.81102 
.81124 

I.IO 

•26347 
.26409 

3.10 

38 

.80041 

I  IO 

.23403 

3-oo 

38 

.81146 

.26471 

3.10 

40 

9.80063 

0.23464 

40 

9.81168 

0.26533 

42 
44 

.80085 
.80108 

i.  IS 

.23524 
.23585 

3-05 

42 
44 

.81190 
.81212 

I.IO 

.26596 
.26658 

3-10 

46 

.80130 

I.IO 

.23646 

3  05 
3.00 

46 

-81234 

I.IO 

.  26720 

3-io 
3.15 

48 
So 

52 

.80152 
9-80175 
.80197 

i.  IS 

I.IO 
I.IO 

.23706 
0.23767 
.23828 

3-05 
3-05 
3-OS 

48 
So 

52 

.81256 
9.81277 
.81299 

1.05 

I.IO 
I.IO 

-26783 
0.26845 
.26907 

3.10 
3.10 
3-iS 

54 
56 
58 

.80219 
.80241 
.80264 

I.IO 

1.  15 

.23889 
•23949 
.24010 

3-00 
3-05 

54 
56 
58 

.81321 
-81343 
.81365 

I.IO 
I.IO 

.26970 
.27032 
-27095 

3-io 
3-15 

60 

9.80286 

I  IO 

0.24071 

60 

9.81387 

0.27157 

62 
64 
66 

.80308 
.80330 
.80352 

I.IO 
I.IO 

1.  15 

.24132 
•24193 
.24254 

3-05 
3-05 
3-05 

62 
64 
66 

.81408 
.81430 
.81452 

I.IO 
I.IO 
I.IO 

.  27220 
.27273 
•27345 

3-  IS 
3-10 
3-iS 

68 
70 

72 

•80375 
9-80397 
80419 

I.IO 
I.IO 
I.IO 

.24315 
0.24376 
•24437 

3-05 
3-05 
3-05 

68 
70 

72 

.81474 
9-81496 
•81517 

I.IO 

1.05 

I.IO 

.27408 
0.27471 
•27533 

3-iS 
3-10 
3-lS 

74 
76 
78 

.80441 
.80463 
.80485 

I.IO 
I.IO 
I  15 

.24498 
•24559 
.24621 

3-05 
3-10 
3  °5 

74 
76 
78 

.81539 
.81561 
-81583 

I.IO 
I.IO 
I  05 

.27596 
•27659 
.27722 

3-IS 
3-iS 

80 

9.80508 

I  IO 

0.24682 

3  05 

80 

9.81604 

i  10 

0.27785 

3  IS 

82 
84 
86 

.80530 
.80552 
.80574 

I.IO 
I.IO 
I.IO 

•24743 
.24804 
.24866 

3-05 
3-io 
3-05 

82 
84 
86 

.81626 
.81648 
.81670 

I.IO 
I.IO 

1.05 

.27848 
.27911 
•27974 

3-15 
3-15 
3-lS 

88 
9o 

92 

.80596 
9.80618 
.80640 

I.IO 
I.IO 
I.IO 

.24927 
0.24988 
.25050 

3-05 
3-10 
3-OS 

88 
9o 
92 

.81691 
9-81713 
•81735 

I.IO 
I.IO 

i-OS 

.28037 
0.28100 
.28163 

3-15 
3-15 
3-15 

94 
96 
98 

.80662 
.80684 
.80707 

I.IO 

I.  IS 

I.  IO 

.25111 
.25173 
.25234 

3-10 
3-05 
3  10 

94 
96 
98 

.81756 
.81778 
.81800 

I.IO 
I.IO 

i  05 

.28226 
.28290 
.28353 

3-20 

3.15 

100 

9.80729 

9.25296 

100 

9.81821 

0.28416 

(223) 


TABLE  XXVI.  —  (Continued) 


Hun- 

7 

D° 

Hun- 

7 

L° 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9.81821 

0.28416 

00 

9-82894 

0.31630 

02 
04 
06 
08 
10 

13 
14 

16 
18 

.81843 
.81865 
.81886 
.81908 
9.81929 
•81951 

•81973 
.81994 
.82016 

.10 

.05 

.10 

•  05 

.10 
.10 

•  05 

.10 

.28479 
.28543 
.28606 

.28670 
0.28733 
.28797 
.28860 
.28924 
.28987 

3-20 

3  15 
3-20 

3-15 
3.20 
3-15 
3.20 
3-15 

02 
04 
06 
08 
10 
12 

14 

16 
18 

.82915 
.82936 
.82958 
.82979 
9.83000 
.83021 
.83042 
.83064 
.83085 

.05 

.10 

•  05 
.05 
.05 
•  05 

.10 

.05 

•31695 
.31760 
.31826 
.31891 
0.31957 
.32022 

.32088 
•32153 
.32219 

3-25 
3-30 
3-25 
3-30 
3.25 
3-30 

3-25 
3.30 

20 

9.82037 

0.29051 

20 

9.83106 

0.32285 

22 
34 
26 

28 
30 
32 

34 
36 
38 

.82058 
.82080 
.82102 
.82124 
9-82145 
.82167 
.82188 
.82210 
.82231 

.10 
.10 

.10 

.05 
.10 
•  05 

.10 

.05 

.29114 
.29178 
.29242 
.29306 
0.29370 
•29434 
.29498 
.29562 
.29626 

3.20 
3-20 
3-20 
3.20 
3.20 
3-20 
3.20 
3-20 

22 

34 
26 

28 
30 
33 

34 
36 
38 

.83127 
.83148 
.83169 

.83191 
9.83212 
•83233 
.83254 
.83275 
.83296 

.05 
.05 
.10 

.05 
.05 
.05 
.05 
•  05 

•32350 
.32416 
.32482 

.32548 
0.32614 
.32680 

•32746 
.32812 
.32878 

3-30 
3.30 
3-30 
3-30 
3-30 
3-30 
3.30 
3-30 

40 

9-82253 

0.29690 

40 

9-83317 

0.32944 

43 
44 
46 

48 
50 

53 

54 
56 
58 

.82274 
.82296 
•82317 
•82339 
9.82360 
.82381 
.82403 
.82424 
.82446 

.10 

•  05 

.10 

•  05 
.05 
.10 

•  05 
.10 

.29754 
.29818 
.29882 
.29946 
0.30010 
•30075 

•30139 
.30203 
.30268 

3-20 
3.20 
3-20 

3-20 

3.25 

3-20 
3-20 

3  25 

42 
44 
46 
48 
50 

53 

54 
56 
58 

.83338 
.83359 
.83381 
.83402 
9-83423 
.83444 

.83465 
.83486 
.83507 

.05 

.10 

.05 
.05 

.05 
•  05 
.05 
•  05 

.33010 
•33076 
•33142 
•33209 
0.33285 
•33341 
•33408 
•33474 
•33541 

3-30 
3-30 
3-35 
3-30 
3-30 
3-35 
3  30 
3-35 

60 

9.82467 

0.30332 

60 

9-83528 

0.33607 

62 
64 
66 

68 
?o 

73 

74 
76 
78 

.82489 
.82510 
.82531 
.82553 
9-82574 
•82595 

.82617 
.82638 
.82660 

.05 
•  05 
.10 

.05 
•  05 

.10 

•  05 

.10 

•30397 
.30461 
.30526 

•30590 
0.30655 
.30720 

•30784 
.30849 
•30914 

3-20 
3-25 

3.20 

3-25 
3-25 
3-20 

3-25 
3-25 

62 
64 
66 

68 
70 

73 

74 
76 
78 

•83549 
•83570 
•83591 
.83612 
9-83633 
.83654 
.83675 
.83696 
.83717 

•  05 
.05 
•  05 
•  05 
.05 
•  05 
•  05 
•  05 

•33674 
•33741 
•33807 

•33874 
0-33941 
.34008 

.34075 
.34142 
•34209 

3-35 
3-30 
3-35 
3-35 
3-35 
3-35 
3-35 
3-35 

80 

9.82681 

0.30979 

80 

9.83738 

0.34276 

82 
84 
86 

88 

90 

93 

94 
96 
98 

.82702 
.82724 
.82745 
.82766 
9.82787 
.82809 
.82830 
.82851 
.82873 

.10 

.05 
.05 
•  05 

.10 

•  05 

.05 

.10 

•31044 
.31109 
•3II74 
.31239 
0.31304 
.31369 
.31434 
•31499 
.31564 

3-25 
3-25 
3-25 
3-25 
3-25 
3-25 
3-25 
3-25 

82 
84 
86 

88 
9o 

93 

94 
96 
98 

.83759 
.83780 
.83800 
.83821 
9.83842 
.83863 
.83884 
-83905 
.83926 

.05 
.00 
.05 
.05 
•  05 
.05 
•  05 
.05 

•34343 
•34410 
•34477 

•34544 
0.34611 
.34679 
.34746 
.34814 
.34881 

3  35 
3  35 
3-35 
3  35 
3-40 
3  35 
3-40 
3-35 

100 

9.82894 

0.31630 

100 

9-83947 

0.34948 

(224) 


TABLE  XXVI.  —  (Continued) 


Hun- 

7 

2° 

Hun- 

73 

dredths 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

dredths 

Vers 

Diff. 
.001 

Exsec 

Diflf. 

.001 

00 

9-83947 

0.34948 

00 

9-84981 

0.38387 

02 
04 
06 
08 
xo 

12 

14 
16 
18 

.83968 
.83988 
.84009 
-84030 
9.84051 
.84072 

.84093 
.84113 
.84134 

.00 

.05 
.05 

.05 
.05 
.05 

.00 

.05 

.35016 
.35084 
.35151 
.35219 
0.35287 
•35354 
•35422 
•35490 
•35558 

3-40 
3-35 
3-40 
3-40 
3-35 
3-40 
3-40 
3-40 

02 
04 
06 
08 
IO 
12 

14 
16 
18 

.85001 
.85021 
.85042 
.85062 
9.85083 
.85104 
.85124 
.85144 
.85165 

.00 
.05 

.00 

.05 
.05 
.00 

.00 

.05 

.38457 
•38527 
.38597 
.38668 
0.38738 
•38809 

•38879 
.38949 
.39020 

3.50 
3-50 
3-55 
3-50 
3-55 
3-50 
3-50 
3  55 

20 

9.84155 

0.35626 

20 

9-85I85 

0.39090 

22 

24 
26 

28 

30 
3* 
34 
36 
38 

.84176 
.84197 
.84217 
.84238 
9  84259 
.84280 

.84300 
.84321 
.84342 

.05 

.00 

.05 
.05 
•  05 
.00 

-05 
.05 

.35694 
.35762 
.35830 

.35899 
0.35967 
.36035 
.36103 
.36172 
.36240 

3-40 
3-40 
3-45 
3-40 
3.40 
3-40 

3-45 
3-40 

22 

24 
26 

28 
30 
32 

34 
36 
38 

.85205 
.85226 
.85246 
.85267 
9.85287 
.85307 
.85328 
•85348 
•85368 

-05 

.00 

.05 

.00 
.00 

•  05 

.00 

.00 

.39161 
.39232 
•39303 
•39373 
0.39444 
•39515 
.39586 
.39667 
•39728 

3-55 
3-55 
3-50 

3-55 
3-55 
3-55 
3  55 
3-55 

•>  fa 

40 

9-84363 

0.36309 

40 

9-85389 

0.39800 

42 
44 
46 

48 
50 
5* 

54 
56 
58 

.84383 
.84404 
.84425 

-84445 
9.84466 
.84487 

.84507 
.84528 
.84549 

.05 
.05 
.00 

.05 
.05 

.00 

.05 
.05 

.36377 
.36446 
.36514 

.36583 
0.36652 
.36721 

.36789 
.36858 
•36927 

3-45 
3-40 
3  45 
3-45 
3-45 
3-40 

3-45 
3-45 

42 
44 
46 

48 
So 

52 

54 
56 
58 

•85409 
.85429 
.85450 
.85470 
9.85490 
.85511 
.85531 
.85551 
.85572 

.00 

.05 
.00 

.00 

.05 

.00 

.00 

.05 

.39871 
•39942 
.40013 
.40085 
0.40156 
.40228 
.40299 
.40371 
•40443 

3-55 
3-55 
3.6o 

3  55 
3-60 
3-55 
3-Co 
3-60 

3rr 

60 

9-84569 

QC 

0.36996 

60 

9.85592 

0.40514 

•>  go 

62 
64 
66 

68 
70 

72 

74 
76 
78 

.84590 
.84611 
.84631 
.84652 
9.84672 
•84693 
.84714 
•84734 
.84755 

.05 
.00 
•  05 
.00 
.05 
•  05 
.00 
.05 

•37065 
.37134 
.37204 

•37273 
0.37342 
•374II 
.37481 
•37550 
.37619 

3-45 
3-50 
3-45 
3-45 
3-45 
3-50 

3-45 
3-45 

62 
64 
66 

68 
70 

72 

74 
76 
78 

.85612 
.85632 
.85653 
.85673 
9-85693 
.85713 
.85733 
.85754 
.85774 

.00 

.05 

.00 

.00 

.00 
.00 

.05 

.00 

.40586 
.40658 
.40730 
.40802 
0.40874 
.40946 
.41018 
.41090 
.41163 

3.60 
3.60 
3.60 
3.60 
3.60 
3.60 
3.60 
3.65 
-j  60 

80 

9.84775 

0.37689 

80 

9-85794 

0.41235 

•»  go 

82 
84 
86 

88 
90 
92 

94 
96 
98 

.84796 
.84816 
.84837 

.84857 
9.84878 
.84899 

.84919 
.84940 
.84960 

.00 
•  05 
.00 

.05 
.05 
.00 

.05 
.00 

•37759 
.37828 
.37898 
•37968 
0.38037 
•38107 

.38177 
•38247 
.38317 

3-45 
3-50 
3-50 

3-45 
3-50 
3-50 
3-50 
3-50 

82 
84 
86 
88 

90 

92 

94 
96 
98 

.85814 
.85834 
•85855 
.85875 
9.85895 
.85915 
.85935 
.85955 
.85975 

.00 
.05 

.00 
.00 

.00 
.00 
.00 

.00 

.41307 
.41380 
.41452 

•41525 
0.41598 
.41670 

.41743 
.41816 
.41889 

3-65 
3.60 
3-65 

3-65 
3.60 
3.6s 
3-65 
3-65 

->    fir 

100 

9-84981 

0.38387 

100 

9.85996 

0.41962 

(225) 


TABLE  XXVI.  —  (Continued} 


Hun- 

74° 

Hun- 

75° 

dredths 

Vers 

Diff. 

Exsec 

Diff. 

dredths 

Vers 

Diff. 

Exsec 

Diff. 

.001 

.001 

00 

9.85996 

0.41962 

T.    6* 

00 

9-86992 

0.45693 

7    80 

02 

.86016 

•42035 

02 

.87012 

.45769 

04 

.86036 

I.OO 

.42108 

3-65 

04 

.87032 

I.OO 

.45846 

3-85 

06 

.86056 

.42181 

3.65 

06 

.87052 

•45922 

3-80 

08 

.86076 

' 

•42254 

3-  5 

08 

.87071 

•45999 

3-°5 

10 

9.86096 

I.OO 

0.42328 

3-70 

10 

9-87091 

I.OO 

0.46075 

3-80 

12 

.86116 

I.OO 

.42401 

3-65 
3.65 

12 

.87111 

I.OO 

.46152 

3.8o 

14 

.86136 

.42474 

14 

.87131 

.  46228 

16 

.86156 

I.OO 

•42548 

3-70 

16 

.87150 

•  95 

.46306 

3-90 

18 

.86176 

I.OO 

.42621 

3.65 

18 

.87170 

I.OO 

•46383 

3-85 

30c 

20 

9.86196 

0.42695 

7  6=; 

20 

9-87190 

0.46460 

22 
24 
26 

.86216 
.86236 
.86257 

I.OO 

1.05 

.42768 
.42842 
.42916 

3-70 
3-70 

22 

24 
26 

.87209 
.87229 
.87249 

I.OO 
I.OO 

.46537 
.46614 
.46691 

3.85 

3-85 

28 
30 
32 

.86277 
9.86297 
.86317 

I.OO 
I.OO 
I.OO 

.42990 
0.43064 
.43138 

3-70 
3-70 
3-70 

28 
30 
32 

.87268 
9.87288 
•87308 

I.OO 
I.OO 

•95 

.46769 
0.46846 
.46923 

3-85 
3-85 
3.90 

34 

.86337 

.43212 

34 

•87327 

.47001 

36 
38 

.86357 
.86377 

I.OO 

.43286 
.4336o 

3-70 
3-70 

36 
38 

•87347 
•87367 

I.OO 

.47079 
.47156 

3-9° 
3-85 

-1    QQ 

40 

9-86397 

0.43434 

40 

9.87386 

0.47234 

42 
44 
46 

.86417 
.86436 
.86456 

•  95 

I.OO 

•43509 
.43583 
.43657 

3-70 
3-70 

42 

44 
46 

.87406 
•87425 
.87445 

•  95 

I.OO 

•47312 
•47390 
.47468 

3-90 
3-90 

48 

.86476 

' 

•43732 

48 

•87465 

' 

.47546 

So 
52 

9.86496 
.86516 

I.OO 
I.OO 

0.43806 
.43881 

3-70 
3-75 

50 

52 

9.87484 
•87504 

•95 

I.OO 

0.47624 
.47702 

3.90 
3-90 

•}     QC 

54 
56 
58 

.86536 
.86556 
.86576 

I.OO 
I.OO 

•43956 

•44030 
.44105 

3-70 
3-75 

54 
56 
58 

.87523 
•87543 
.87562 

I.OO 

•  95 

.47781 
.47859 
•47938 

3-90 
3-95 

7  QO 

60 

9.86596 

0.44180 

60 

9-87582 

Qf 

0.48016 

3  95 

62 

.86616 

.44255 

62 

.87601 

.48095 

64 
66 

.86636 
.86656 

I.OO 
I.OO 

95 

•44330 
.44405 

3-75 
3-75 
3  80 

64 
66 

.87621 
.87641 

I.OO 
I.OO 

•  95 

.48173 
.48252 

3-9° 
3-95 
3-95 

68 

.86675 

.44481 

68 

.87660 

•48331 

70 
72 

9-86695 
.86715 

I.OO 
I.OO 
I.OO 

0.44556 
.44631 

3-75 
3-75 
3-75 

70 

72 

9.87680 
.87699 

•  95 

I.OO 

0.48410 
.48489 

3-95 
3-95 
3-95 

74 
76 

.86735 
.86755 

I.OO 

.44706 
.44782 

3-80 

74 
76 

.87719 
.87738 

•95 

.48568 
.48647 

3-95 

78 

.86775 

.44857 

3-75 

78 

•87758 

.48727 

3  95 

80 

9.86795 

0-44933 

7   8O 

80 

9-87777 

0.48806 

3  95 

82 
84 
86 

.86814 
.86834 
.86854 

I.OO 
I.OO 
I.OO 

.45009 
•45084 
.45160 

3-75 
3-80 
3.8o 

82 
84 
86 

.87796 
.87716 
.87835 

I.OO 

•  95 

I.OO 

.48885 
•48965 
.49044 

4.00 
3-95 
4.00 

88 
90 
92 

.86874 
9.86894 
.86913 

I.OO 

•95 

.45236 
0.45312 
•45388 

3-80 
3-80 
3  80 

88 
90 
92 

.87855 
9.87874 
.87894 

•  95 

I.OO 

•  95 

.49124 
0.49204 
.49284 

4.00 
4.00 
4.00 

94 
96 
98 

.86933 
.86953 
.86973 

I.OO 
I.OO 

.45464 
•45540 
.45617 

3.8o 
3-85 

380 

94 
96 
98 

.87913 
.87933 
.87952 

I.OO 

•95 

.49364 
.49444 
.49525 

4.00 
4-05 
3-95 

100 

9.86992 

0.45693 

100 

9.87971 

0.49604 

(226) 


TABLE  XXVI.  —  (Continued) 


Hun- 
dredths 

76° 

Hun- 
dredths 

77° 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

02 

04 

06 
08 

10 
12 

14 
16 
18 
20 
22 
24 
26 

28 
30 
32 

34 
36 
38 
40 
42 
44 
46 
48 
50 
52 
54 
56 
58 
60 
62 
64 
66 

68 
70 

72 

74 
76 
78 
80 
82 
84 
86 

88 
90 
92 
94 
96 
98 
100 

9-87971 

1.  00 

•  95 

1.  00 

•95 
•95 

I.OO 

•95 
-95 

I.OO 

•95 
•95 

I.OO 

•  95 
•95 

I.OO 

•95 
•95 

I.OO 

•95 
•95 
•95 

I.OO 

•  95 
•95 
-95 

I.OO 

•95 
•95 
•95 
•  95 

I.OO 

•  95 
•  95 
•95 
•  95 
•  95 

I.OO 

•  95 
•  95 
•95 
•95 
•  95 
•  95 
•95 

I.OO 

•  95 
•95 
•95 
•  95 
•95 

0.49604 

4.00 
4.00 
4-05 
4.00 

4-05 
4-05 
4.00 

4-05 
4-05 
4-05 
4-05 

4-05 
4.10 
4-05 
4.10 
4-05 
4.10 

4-05 
4.10 
4.10 
4.10 
4-10 
4.10 
4.10 

4-iS 
4.10 
4-15 
4.10 
4.15 
4-15 
4-15 
4.15 
4.15 
4-15 
4-iS 
4-15 
4.20 

4-15 
4.20 
4.20 
4.20 

4-15 
4.20 
4-25 
4.20 
4.20 
4.20 

4-25 
4.20 
4-25 

00 

02 
04 
06 
08 
10 
12 

14 

16 
18 
20 

22 
24 
26 
28 
30 
32 

34 
36 
38 
40 

42 
44 
46 

48 
So 
52 

54 
56 
58 
60 
62 
64 
66 
68 
70 
72 

74 
76 
78 
80 
82 
84 
86 

88 
90 
92 

94 
96 
98 
100 

9-88933 

•95 
•95 
•95 
•95 
•  95 
•95 
-95 
-95 
•  95 
•95 
•95 
•  95 
•  95 
•95 
•  95 
•  95 
•95 
•95 
•95 
•95 
•95 
•95 
•90 
•95 
•95 
•95 
•95 
•95 
•95 
•95 
•90 
•  95 
•95 
•  95 
•  95 
•  95 
.90 

•95 
•95 
•  95 
•95 
.90 
•  95 
•95 

•  95 
.90 
•  95 
•95 
•95 
.90 

0.53724 

4-25 
4-25 
4-25 
4-25 
4-25 
4-25 
4.30 
4-25 
4-30 
4-  2S 
4-30 
4-30 
4-30 
4-30 
4-30 
4-30 
4-35 
4-30 
4-35 
4-35 
4-30 
4-35 
4-35 
4-35 
4.40 
4-35 
4-35 
4.40 
4.40 
4-35 
4.40 

4-40 
4.40 
4.40 

4-45 
4-40 
4-45 
4-40 
4-45 
4-45 
4-45 
4-45 
4-45 
4-45 
4-50 
4-45 
4-50 

4.50 
4-45 
4-50 

.87991 
.88010 
.88030 
.88049 
9.88068 
.88088 
.88107 
.88126 
.88146 

.49684 
.49764 
.49845 

.49925 

0.50006 
.50087 

.50167 
.  50248 
.50329 

.88952 
.88971 
.88990 
.89009 
9.89028 
.89047 
.89066 
.89085 
.89104 

•53809 
.53894 
•53979 
.54064 
0.54149 
•54234 
•54320 
.54405 
•54491 

9.88165 

0.50410 

9-89123 

0.54576 

.88184 
.88204 
.88223 
.88242 
9.88262 
.88281 
.88300 
.88320 
•88339 

•50491 
.50572 
.50654 

.50735 
0.50817 
.50898 
.50980 
.51061 
•5II43 

.89142 
.89161 
.89180 
.89199 
9.89218 
.89237 
.89256 
.89275 
.89294 

.54662 
.54748 
.54834 
•54920 
0.55006 
.55092 

•55179 
•55265 
•55352 

9.88358 

0.51225 

9.89313 

0.55439 

.88377 
.88397 
.88416 

-88435 
9.88454 
.88474 

.88493 
.88512 
.88531 

•51307 
.51389 
.51471 

.51553 
0.51636 
•51718 
.51801 
.51883 
.51966 

•89332 
.89351 
•89369 
.89388 
9.89407 
.89426 

•89445 
.89464 
-89483 

•55525 
•556i2 
•55699 
•55786 
0.55874 
.55961 
.56048 
.56136 
.56224 

9-88550 

0.52049 

9.89502 

0.56311 

.88570 
.88589 
.88608 

.88627 
9.88646 
.88665 
.88685 
.88704 
.88723 

.52132 
.52215 
.52298 

.52381 
0.52464 
•52547 
.52631 
.52714 
.52798 

.89520 
•89539 
.89558 

•89577 
9.89596 
.89615 

.89633 
.89652 
.89671 

.56399 
.56487 
.56575 
.56663 
0.56752 
.56840 

.56929 
•57017 
.57io6 

9.88742 

0.52882 

9.89690 

0.57195 

.88761 
.88780 
.88799 
.88818 
9.88838 
.88857 
.88876 
.88895 
.88914 

.52966 
•53049 
.53133 
•53218 
0.53302 
-53386 
•53470 
•53555 
.53639 

.89709 
.89727 
•89746 

.89765 
9.89784 
.89802 

.89821 
.89840 
.89859 

.57284 
•57373 
.57462 

•57551 
0.57641 
•57730 
.57820 
•57910 
•57999 

9-88933 

0.53724 

9.89877 

o  .  58089 

(227) 


TABLE   XXVI.  —  (Continued') 


Hun- 
dredths 

78° 

Hun- 

dredths 

79° 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

02 

04 
06 
08 

10 
12 

14 

16 
18 
20 

22 

24 
26 
28 
30 
32 

34 
36 
38 
40 
42 
44 
46 
48 
50 
5* 

54 
56 
58 
60 
62 
64 
66 

68 
70 
72 

74 
76 
78 
80 
82 
84 
86 

88 
90 

92 

94 
96 
98 
100 

9.89877 

•  95 
•95 
.90 
•  95 
•  95 
•  95 
.90 

•  95 
•  95 
•  90 
•95 

•95 
.90 
•  95 
.90 
•  95 
•95 
.90 
•95 
•90 
•  95 
•  95 
•90 
.90 

•95 
•  95 

.90 

•  95 
•  90 
•  95 
•  95 
•90 
•  95 
.90 

•  95 

.90 
.90 

•95 
•90 
•  95 
•  90 
•  95 
•  90 
•95 
.90 
.90 
•95 
.90 
•  95 
•  90 

0.58089 

4-55 
4-50 
4-50 
4-55 
4-50 
4-55 
4-55 
4-55 
4-55 
4-55 
4-55 

4-55 
4.60 
4.60 

4-55 
4.60 
4.60 
4.60 
4-65 
4.60 

4-65 
4.60 
4-65 

4.60 

4.70 
4-65 
4-65 

4-70 
4.65 
4-70 

4-65 
4.70 
4.70 
4-75 
4-70 
4.70 
4-75 
4-75 
4-70 
4-75 
4-75 
4.80 
4-75 
4-75 
4-80 
4.80 
4.80 
4.80 
4.80 
4.80 

00 

02 
04 
06 

08 
10 

12 

14 

16 
18 
20 

22 
24 
26 

28 
30 
32 

34 
36 
38 
40 

42 
44 
46 
48 
50 
52 

54 
56 
58 
60 
62 
64 
66 

68 
70 

72 

74 
76 
78 
80 
82 
84 
86 

88 
90 
92 

94 
96 
98 

9-90805 

•90 
•95 
•  90 
•  95 
.90 
.90 
•  95 
•  90 
•  90 
•95 
•90 
•  90 
•95 
.90 

•90 
•  95 
.90 

•  90 
•90 
•95 
•  90 
.90 
.90 
•95 
.90 
.90 
.90 
.90 
•95 
.90 

.90 
.90 
•90 
•  95 
.90 
•  90 
•90 
.90 
.90 
•  95 
.90 
.90 
•  90 
.90 

•90 
•90 
.90 

•  90 
.90 
.90 

0.62745 

4.85 

4.80 
4.80 
4.80 

4.85 
4.85 
4.85 
4.90 

4.85 
4.90 
4.90 
4-90 
4-90 
4.90 

4-95 
4.90 
4-95 
4-95 
4-95 
4-95 
5.00 

5-05 
S-oo 
5.00 
S.oo 
S.oo 
S.oo 
5.00 
5-05 
5-05 
S.oo 

5-05 
5.05 
5-05 
5-05 
5.10 
5-10 
S.io 
5.10 
S.io 
5-15 
S.io 
5-iS 
5-iS 
S.iS 
5.20 
5-iS 
5.20 

5-20 

5.15 

.89896 
.89915 
.89933 
.89952 
9.89971 
.89990 
.90008 
.90027 
.90046 

.58180 
.58270 
•58360 

.58451 
0.58541 
.58632 

.58723 
.58814 
.58905 

.90823 
.90842 
.90860 

.90879 
9.90897 
.90915 

.90934 
.90952 
.90970 

.62842 
.62938 
.63036 
.63132 
0.63229 
.63326 

.63423 
.63521 
.63618 

9.90064 

0.58996 

9.90989 

0.63716 

.90083 
.  90102 
.90120 

-90I39 
9.90157 
.90176 

.90195 
.90213 
.90232 

.59087 
.59178 
.59270 
.59362 
0-59453 
•59545 
.59637 
.59729 
.59822 

.91007 
.91025 
.91044 
.91062 
9.91080 
.91099 
.91117 
.9"35 
•9II53 

.63814 
.63912 
.64010 

.64108 
0.64207 
•64305 
.64404 
.64503 
.  64602 

9.90250 

0.59914 

9.91172 

o  .  64701 

.90269 
.90288 
.90306 
.90324 
9.90343 
.90362 

.90380 
•90399 
.90417 

.60007 
.60099 
.60192 
.60284 
0.60378 
.60471 
.60564 
.60658 
.60751 

.91190 
.91218 
.91226 

.91245 
9.91263 
.91281 

.91299 
.91317 
.91336 

.64801 
.64900 
.65000 
.65100 
0.65200 
.65300 
.65400 
.65500 
.65601 

9-90436 

0.60845 

9-91354 

0.65702 

•90455 
.90473 
.90492 

.90510 
9.90529 
.90547 
•90565 
.90584 
.90602 

.60938 
.61032 
.61126 
.61221 
0.61315 
.61409 
.61504 
.61599 
.61693 

.91372 
.91390 
.91408 

.91427 
9.9I445 
•91463 

.91481 
•91499 
.91517 

.65802 
.65903 
.66005 
.66106 
0.66207 
.66309 
.66411 
.66513 
.66615 

9  .  90621 

0.61788 

9.9I536 

0.66717 

.90639 
.90658 
.90676 

•90695 
9.90713 
•90731 
•90750 
.90768 
.90787 

.61883 
.61979 
.62074 
.62169 
o  .  62265 
.  62361 

.62457 
.62543 
.62649 

.91554 
.91572 
.91590 
.91608 
9.91626 
.91644 
.91662 
.91680 
.91698 

.66820 
.66922 
.67025 
.67128 
0.67231 
.67335 
-67438 
.67542 
.67646 

9-90805 

0.62745 

100 

9.91716 

0.67749 

(228) 


TABLE  XXVI.  -  (Continued) 


Hun- 

dredths 

80° 

Hun- 

dredths 

81° 

Vers 

Diff. 

.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9.91716 

0.67749 

00 

9.92612 

QO 

0.73179 

5  65 

02 

04 
06 

08 

IO 
12 

14 
16 
18 

•9I73S 
•9!753 
.91771 
.91789 
9.91807 
.91825 

.91843 
.91861 
.91879 

•95 
.90 
.90 
.90 
.90 
.90 
.90 
.90 
.90 

.67854 
.67958 
.68062 

.68167 
0.68272 
.68377 
.68482 
.68587 
.68693 

5.20 

5-20 

5.25 
5.25 
5.25 
5.25 
5.25 
5.30 

02 
04 
06 
08 

10 
12 

14 

16 
18 

.92630 
.92647 
.92665 

.92683 
9.92701 
.92718 
.92736 
.92754 
.92771 

.85 

.90 
.90 

.90 
.85 
.90 

.90 
.85 

.73292 
.73406 
•73520 

.73634 
0.73749 
.73863 
•73978 
.74093 
.74208 

5-70 
5-70 
5-70 
5-75 
5-70 
5-75 
5-75 
5-75 

er  go 

20 

9.91897 

•9° 

0.68799 

20 

9.92789 

0.74324 

5  80 

22 
24 

26 

.91915 
.91933 
.91951 

•9° 
.90 
.90 
9° 

.68904 
.69010 
.69117 

5.30 

5-35 
5-30 

22 

24 
26 

.92807 
.92824 
.92842 

.85 
•  90 
•9° 

•74440 
.74556 
.74671 

5-80 

5-85 
5-85 

28 
30 
32 

.91969 
9.91987 
.92005 

.90 
.90 
90 

.69223 
0.69330 
•69436 

5-35 
5-30 
5-35 

28 
30 
32 

.92860 
9.92877 
.92895 

.85 
.90 
-90 

.74788 
0.74905 
.75022 

5-85 
5-85 
5-85 

34 
36 
38 

.92023 

.92041 
.92059 

.90 
.90 

.69543 
.69650 
.69758 

5-35 
5-40 

34 
36 
38 

.92913 
.92930 
.92948 

-85 

•  90 

QO 

•75139 
.75256 
•75373 

5-85 
5-85 
5  9° 

40 

9.92077 

0.69865 

40 

9-92966 

Qe 

0.75491 

42 
44 
46 
48 
SO 

52 

.92095 
.92111 
.92130 

.92148 
9.92166 
.92184 

•  9° 
.90 
•  95 
•  90 
.90 
.90 
90 

•69973 
.70080 
.70189 
.70297 
0.70405 
.70514 

5-35 
5-45 
5-40 
5-40 
5-45 
5  45 

42 
44 
46 

48 
50 
52 

.92983 
.93001 
.93018 
.93036 
9-93054 
.93071 

.90 

.85 
•  90 
.90 
.85 
•9° 

.75609 
.75727 
.75846 

.75965 
0.76083 
.76203 

5.90 
5.95 
5.95 
5.90 

6.00 
5-95 

54 
56 
58 

.  92202 
.92220 
.92238 

.90 
.90 

.70623 

.70732 
.70841 

5-45 
5-45 

54 
56 
58 

.93089 
.93106 
.93124 

.85 
•  90 

.76322 
.76442 
.76561 

6.00 
5-95 
6  05 

60 

9.92256 

.90 

0.70950 

60 

9.93142 

g^ 

0.76682 

6  oo 

62 
64 
66 

.92274 
.92291 
.92309 

.85 
.90 

QO 

.71060 
.71169 
.71279 

5-45 
5-50 
5-5O 

62 
64 
66 

•93159 
.93176 
.93194 

.85 
•  90 
.90 

.76802 
.76922 
•77043 

6.00 
6.05 
6.10 

68 
70 

.92327 
9-92345 

.90 

•71389 

0.71500 

5-55 

68 
70 

.93212 
9.93229 

.85 

.77165 
0.77286 

6.05 

72 

.92363 

.90 

•  9° 

.71610 

5-5O 
5-55 

72 

•93247 

.90 
.85 

.77407 

6.10 

74 
76 

.92381 
.92398 

•  85 

.71721 
.71832 

5-55 

74 
76 

.93264 
•93282 

.90 

.77529 
.77651 

6.10 

78 

.92416 

.90 

.71943 

5-55 

78 

•93299 

•  o5 

•77774 

6  10 

80 

9.92434 

•9° 

0.72054 

<;  60 

80 

9.93317 

gc 

0.77896 

6  15 

82 
84 
86 

.92452 
.92470 
.92487 

.90 
.85 
.90 

.72166 
.72278 
.72389 

5.6o 
5-55 
5.65 

82 
84 
86 

•93334 
•93352 
.93369 

.90 

.85 

.90 

.78019 
.78142 
.78265 

6.15 
6.15 

6.20 

88 
90 
92 

.92505 
9.92523 
.92541 

•  90 
.90 
.90 

.72502 
0.72614 
.72726 

5.60 
S.6o 
5.65 

88 
90 
92 

.93387 
9-93404 
•93422 

.85 
.90 
•  85 

.78389 
0.78513 
.78637 

6.20 
6.20 
6.20 

94 
96 
98 

.92559 
.92576 
.92594 

.85 
.90 

.72839 
.72952 
.73065 

5-65 
5-65 

94 
96 
98 

•93439 
•93457 
•93474 

•  90 
.85 

.78761 
.78886 
.79011 

6.25 
6.25 
6  25 

100 

9.92612 

0.73179 

100 

9-93492 

0.79136 

(229) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

82° 

Hun- 

dredths 

83° 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

Yers 

Diff. 
.001 

Exsec 

Diff. 

.001 

00 

9-93492 

Or 

0.79136 

69C 

00 

9-94356 

0.85766 

02 

04 

.93509 
.93526 

•85 

.79261 
.79387 

6.30 

02 
04 

-94373 
-94390 

.85 

.85907 
.86048 

7.05 
7-05 

06 

•93544 

•  90 
.85 

•79513 

6  35 

06 

•94407 

•  85 
85 

.86190 

7.10 
7  10 

08 

•93561 

.79640 

08 

.94424 

.86332 

IO 
12 

9-93579 
•93596 

.90 
.85 

0.79766 
.79893 

6.30 
6.35 
6  •« 

IO 
12 

9-94442 
•94459 

.90 
.85 

0- 

0.86474 
.86616 

7.10 
7.10 

14 

•93614 

.80020 

14 

.94476 

.86759 

16 

.93631 

•  °5 

.80147 

•  35 

16 

•94493 

.85 

.86903 

18 

.93648 

•  85 

.80275 

18 

•94510 

•  85 

Of 

.87046 

7-15 

20 

9.93666 

0.80403 

20 

9-94527 

Qp 

0.87190 

22 
24 
26 

.93683 
•93700 
•93718 

-85 
.90 
•  85 

.80531 
.80659 
.80788 

6.40 
6.45 
6.45 

22 
24 
26 

•94544 
.94561 
•94578 

.85 
-85 
•  85 

.87335 
.87470 
.87625 

7-25 
7-25 
7.25 

28 
30 
32 

•93735 
9-93752 
•93770 

-85 

.90 
.85 

.80917 
0.81046 
.81176 

6.45 
6.50 
6.50 

28 

30 

32 

•94595 
9.94612 
.94629 

.85 
.85 
•  85 

.87770 
0.87916 
.88062 

7-30 
7-30 
7-35 

34 
36 
38 

.93787 
•93804 
.93822 

.85 

.90 

fir 

.81306 
.81436 
.81567 

6.50 
6.55 

34 
36 
38 

.94646 
.94663 
.94680 

.85 
.85 

g- 

.88209 
.88356 
.88504 

7-35 

7.40 

40 

9.93839 

0- 

0.81697 

6  60 

40 

9-94697 

8? 

0.88651 

42 

.93856 

.81829 

42 

•94714 

.88800 

44 
46 

.93874 
.93891 

.90 

.85 
•  85 

.81960 
.82092 

•  55 
6.60 
6.60 

44 
46 

•94731 
•94748 

•85 

.85 
85 

.88948 
.89097 

7-4O 
7-45 

7.50 

48 
50 
52 

.93908 
9-93926 
•93943 

.90 
.85 
.85 

.82224 
0.82356 
.82488 

6.60 
6.60 
6.65 

48 
50 

52 

.94765 
9-94782 
•94799 

.85 
.85 
.85 

.89247 
0.89397 
•89547 

7-50 
7-50 
7.50 

54 
56 
58 

.9396o 
•93977 
•93995 

.85 
.90 

c- 

.82621 
.82755 
.82888 

6.70 
6.65 

54 
56 
58 

.94816 
.94833 
.94850 

.85 
.85 

0- 

.89697 
.89848 
.90000 

7-55 

7.60 

7  60 

60 

9.94012 

Or 

0.83022 

60 

9.94867 

Of 

0.90152 

62 
64 
66 

.94029 
.94047 
.94064 

.90 

.85 
85 

.83156 
.83290 
.83425 

6.70 
6-75 
6.75 

62 
64 
66 

.94884 
.94901 
.94918 

.85 
.85 
85 

.90304 
.90457 
.90610 

7-65 
7-65 
7.7O 

68 
70 

72 

.94081 
9.94098 
•94II5 

.85 
.85 
•90 

.83560 
0.83696 
.83831 

6.80 
6.85 
6.85 

68 
70 

72 

•94935 
9-94952 
.94969 

.85 
.85 
.85 

.90764 
0.90918 
.91072 

7.70 
7.70 

7-75 

74 
76 
78 

.94133 
•94150 
.94167 

.85 
.85 

.83968 
.84104 
.84241 

6.80 
6.85 
6  85 

74 
76 
78 

.94986 
-95003 
.95020 

.85 
.85 

.91227 
.91383 
.91538 

7.80 
7-75 
7  80 

80 

9.94184 

0- 

0.84378 

6  85 

80 

9-95037 

'  S 

0.91694 

7  8? 

82 
84 
86 

.94201 
.94219 
.94236 

.90 

-85 
.85 

.84515 
.84653 
.84791 

6.90 
6.90 
6.90 

82 
84 
86 

.95053 
.95070 
.95087 

.85 
.85 
.85 

.91851 
.92008 
.92166 

7-85 
7-90 
7.90 

88 
90 

92 

.94253 
9.94270 
.94287 

.85 
-85 
.85 

.84929 
0.85068 
.85207 

6.95 
6.95 
6.95 

88 
90 

92 

•95104 
9-95I2I 
.95138 

.85 
.85 

.92324 
0.92482 
.92641 

7-90 
7-95 
8.00 

94 

.94304 

.85346 

94 

.95155 

.92801 

96 

•94322 

•  90 

.85486 

7.00 

96 

.95171 

.92961 

98 

•94339 

.85 

g- 

.85626 

7.00 

98 

.95188 

•  85 

gr 

.93121 

8  05 

100 

9-94356 

0.85766 

100 

9-95205 

0.93282 

(230) 


TABLE  XXVI.  —  (Continued} 


Hun- 
dredths 

84° 

Hun- 
dredths 

85° 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

00 

9-95205 

Oe 

0.93282 

8ne 

00 

9.9604P 

go 

1.  02010 

02 
04 
06 

.95222 
.95239 
.95256 

.85 
.85 

.80 

•93443 
.93605 
.93767 

8.10 
8.10 
8.15 

02 
04 
06 

.96056 
-96073 
.96089 

.85 
.80 
.85 

.02200 
.02391 
.02583 

9-55 
9.60 
9.60 

08 

10 
12 

.95272 
9.95289 
.95306 

.85 
.85 

Oe 

-93930 
0.94093 
•94257 

8.15 
8.  20 

08 

10 
12 

.96106 
9.96122 
.96139 

.80 

.85 
go 

.02775 
1.02968 
.03162 

9-65 
9.70 

14 

16 
18 

.95323 
•95340 
.95356 

.85 

.80 

Or 

.94421 
•94586 
•94751 

8.25 
8.25 

8    -jO 

14 
16 
18 

.96155 
.96172 
.96188 

.85 

.80 

.03356 
.03551 
.03747 

9-75 
9.80 

90- 

20 

9-95373 

gr 

0.94917 

20 

9  96205 

go 

1.03944 

22 

-95390 

.95183 

22 

.96221 

.04141 

24 
26 

•95407 
.95424 

.85 

•  85 

.80 

.95250 
•95417 

8.35 
8.35 
8.40 

24 
26 

.96238 
.96254 

.85 
.80 
85 

.04339 
.04538 

9.90 
9-95 

10  OO 

28 

•95440 

.95585 

28 

.96271 

.04738 

30 
32 

9-95457 
•95474 

•  8S 

•  85 
•  85 

0.95754 
.95922 

8.45 
8.40 
8.50 

30 
32 

9.96287 
.96304 

.80 
.85 
.80 

1.04938 
.05140 

10.  OO 
10.10 
10.10 

34 
36 
38 

•95491 
.95507 
.95524 

.80 
•  85 

X- 

.96092 
.96262 
•96432 

8.50 
8.50 

See; 

34 
36 
38 

.96320 
.96337 
.96353 

.85 
.80 

.05342 

.05544 
.05748 

10.10 
10.20 

40 

9-95541 

go 

0.96603 

8  60 

40 

9-96369 

Of 

1.05953 

42 
44 
46 

•95557 
•95574 
•95591 

.85 
.85 
•  85 

.96775 
.96947 
.97120 

8.60 
8.65 

8.65 

42 
44 
46 

.96386 
.96402 
.96419 

.80 

.85 
.80 

.06158 
.06364 
.06571 

10.30 
10.35 
10.40 

4* 

.95608 

.97293 

48 

.96435 

.06779 

50 
52 

9.95624 
.95641 

•  85 
.85 

0.97467 
.97641 

8.70 
8.75 

50 
52 

9.9645I 
.96468 

.85 
.80 

1.06987 
.07197 

10.50 
10.50 

54 
56 
58 

.95658 
.95674 
.95691 

.80 

.85 

«- 

.97816 
•97992 
.98168 

8.80 
8.80 
8  85 

54 
56 
58 

.96484 
.96501 
.96517 

.85 
.80 

.07407 
.07618 
.07830 

10.55 
10.  60 

rn  fie 

60 

9.95708 

go 

0.98345 

8  81 

60 

9.96533 

0- 

1.08043 

62 
64 
66 
68 
70 

72 

•95724 
•95741 
•95758 

•95774 
9-95791 
.95807 

.85 
.85 
.80 

.85 
.80 
.85 

.98522 
.98700 
.98879 
.99058 
0.99237 
.99418 

8.90 
8-95 
8.95 
8-95 
9-05 
9-05 

62 
64 
66 

68 
70 

72 

.96550 
.96566 
.96582 

.96599 
9-96615 
.96632 

.80 

.80 
.85 
.80 
.85 
.80 

.08257 
.08472 
.08687 
.08904 
1.09121 
.09340 

10.75 

10.75 
10.85 

10.85 
10.95 
10.95 

74 
76 
78 
80 
82 
84 
86 

88 

.95824 
.95841 
.95857 

.85 
.80 
.85 
.85 
.80 
•  85 
.80 

•99599 
.99780 
.99963 

9-05 
9-iS 
9-iS 
9-15 
9.20 
9-25 
9-25 

74 
76 
78 
80 
82 
84 
86 

88 

.96648 
.96664 
.96680 

.80 
.80 
.85 
.80 
.80 
.85 
.80 

.09559 
.09779 

.IOCOO 

11.00 

11.05 
ii.  15 
ii.  IS 

II.  25 
II.  25 

11.30 

9.95874 

i  .  00146 

9.96697 

I.  10223 

.95891 
.95907 
.95924 
•95940 

.00329 
.00513 
.00698 

.00883 

.96713 
.96729 
.96746 

.96762 

.10446 
.  10671 
.10896 

.11122 

90 

92 

9-95957 
•95973 

.85 
.80 
.85 

1.01069 
.01256 

9-30 
9-35 
9.40 

90 

92 

9-96778 
.96795 

.80 
.85 
.80 

I.  I  1349 
.11578 

11-35 
ii.  45 
II  45 

94 

•95990 

.01444 

94 

.96811 

11807 

96 

.96007 

.85 

.01633 

9-45 

96 

.96827 

.80 

.  12038 

il.SS 

98 
100 

.96023 

.85 

.01821 

9.40 
9-45 

98 
100 

.96843 

.80 
.85 

.12269 

11-55 
ii.  60 

9.96040 

I.O2OIO 

9.96860 

1.12501 

(231) 


TABLE  XXVI.  —  (Continued) 


Hun- 

dredths 

86° 

Hun- 

dredths 

87° 

Vers 

Diff. 

.001 

Exsec 

Diff. 

.001 

Vets 

Diff. 

.001 

Exsec 

Diff. 

.001 

00 

9.96860 

80 

.1  .  12501 

00 

9.97665 

80 

1-25785 

02 
04 
06 

.96876 
.96892 
.96908 

.80 
.80 
.85 

'    .12735 
.12969 
.13205 

11.70 
11.80 
11.85 

02 
04 
06 

.97681 
.97697 
•97713 

.80 
.80 
.80 

.26092 
.  26400 
.26710 

15.40 
15-50 
15.60 

08 

.96925 

.13442 

08 

.97729 

.  27022 

10 

12 

9.96941 
.96957 

.80 
.80 

I  .  13680 
.13919 

11-95 
12.05 

IO 
12 

9-97745 
.97761 

.80 
.80 

1.27336 
.27652 

15.70 
15.80 
15-95 

14 

16 
18 

.96973 
.96990 
.97006 

.85 
.80 
80 

.14160 
.14401 
.14644 

12.05 
12.15 

14 

16 
18 

•97777 
•97793 
.97809 

.80 
.80 
80 

.27971 
.28291 
.28614 

16.00 
16.15 

20 

9.97022 

80 

1.14888 

20 

9.97825 

80 

1.28939 

22 
24 
26 

.97038 
•97054 
.97071 

.80 
.85 
.80 

.15133 
.15379 
.  15626 

12.30 
12.35 
12.45 

22 

24 
26 

.97841 
.97857 
.97873 

.80 
.80 
.80 

.29266 
•29595 
.29926 

16.45 
16.55 
16  70 

28 
30 
32 

.97087 
9.97103 
.97"9 

.80 
.80 
.80 

.15875 
1.16125 
.16376 

12.50 
12.55 
12.65 

28 
30 
32 

.97889 
9-97904 
.97920 

•  75 

.80 
.80 

.30260 
1.30596 
.30935 

16.80 
i6.95 
17.05 

34 

.97135 

.16619 

34 

.97936 

.31276 

36 
38 

.97151 
.97168 

.85 

80 

.16883 
.17138 

12.70 
12.75 

36 
38 

•97952 
.97968 

.80 
go 

.31619 
•31965 

I7-I5 
17-30 

40 

9.97184 

80 

I.  17394 

40 

9.97984 

80 

1.32314 

42 
44 
46 

.97200 
.97216 
.97232 

.80 
.80 
.80 

.17652 
.17910 
.18172 

12.90 
13.10 
13.10 

42 
44 
46 

.98000 
.98016 
.98031 

.80 
•  75 
.80 

.32665 
.33018 
•33375 

17-65 
17-85 
1,7.90 

48 

.97248 

.18434 

48 

.98047 

•33733 

50 

52 

9.97264 
.97280 

.80 
.85 

1.18697 
.18961 

13.15 
13-20 
13.35 

50 

52 

9-98063 
.98079 

.80 
.80 

1.34095 
.34460 

18.25 
18.35 

54 
56 
58 

.97297 
•97313 
.97329 

.80 
.80 
80 

.  19228 

.19495 
.  19764 

13.35 
13-45 

54 
56 
58 

.98095 
.98111 
.98126 

.80 

•  75 
go 

.34827 
•35197 
-35570 

18.50 
18.65 
18  80 

60 

9-97345 

i.  20035 

60 

9.98142 

go 

1.35946 

62 
64 
66 

.97361 
•97377 
•97393 

.80 
.80 
.80 

.20307 
.20580 
•20855 

13-65 
13-75 
13.85 

62 
64 
66 

.98158 
.98174 
.98190 

.80 
.80 

•  75 

.36325 
.36707 
.37092 

19.10 
19-25 
19-45 

68 
70 

72 

.97409 
9-97425 
•97441 

.80 
.80 
.80 

.21132 
1.21410 
.21690 

13.90 
14.00 
14.05 

68 
70 

72 

.98205 
9.98221 
•98237 

.80 
.80 
.80 

.37481 
1.37872 
.38267 

19-55 
19-75 
19.90 

74 
76 
78 

•97457 
•97473 
.97489 

.80 
.80 
80 

.21971 
.22254 
.22539 

14.15 
14-25 

74 
76 
78 

.98253 
.98268 
.98284 

•  75 
.80 
go 

.38665 
.39067 
•39472 

20.  10 
20.25 

80 

9-97505 

80 

1.22825 

80 

9.98300 

go 

I.3988I 

20  60 

82 
84 
86 

•97521 
•97537 
•97553 

.80 
.80 
.80 

.23113 
.23403 
.23695 

14.50 

14.60 
14.65 

82 
84 
86 

.98316 
.98331 
.98347 

•  75 
.80 
.80 

.40293 
.40709 
.41128 

20.8O 
20.95 
21.  2O 

88 
90 
92 

.97569 
9.97585 
.97601 

.80 
.80 
.80 

.23988 
1.24283 

.24580 

14-75 
14.85 
14.90 

88 
90 

92 

.98363 
9.98379 
.98394 

.80 
•  75 
.80 

.41552 
I.4I979 
.42410 

21.35 

21.55 
21.75 

94 
96 
98 

.97617 
.97633 
.97649 

.80 
.80 
80 

.24878 
.25179 
.25481 

14-95 
15.10 

94 
96 
98 

.98410 
.98426 
.98442 

.80 
.80 

.42845 
.43284 
.43728 

21.95 

22.20 

22  35 

100 

9-97665 

1.25785 

100 

9.98457 

I-44I75 

(232) 


TABLE   XXVI.  —  (Continued) 


Hun- 
dredths 

88° 

Hun- 
dredths 

89° 

Vers 

Difif. 
.001 

Exsec 

Diff. 

.001 

Vers 

Diff. 
.001 

Exsec 

Diff. 
.001 

00 

9-98457 

I-44I75 

00 

9-99235 

80 

1.75050 

02 
04 
06 

.98473 
.98489 
•98504 

.80 
•  75 
80 

.44627 
•45084 
•45545 

22.85 
23.05 
23  25 

02 

04 
06 

.99251 
.99266 
.99282 

•  75 
.80 
•  75 

•75943 
•76853 
.77783 

45.50 
46.50 

47-45 

08 
10 

12 

.98520 
9-98536 
.98551 

.80 
•  75 
.80 

.46010 
I  .  46481 
.46956 

23-55 
23-75 

24.00 

08 

IO 
12 

.99297 
9.99312 
•99328 

•  75 
.80 
•  75 

.78732 
1.79702 
.80694 

48.50 
49.60 
50.65 

14 

16 

.98567 
.98583 

.80 

.47436 
•47921 

24.25 

14 

16 

•99343 
•99359 

.80 

.81707 
.82744 

51.85 

18 

.98598 

•  75 
80 

.48411 

24.50 

18 

•99374 

•  75 

.83806 

53-10 

20 

9.98614 

80 

1.48906 

2C  o1? 

20 

9-99389 

80 

1.84894 

ctr  75 

22 

24 

26 

.98630 
.98645 
.98661 

•  75 
.80 
•  75 

.  49407 
.49913 
•50425 

25-30 
25.60 
25.85 

22 

24 

26 

.99405 
.99420 
•99435 

•  75 
•  75 
.80 

.86009 
.87152 
.88326 

57.15 

58.70 
60.15 

28 
30 
32 

.98676 
9.98692 
.98708 

.80 
.80 
•  75 

.50942 
1.51466 
.51995 

26.20 
26.45 
26.80 

28 
30 
32 

•99451 
9.99466 
.99481 

•  75 
•  75 
.80 

.89531 
1.90770 
.92044 

61.95 
63.70 
65.60 

34 
36 
38 

.98723 
.98739 
.98755 

.80 
.80 

.52531 
•53073 
.53621 

27.IO 
27.40 

34 
36 
38 

•99497 
•99512 
•99527 

•  75 
•  75 
80 

.93356 
.94707 
.96101 

67.55 

69.70 

40 

9.98770 

80 

1.54176 

28  10 

40 

9-99543 

I-  97541 

42 
44 
46 

.98786 
.98801 
.98817 

•  75 
.80 
•  75 

.54738 
.55306 
.55882 

28.40 
28.80 
29.15 

42 
44 
46 

-99558 
•99573 
.99589 

•  75 
.80 
•  75 

.99028 
2.00568 
.02162 

77.00 
79.70 
82.75 

48 
50 
52 

.98832 
9.98848 
.98864 

.80 
.80 
•  75 

•56465 
1.57056 
.57654 

29-55 
29.90 
30.35 

48 
50 

52 

.99604 
9-99619 
.99635 

-75 
.80 
-75 

.03817 
2.05535 
.07323 

85.90 
89.40 

93-20 

54 
56 
58 

.98879 
.98895 
.98910 

.80 
•  75 
80 

.58261 
.58875 
•59498 

30.70 

31  15 

54 
56 
58 

.99650 
.99665 
.99680 

.75 
•  75 
80 

.09187 
-III33 
.13168 

97-30 
101.75 

60 

9.98926 

7S 

1.60130 

60 

9.99696 

2.15302 

62 
64 
66 

.98941 
.98957 
.98972 

.80 
•  75 
.80 

.60770 
.61419 
.62078 

32-45 
32-95 
33-45 

62 
64 
66 

•997II 
.99726 
•99742 

•  75 
.80 
•  75 

.17545 
.19909 
.22406 

118.20 
124.85 
132.40 

68 
70 

72 

.98988 
9.99003 
.99019 

•  75 
.80 
•  75 

.62747 
1.63425 
.64114 

33-90 
34-45 
34-95 

68 
70 

72 

•99757 
9.99772 
.99787 

-75 
•  75 
•  75 

.25054 
2.27872 
•30884 

140.90 
150.60 
161.70 

74 
76 
78 

.99034 
.99050 
.99065 

.80 
•  75 
.So 

.64813 
•65523 
•66245 

35-50 
36.10 
36  65 

74 
76 
78 

.99802 
.998i8 
•99833 

.80 
-75 

75 

.34118 
.37609 
•41403 

174-55 
189.70 

80 

9.99081 

75 

1.66978 

"V7  2<\ 

80 

9.99848 

7C 

2.45557 

82 
84 
86 

.99096 
.99112 
.99127 

.80 
•  75 
.80 

•67723 
.68481 
.69252 

37-90 
38.55 

39-20 

82 
84 
86 

.99863 
.99879 
.99894 

.80 
-75 
•  75 

.50148 
•55279 
.61093 

256.55 
290.70 
335-50 

88 
90 

92 

•99143 

9.99158 
.99174 

•  75 
.80 
•  75 

.70036 
1.70834 
.71646 

39-90 
40.60 
41-35 

88 
90 

92 

.99909 
9.99924 
•99939 

•  75 
-75 
•  75 

.67803 
2.75736 
.85443 

396.65 
485.45 
625-45 

94 
96 
98 

.99189 
.99204 
.99220 

•  75 
.80 
•  75 

•72473 
•73316 
•74174 

42.15 
42.90 
43  80 

94 
96 
98 

•99954 
•99970 
•99985 

.80 
•  75 

•97952 
3.I5576 
.45694 

881.20 
1505-90 

100 

9-99235 

I  •  75050 

100 

o.ooooo 

00 

(233) 


TABLE   XXVII.  —  NATURAL  SINES,  TANGENTS,  COTANGENTS 
AND  COSINES 


Deg. 

Sin 

d. 

Tan 

d. 

Cotan 

d. 

Cosin 

d. 

P.  P. 

0.0 

o.oooo 

o.oooo 

inf. 

I.OOOO 

90.0 

i 

0.0017 

To 

0.0017 

To 

572-9572 

I.OOOO 

9 

2 

0.0035 

0.0035 

286.4777 

I.OOOO 

8 

3 

0.0052 

17 
18 

0.0052 

17 
18 

190.9842 

I.OOOO 

0 

7 

4 

0.0070 

0.0070 

143.2371 

I.OOOO 

6 

5 

0.0087 

17 
18 

0.0087 

17 
18 

114-5887 

I.OOOO 

5 

6 

0.0105 

17 

0.0105 

17 

95.4895 

0.9999 

o 

4 

7 

O.OI22 

To 

O.OI22 

To 

81.8470 

0.9999 

3 

8 

O.OI40 

O.OI4O 

71-6151 

0.9999 

2 

9 

0.0157 

18 

0.0157 

18 

63.6567 

0.9999 

I 

1.0 

0.0175 

0.0175 

57.2900 

0.9998 

89.0 

i 

0.0192 

0.0192 

52.0807 

0.9998 

9 

2 

0.0209 

18 

0.0209 

18 

47-7395 

.... 

0.9998 

8 

18 

3 

0.0227 

0.0227 

44  .  0661 

0.9997 

7 

I   1.8 

4 

0.0244 

17 

0.0244 

40.9174 

0.9997 

6 

2   3.6 

5 

0.0262 

0.0262 

38.1885 

.... 

0-9997 

5 

3   5-4 

6 

0.0279 

17 
18 

0.0279 

18 

35-8006 

0.9996 

o 

4 

4   7-2 
5   9  o 

7 

0.0297 

0.0297 

33.6935 

0.9996 

3 

6  10.8 

8 

0.0314 

18 

0.0314 

18 

31-8205 

0-9995 

o 

2 

7  12.6 

9 

0.0332 

0.0332 

30.1446 

0-9995 

I 

8   14.4 

2.0 

0.0349 

0.0349 

18 

28.6363 

0-9994 

88.0 

9  16.2 

i 

o  .  0366 

18 

0.0367 

27.2715 

0-9993 

9 

2 

0.0384 

17 

0.0384 

18 

26.0307 

0-9993 

i 

8 

3 

0.0401 

18 

0.0402 

17 

24.8978 

0.9992 

T 

7 

4 
5 

0.0419 
0.0436 

17 
18 

0.0419 
0.0437 

18 
17 

23.8593 
22.9038 

9555 
8821 

0.9991 
0.9990 

I 

o 

6 

5 

6 

0.0454 

17 

0.0454 

18 

22.0217 

8168 

0.9990 

I 

4 

7 
8 
9 

0.0471 
0.0488 
0.0506 

17 
18 

0.0472 
0.0489 
0.0507 

17 
18 

21  .  2049 
20.4465 
19.7403 

7584 
7062 

0.9989 
0.9988 
0.9987 

I 
I 

3 

2 
I 

3.0 

0.0523 

18 

0.0524 

18 

I9.08ll 

6166 

0.9986 

I 

87.0 

17 

i 

2 

3 

0.0541 

0.0558 
0.0576 

17 
18 
17 

0.0542 
0-0559 
0.0577 

17 
18 

18.4645 
17.8863 
17.3432 

5782 
5431 
5113 

0.9985 
0.9984 
0.9983 

I 
I 

I 

9 
8 
7 

i   1.7 
2   3-4 
3   5-1 

4 
5 
6 

0.0593 

0.0610 
0.0628 

18 

0.0594 
0.0612 
0.0629 

18 
17 
18 

16.8319 
16.3499 
15.8945 

4820 
4554 
4307 

0.9982 
0.0981 
0.9980 

I 
I 
I 

6 

5 
4 

4   6.8 
5   8.5 

6   10.2 

7   H-9 

7 
8 
9 

0.0645 
0.0663 
0.0680 

18 
17 
18 

0.0647 
0.0664 
0.0682 

17 
18 

15.4638 
15.0557 
14.6685 

4081 
3872 
3678 

0.9979 
0.9978 
0.9977 

I 
I 

3 

2 
I 

8   13.6 
9   15-3 

4.0 

0.0698 

17 

0.0699 

18 

14.3007 

35oo 

0.9976 

2 

86.0 

i 

2 

0.0715 
0.0732 

17 
18 

0.0717 
0.0734 

17 
18 

13.9507 
13.6174 

3333 
3178 

0.9974 
0-9973 

I 
I 

9 
8 

3 

0.0750 

0.0752 

17 

13.2996 

3034 

0.9972 

I 

7 

4 
5 
6 

0.0767 
0.0785 

0.0802 

18 
17 
17 

0.0769 
0.0787 
0.0805 

18 
18 
17 

12.9962 
I2.7O62 
12.4288 

2900 
2774 
2656 

0.9971 
0.9969 
0.0968 

2 

I 
2 

6 
5 

4 

7 
8 
9 

0.0819 
0.0837 
0.0854 

18 
17 
18 

0.0822 
0.0840 
0.0857 

18 
17 
18 

12  .  1632 
11.9087 
11.6645 

2545 
2442 
2344 

0.9966 
0.9965 
0.9963 

I 

2 

I 

3 

2 
I 

5.0 

0.0872 

0.0875 

11.4301 

0.9962 

85  0 

Cosin 

d. 

"otan 

d.     Tan 

d. 

Sin    d. 

Deg. 

(234) 


TABLE  XXVII.  —  (Continued) 


Deg. 

Sin 

d. 

Tan 

d. 

Cotan 

d. 

Cosin 

d. 

P.P. 

50 

o  .  0872 

0.0875 

11.4301 

0.9962 

85  0 

i 

0.0889 

0.0892 

18 

11.2048 

2166 

0.9960 

9 

2 
3 

0.0906 
0.0924 

18 
17 

0.0910 
0.0928 

18 
17 

10.9882 
10.7797 

2085 
2008 

0-9959 
0-9957 

2 

I 

8 

7 

4 
5 
6 

0.0941 
0.0958 
0.0976 

17 
18 
17 

0.0945 
0.0963 
0.0981 

18 
18 
17 

10.5789 
10.3854 
10.1988 

1935 
1866 
1801 

0.9956 
0.9954 
0.9952 

2 
2 
I 

6 
5 

4 

7 
8 

0.0993 

O.IOII 

18 

0.0998 
0.1016 

18 

10.0187 
9-8448 

1739 
1680 

0.9951 
0.9949 

2 

3 

2 

9 

o  .  1028 

0-1033 

18 

9.6768 

0.9947 

I 

6.0 

0.1045 

18 

0.1051 

18 

9-5144 

0.9945 

84.0 

i 

2 

3 

0.1063 
0.1080 
0.1097 

17 
17 
18 

0.1069 
0.1086 
0.1104 

17 
18 
18 

9-3572 
9-2052 
9-0579 

1520 
1473 
1427 

0-9943 
0.9942 
0.9940 

I 
2 
2 

9 
8 
7 

18 

I   1.8 
2   3-6 

4 
5 
6 

0.1115 
0.1132 
0.1149 

17 
17 

18 

O.II22 

0.1139 
0.1157 

17 
18 
18 

8.9152 
8.7769 
8.6427 

1383 
1342 
1301 

0-9938 
0-9936 
0-9934 

2 

2 
2 

6 
5 
4 

3   5-4 
4   7-2 
5   9-0 
6   10.8 

7 
8 
9 

0.1167 
0.1184 

O.I2OI 

17 
17 
18 

0.1175 
0.1192 

O.I2IO 

17 
18 
18 

8.5126 
8.3863 
8.2636 

1263 
1227 

IIQ-J 

0.9932 
0-9930 
0.9928 

2 
2 

3 

2 
I 

7   12.6 
8   14.4 
9  16.2 

7.0 

0.1219 

0.1228 

18 

8.1443 

0.9925 

83.0 

i 

0.1236 

0.1246 

8.0285 

0.9923 

9 

2 
3 

0.1253 
0.1271 

18 

0.1263 
0.1281 

18 
18 

7.9158 
7.8062 

1096 
1066 

0.9921 
0.9919 

2 
2 

8 

7 

4 

0.1288 

17 

0.1299 

18 

7.6996 

IO38 

0.9917 

3 

6 

5 

0.1305 

18 

0.1317 

17 

7-5958 

IOII 

0.9914 

2 

5 

6 

0.1323 

17 

0.1334 

18 

7-4947 

985 

0.9912 

2 

4 

7 

0.1340 

17 

0.1352 

18 

7.3962 

960 

0.9910 

3 

8 

9 

0.1357 

0.1374 

17 
18 

0.1370 
0.1388 

18 

7-3002 
7.2066 

936 

012 

0.9907 
0.9905 

2 

2 
I 

8.0 

0.1392 

17 

0.1405 

18 

7-II54 

890 

0.9903 

82  0 

17 

i 

0.1409 

0.1423 

18 

7.0264 

8fio 

0.9900 

9 

i   1.7 

2 

3 

0.1426 
0.1444 

18 
17 

0.1441 
0.1459 

18 
18 

6-9395 
6.8548 

847 

828 

0.9898 
0.9895 

3 
2 

8 

7 

2   3-4 
3   5-1 

4 

0.1461 

0.1477 

18 

6.7720 

808 

0.9893 

6 

4   6.8 

5 
6 

0.1478 
0.1495 

17 

18 

0.1495 
0.1512 

17 
18 

6.6912 
6.6122 

790 

772 

0.9890 
0.9888 

2 

3 

5 
4 

5   8.5 

6   IO.2 

7  H-9 

7 
8 
9 

O.I5I3 
0.1530 
0.1547 

17 
17 

0.1530 
0.1548 
0.1566 

18 
18 
18 

6-5350 
6.4596 
6.3859 

754 
737 

0.9885 
0.9882 
0.9880 

3 

2 

3 

2 
I 

8  13.6 
9  15-3 

9.0 

0.1564 

18 

0.1584 

18 

6.3138 

706 

0.9877 

81.0 

i 

2 
3 

0.1582 
0.1599 
0.1616 

17 
17 
17 

0.1602 
0.1620 
0.1638 

18 
18 
17 

6.2432 
6.1742 
6.1066 

690 
676 
661 

0.9874 
0.9871 
0.9869 

3 

2 
3 

9 
8 
7 

4 
5 
6 

0.1633 
0.1650 
0.1668 

i? 
18 
17 

0-1655 
0.1673 
0.1691 

18 
18 
18 

6.0405 
5-9758 
5.9124 

647 
634 
622 

0.9866 
0.9863 
0.9860 

3 
3 
3 

6 
5 
4 

7 

0.1685 

0.1709 

18 

5.8502 

608 

.0.9857 

3 

8 

0.1702 

17 

0.1727 

18 

5.7894 

597 

0.9854 

2 

9 

0.1719 

17 

0.1745 

18 

5.7297 

1584 

0.9851 

I 

10  0 

0.1736 

0.1763 

5.6713 

0.9848 

80  0 

Cosin 

d. 

Cotan 

d. 

Tan 

d. 

Sin 

d. 

Deg. 

(235) 


TABLE  XXVII.  —  (Continued) 


Deg. 

Sin 

d. 

Tan 

d. 

Cotan 

d. 

Cosin 

d. 

] 

3.  P. 

10.0 

0.1736 

18 

0.1763 

18 

5.6713 

0.9848 

80.0 

i 

2 

0.1754 
0.1771 

17 

0.1781 
0.1799 

18 

5.6140 
5.5578 

562 

0.9845 
0.9842 

3 

9 
8 

3 

0.1788 

0.1817 

18 

5-5026 

552 

0.9839 

3 

7 

4 

0.1805 

0.1835 

5.4486 

0.9836 

6 

5 

0.1822 

17 

0.1853 

18 

5-3955 

531 

0.9833 

3 

5 

6 

0.1840 

0.1871 

5-3435 

520 

0.9829 

4 

4 

19 

7 
8 

0.1857 
0.1874 

17 

0.1890 
0.1908 

*9 
18 

5.2924 
5.2422 

502 

0.9826 
0.9823 

3 
3 

3 

2 

i 

2 

3-8 

9 

0.1891 

17 

0.1926 

18 

5.1929 

493 

.0, 

0.9820 

3 

I 

3 

5-7 

11.0 

0.1908 

0.1944 

18 

5.1446 

/17fi 

0.9816 

79.0 

5 

7.0 
9-5 

i 

2 

0.1925 
0.1942 

0.1962 
0.1980 

18 

5-0970 
5.0504 

466 

0.9813 
0.9810 

3 

9 
8 

6 

7 

n.  4 
13-3 

3 

0.1959 

18 

0.1998 

18 

5-0045 

459 

0.9806 

4 

7 

8 

15.2 

4 

0.1977 

0.2016 

4-9594 

0.9803 

6 

9 

17.1 

5 
6 

0.1994 

0.20II 

17 
17 
17 

0.2035 
0.2053 

19 
18 
18 

4-9152 
4.8716 

442 
436 

428 

0.9799 
0.9796 

4 
3 

4 

5 

4 

7 

0.2028 

0.2071 

4.8288 

0.9792 

3 

8 

0.2045 

17 

0.2089 

18 

4.7867 

421 

0.9789 

3 

2 

9 

0.2,062 

17 

0.2107 

18 

4-7453 

414 

0.9785 

4 

I 

12.0 

0.2079 

0.2126 

18 

4-7046 

0.9781 

78.0 

i 

0.2096 

0.2144 

4.6646 

0.9778 

9 

18 

2 

0.2113 

I? 

0.2162 

.6252 

394 

0-9774 

4 

8 

i 

1.8 

3 

0.2130 

i? 

0.2180 

.5864 

388 

0.9770 

4 

7 

2 

3-6 

4 
5 
6 

0.2147 
0.2164 
0.2181 

17 
17 
17 
17 

0.2199 
0.2217 
0.2235 

19 
18 
18 
19 

.5483 
.5107 
•  4737 

38i 
376 

370 
364 

0.9767 
0.9763 
0.9759 

3 
4 
4 
4 

6 
5 
4 

3 

4 
5 
6 

5-4 

7-2 

9-0 
10.8 

7 

0.2198 

0.2254 

18 

•  4373 

•li-g 

0-9755 

3 

7 

12.6 

8 

9 

0.2215 
0.2233 

18 

0.2272 
0.2290 

18 

•  4015 
.3662 

353 

0-9751 
0.9748 

3 

2 
I 

8 
q 

14.4 

16.2 

13.0 

0.2250 

0.2309 

18 

4.3315 

0-9744 

77.0 

i 

0.2267 

0.2327 

4.2972 

0.9740 

9 

2 

0.2284 

i? 

0.2345 

4-2635 

337 

0.9736 

4 

8 

3 

0.2300 

0.2364 

19 
18 

4-2303 

332 

0-9732 

4 

7 

4 

0.2317 

0.2382 

4.1976 

0.9728 

6 

6 

0.2334 
0.2351 

17 

o  .  2401 
0.2419 

19 
18 
19 

4.1653 
4  1335 

323 
3i8 
313 

0-9724 
0.9720 

4 
4 

5 
4 

17 

7 

0.2368 

0.2438 

4.1022 

0-9715 

3 

i 

1-7 

8 

0.2385 

17 

0.2456 

18 

4-0713 

309 

0.9711 

4 

2 

2 

3-4 

9 

0.2402 

0.2475 

19 

18 

4.0408 

305 

0.9707 

4 

I 

3 

5-1 

14.0 

0.2419 

0.2493 

4.0108 

2Ofi 

0.9703 

76.0 

4 

6.8 

i 

2 
3 
4 

0.2436 
0.2453 
0.2470 

0.2487 

17 
17 

0.2512 
0.2530 
0.2549 
0.2568 

18 
19 
19 

3-9812 
3-9520 
3.9232 
3-8947 

292 
288 

285 

0.9699 
0.9694 
0.9690 

0.9686 

5 
4 
4 

9 
8 
7 
6 

6 

7 
8 
9 

8.5 

IO.2 

ii.  9 
13-6 
15.3 

5 

0.2504 

17 

0.2586 

3-866? 

0.9681 

5 

6 

0.2521 

17 

0.2605 

19 
18 

3.8391 

276 

0.9677 

4 

4 

7 

0.2538 

0.2623 

3.8n8 

0.9673 

3 

8 

0.2554 

16 

0.2642 

19 

3-7848 

270 

0.9668 

5 

2 

9 

0.2571 

i? 

0.2661 

19 

To 

3.7583 

265 
262 

0.9664 

4 

I 

15  0 

0.2588 

0.2679 

3-7321 

0.9659 

75  0 

Cosin 

d. 

Cotan 

d. 

Tan 

d. 

Sin 

d. 

Deg. 

(236) 


TABLE  XXVII.  —  (Continued") 


Deg. 

Sin 

d. 

Tan 

d. 

Cotan 

d. 

Cosin 

d. 

P.P. 

18.0 

0.2588 

0.2679 

3-7321 

0.9659 

78.0 

i 

0.2605 

0.2698 

3.7062 

0.9655 

9 

2 

0.2622 

i? 

0.2717 

19 

3.6806 

250 

0.9650 

5 

8 

3 

0.2639 

17 

0.2736 

19 
18 

3.6554 

252 
249 

0.9646 

4 
5 

7 

19 

4 
6 

0.2656 
0.2672 
0.2689 

16 
17 

0.2754 
0.2773 
0.2792 

19 
19 
19 

3-6305 
3.6059 
3.58i6 

246 
243 
240 

0.9641 
0.9636 
0.9632 

5 
4 
5 

6 
5 
4 

i 

2 

3 

1-9 
3-8 
5-7 

7 

0.2706 

0.2811 

3.5576 

0.9627 

3 

4 

7-6 

0.2723 

i? 

0.2830 

19 

3-5339 

237 

0.9622 

5 

2 

5 

9-5 

9 

0.2740 

16 

0.2849 

19 

18 

3-5105 

234 

0.9617 

5 

I 

6 

II.  4 

16.0 

0.2756 

0.2867 

3.4874 

228 

0.9613 

74.0 

7 

13-3 

i 

2 

0.2773 
0.2790 

17 

0.2886 
0.2905 

19 

3-4646 
3-4420 

226 

0.9608 
0.9603 

5 

9 
8 

9 

15.2 
17.1 

3 

0.2807 

16 

0.2924 

19 
19 

3.4197 

223 

220 

0.9598 

5 

7 

4 

0.2823 

0.2943 

3-3977 

0-9593 

6 

5 

0.2840 

i? 

0.2962 

19 

3-3759 

0.9588 

5 

5 

18 

6 

0.2857 

i? 

0.2981 

19 
19 

3-3544 

215 

212 

0.9583 

5 

4 

i 

1.8 

7 

0.2874 

0.3000 

3-3332 

0.9578 

3 

2 

3-6 

8 

9 

0.2890 
0.2907 

17 

0.3019 
0.3038 

19 
19 

3-3122 
3.2914 

208 

0.9573 
0.9568 

5 
5 

2 
I 

3 
4 

5-4 

7-2 

17.0 

0.2924 

if) 

0.3057 

3-2709 

0.9563 

73  0 

5 
g 

9-0 
10  8 

i 

0.2940 

0.3076 

3-2506 

0.9558 

9 

7 

12.6 

2 
3 

0.2957 
0.2974 

16 

0.3096 
0.3H5 

19 
19 

3.2305 
3.2106 

199 
196 

0.9553 
0-9548 

5 
6 

8 
7 

8 
9 

14.4 
16.2 

4 

0.2990 

0-3134 

3.I9IO 

0-9542 

6 

5 

0.3007 

17 

0.3153 

19 

3.1716 

194 

0-9537 

5 

5 

6 

0.3024 

17 

0.3172 

19 

3.1524 

192 

0-9532 

5 

4 

8 

9 

0.3040 
0.3057 
0.3074 

17 
17 
16 

0.3191 
0.3211 
0.3230 

20 
19 

3-1334 
3.II46 
3-0961 

188 
185 

0.9527 
0.9521 
0.9516 

6 
5 

3 

2 
I 

i 

2 

1-7 
3-4 

18.0 

0.3090 

0.3249 

3-0777 

182 

0.95H 

fi 

72.0 

3 

4 

5-1 
6  8 

i 

2 

3 

0.3107 
0.3123 
0.3140 

16 
17 
16 

0.3269 
0.3288 
0.3307 

19 

19 

20 

3-0595 
3.0415 
3-0237 

180 
178 
176 

0.9505 
0.9500 
0.9494 

5 
6 

9 
8 
7 

5 

6 
7 

8-5 

10.2 

ii.  9 

4 

0.3156 

0-3327 

3.0061 

0.9489 

6 

8 

13.6 

S 

0.3173 

17 

0.3346 

19 

2.9887 

174 

0.9483 

5 

9 

15.3 

6 

0.3190 

17 

Tfi 

0.3365 

19 
20 

2.9714 

173 

170 

0.9478 

5 
6 

4 

8 

9 

0.3206 
0.3223 
0.3239 

17 
16 

0.3385 
0.3404 
0.3424 

19 
20 

2.9544 
2.9375 
2.9208 

169 
167 
166 

0.9472 
0.9466 
o  .  9461 

6 

5 
g 

3 

2 
I 

16 

i  6 

19.0 

0.3256 

16 

0.3443 

2.9042 

164 

0.9455 

6 

71.0 

j 

2 

3-2 

i 

0.3272 

0-3463 

2.8878 

0.9449 

9 

3 

4-8 

2 

3 

0.3289 
0.3305 

17 
16 
i? 

0.3482 
0.3502 

19 

2O 
20 

2.8716 
2.8556 

160 
159 

0.9444 
0.9438 

5 
6 
6 

8 

7 

4 
5 

6.4 
8.0 

4 
S 
6 

0.3322 
0.3338 
0.3355 

16 
17 
16 

0.3522 
0.3541 
o.356i 

19 
2O 

20 

2.8397 
2.8239 
2.8083 

IS8 
156 
154 

0.9432 
0.9426 
0.9421 

6 
5 
6 

6 
5 
4 

b 

7 
8 

9-6 

II.  2 

12.8 

14  4 

7 
8 

o.337i 
0.3387 

16 

0.3581 
0.3600 

19 

2.7929 
2.7776 

153 

0.9415 
0.9409 

6 

3 

2 

9 

0.3404 

17 

0.3620 

2.7625 

151 

0.9403 

g 

I 

20.0 

0.3420 

0.3640 

2-7475 

0-9397 

70.0 

Cosin 

d. 

Cotan 

d. 

Tan 

d. 

Sin 

d. 

Deg. 

(237) 


TABLE  XXVII.  —  (Continued) 


Deg. 

Sin 

d. 

Tan 

d. 

Cotanj 

d. 

Cosin 

d. 

P.P. 

20.0 

0.3420 

0.3640 

2.7475 

0.9397 

70.0 

i 

0.3437 

0.3659 

2.7326 

0-9391 

9 

2 

0.3453 

0.3679 

2.7179 

147 

0.9385 

8 

3 

0.3469 

0.3699 

2.7034 

145 

0-9379 

6 

7 

145 

6 

22 

4 
5 
6 

0.3486 
0.3502 
0.3518 

16 
16 
17 

0.3719 
0-3739 
0-3759 

20 
2O 
20 

2.6889 
2.6746 
2.6605 

143 

141 
141 

0.9373 
0.9367 
o  .  9361 

6 
6 

7 

6 
5 
4 

I 
2 
3 

2.2 

4-4 
6.6 

7 
8 
9 

0.3535 
0.3551 
0.3567 

16 
16 

0.3779 
0.3799 
0.3819 

20 
20 

2  .  6464 
2.6325 
2.6l87 

139 
138 

0.9354 
0.9348 
0.9342 

6 
6 
g 

3 

2 
I 

4 
5 
6 

8.8 
II.  0 

13-2 

21.0 

0.3584 

16 

0.3839 

2  .  6O5I 

3 

0.9336 

69.0 

7 

15-4 

i 

2 

0.3600 
0.3616 

16 

0.3859 
0.3879 

2O 

2.5916 
2.5782 

134 

0.9330 
0.9323 

7 

9 
8 

8 
9 

17.6 
19.8 

3 

0.3633 

16 

0.3899 

20 

2.5649 

133 
132 

0.9317 

6 
6 

7 

4 

0.3649 

0.3919 

2-5517 

0.9311 

6 

5 
6 

0.3665 
0.3681 

16 
16 
16 

0.3939 
0.3959 

20 
20 

2.5386 
2.5257 

131 
129 
128 

0.9304 
0.9298 

7 
6 

7 

5 
4 

i 

21 

2.1 

7 

0.3697 

0.3979 

2.5129 

0.9291 

3 

2 

4-2 

8 
9 

0.3714 
0.3730 

16 
16 

0.4000 
0.4020 

20 

2.5002 
2.4876 

127 
126 

0.9285 
0.9278 

6 

7 

2 
I 

3 

4 

6.3 

8-4 

22.0 

0.3746 

16 

0.4040 

2-4751 

0.9272 

68.0 

5 

10.5 

2 

0.3762 
0.3778 

16 

0.4061 
0.4081 

2O 

2.4627 
2.4504 

123 

0.9265 
0.9259 

6 

9 
8 

7 

14-7 

Tfi  0 

3 

0-3795 

17 
16 

0.4101 

21 

2.4383 

121 
121 

0.9252 

7 
7 

7 

9 

18.9 

4 
5 

0.3811 
0.3827 

16 

0.4122 
0.4142 

20 

2  .  4262 
2.4142 

120 

0.9245 
0.9239 

6 

6 
5 

6 

0.3843 

16 

0.4163 

2O 

2.4023 

119 
117 

0.9232 

7 
7 

4 

7 
8 
9 

0.3859 
0.3875 
0.3891 

16 
16 
16 

0.4183 
0.4204 
0.4224 

21 
20 
21 

2.3906 
2.3789 
2.3673 

117 

116 

0.9225 
0.9219 
0.9212 

6 

7 

3 
2 

I 

i 

2 

17 

3-4 

23.0 

0.3907 

16 

0.4245 

2.3559 

0.9205 

67.0 

3 

S.I 
6  8 

i 

0.3923 

0.4265 

2.3445 

0.9198 

9 

5 

8  5 

2 
3 

0-3939 
0.3955 

16 
16 

0.4286 
0.4307 

21 

20 

2.3332 
2.3220 

112 
III 

0.9191 
0.9184 

7 

7 
6 

8 

7 

6 

7 

10.3 

11.9 

4 

0.3971 

0.4327 

2.3109 

0.9178 

6 

8 

13.6 

5 

0.3987 

16 

0.4348 

2.2998 

III 

0.9171 

7 

5 

9 

15-3 

6 

0.4003 

16 

0.4369 

21 

2.2889 

IO9 

108 

0.9164 

7 
7 

4 

7 
8 

0.4019 
0.4035 

16 

0.4390 
0.4411 

21 

2.2781 
2.2673 

108 

0.9157 
0.9150 

7 

3 

2 

9 

0.4051 

16 
16 

0.4431 

2.2566 

107 
106 

0.9143 

7 

g 

I 

16 

24.0 

0.4067 

16 

0.4452 

21 

2.2460 

0.9135 

66.0 

2 

3-2 

i 

0.4083 

0.4473 

2.2355 

0.9128 

9 

3 

4-8 

2 

0.4099 

0.4494 

2.2251 

0.9121 

7 

8 

4 

6.4 

3 

0.4H5 

0.4515 

2.2148 

103 

0.9114 

V 

7 

5 

8.0 

4 

0.4131 

,t- 

0.4536 

2.2045 

0.9107 

6 

6 

9-6 

5 
6 

0.4147 
0.4163 

16 

0.4557 
0.4578 

21 

2.1943 
2.1842 

101 

0.9100 
0.9092 

7 
8 

5 
4 

7 
8 

II.  2 
12.8 

7 

0.4179 

0.4599 

2.1742 

0.9085 

3 

9 

8 

0.4195 

0.4621 

2.1642 

0.9078 

7 

2 

9 

0.4210 

15 

16 

0.4642 

2.1543 

99 
08 

0.9070 

I 

25  0 

0.4226 

0.4663 

2.1445 

0.9063 

65  0 

Cosin 

d. 

Cotan 

d. 

Tan 

d. 

Sin 

d. 

Deg. 

(238) 


TABLE  XXVII.  —  (Continued) 


Deg. 

Sin 

d. 

Tan 

d. 

Cotan 

d. 

Cosin 

d. 

P.P. 

25  0 

0.4226 

16 

0.4663 

2.1445 

0.9063 

65.0 

I 
2 
3 
4 
5 
6 

7 
8 
9 

0.4242 
0.4258 
0.4274 
0.4289 
0.4305 
0.4321 

0-4337 
0.4352 
0.4368 

16 
16 
IS 
16 
16 
16 

IS 
16 
ffi 

0.4684 
0.4706 
0.4727 
0.4748 
0.4770 
o.479i 
0.4813 
0.4834 
0.4856 

22 
21 
21 
22 
21 
22 
21 
22 

2.1348 
2.1251 
2.II55 
2.1060 
2.0965 
2.0872 

2.0778 
2.0686 
2.0594 

97 
96 
95 
95 
93 
94 
92 
92 

0.9056 
0.9048 
0.9041 

0.9033 
0.9026 
0.9018 
0.9011 
0.9003 
0.8996 

8 

7 
8 

7 
8 
7 
8 

7 

9 
8 
7 
6 
5 
4 
3 

2 
I 

i 

2 

3 

4 
5 
6 

23 

2.3 

4.6 
6-9 

9-2 

II.  5 
13-8 

26.0 

0.4384 

0.4877 

2.0503 

91 

0.8988 

g 

64.0 

7 

16.1 

I 

2 

3 

4 
5 
6 

7 
8 
9 

0-4399 
0.44IS 
0-4431 
0.4446 
0.4462 
0.4478 

0-4493 
0.4509 
0.4524 

16 
16 
IS 
16 
16 
IS 
16 
IS 
16 

0.4899 
0.4921 
0.4942 

0.4964 
o  .  4986 
0.5008 
0.5029 
0.5051 
0.5073 

22 
21 
22 
22 
22 
21 
22 
22 

2.0413 
2.0323 
2.0233 
2.  0145 
2.0057 
1.9970 

1.9883 
1-9797 
I-97II 

90 

90 
90 
88 

88 
87 
87 
86 
86 

0.8980 
0.8973 
0.8965 

0.8957 
0.8949 
0.8942 

0.8934 
0.8926 
0.8918 

7 
8 
8 
8 
7 
8 

8 
8 
g 

9 
8 
7 
6 
5 
4 

3 

2 
I 

9 

i 

2 

3 

4 

18.4 
20.7 

22 

2.2 

4-4 
6.6 
8.8 

27.0 

0.4540 

0.5095 

22 

1.9626 

°5 

0.8910 

63.0 

5 

II.  O 

i 

2 

3 
4 
5 
6 

7 
8 
9 

0.4555 
0-4571 
0.4586 

0.4602 
0.4617 
0.4633 
0.4648 
0.4664 
0.4679 

16 
IS 
16 

IS 
16 
IS 
16 
IS 
16 

0.5117 
O.SI39 
0.5161 

0.5184 
0.5206 
0.5228 
0.5250 
0.5272 
0.5295 

22 
22 
23 
22 
22 
22 
22 
23 

I-9S42 
1-9458 
1-9375 
1.9292 
1.9210 
1.9128 
1.9047 
1.8967 
1.8887 

84 

84 
83 
83 
82 

82 

8l 
80 
80 

0.8902 
0.8894 
0.8886 
0.8878 
0.8870 
0.8862 
0.8854 
0.8846 
0.8838 

8 
8 
8 
8 
8 
8 
8 
8 

9 
8 
7 
6 
5 
4 

3 

2 
I 

7 
8 
9 

I 

2 

IS.4 
17.6 
19-8 

16 

1.6 

3-2 

28.0 

0.4695 

0-5317 

1.8807 

0.8829 

g 

62.0 

3 

4 

4.8 
6  4 

I 

2 
3 
4 
5 
6 

7 
8 
9 

0.4710 
0.4726 
0-4741 
0.4756 
0.4772 
0.4787 
0.4802 
0.4818 
0.4833 

16 
IS 
IS 
16 
15 
IS 
16 
IS 

'0.5340 
0.5362 
0.5384 
0.5407 
0.5430 
O.S452 
0.5475 
0.5498 
0.5520 

22 
22 
23 

23 
22 
23 

23 

22 

1.8728 
1.8650 
1.8572 

I.849S 
1.8418 
1.8341 
1.8265 
1.8190 
1.8115 

79 
78 
78 

77 
77 
77 
76 

75 
75 

0.8821 
0.8813 
0.8805 
0.8796 
0.8788 
0.8780 

0.8771 
0.8763 
0.8755 

8 
8 
9 
8 
8 
9 
8 
8 

9 
8 
7 
6 
5 
4 
3 

2 
I 

5 
6 
7 
8 
9 

8.0 
9-6 

II.  2 
12.8 
14-4 

15 

29  0 

0.4848 

0.5543 

i  .  8040 

75 

0.8746 

g 

61.0 

2 

3-0 

I 

2 

3 

4 
5 
6 

7 
8 
9 

0.4863 
0.4879 
0.4894 
0.4909 
0.4924 
0.4939 
0.4955 
0.4970 
0.4985 

16 
IS 
IS 
IS 
IS 
16 

IS 
IS 

0.5566 
0.5589 
0.5612 

0.5635 
0.5658 
0.5681 

0.5704 
0.5727 
0.57SO 

23 
23 
23 
23 
23 
23 
23 
23 

1.7966 
1.7893 
1.7820 

1.7747 
1.7675 
1.7603 
1-7532 
1.7461 
I-739I 

74 
73 
73 
73 
72 

72 

71 

71 

70 

0.8738 
0.8729 
0.8721 
0.8712 
o  .  8704 
0.8695 
0.8686 
0.8678 
0.8669 

9 
8 
9 
8 
9 
9 
8 
9 

9 
8 
7 
6 
5 
4 
3 

2 
I 

3 

4 
5 
6 
7 
8 
9 

4-5 
6.0 
7-5 
9.0 
10.5 

12.  0 

I3-S 

30  0 

0.5000 

0.5774 

i  •  7321 

70 

0.8660 

9 

60.0 

Cosin 

d. 

Cotan 

d. 

Tan 

d. 

Sin 

d. 

Deg. 

(239) 


TABLE  XXVII.  —  (Continued} 


Deg. 

Sin 

d. 

Tan 

d. 

Cotan 

d. 

Cosin 

d. 

P.P. 

30.0 

0.5000 

0.5774 

1.7321 

0^8660 

60.0 

I 

0.5015 

0.5797 

•  7251 

0.8652 

9 

a 

0.5030 

15 

0.5820 

23 

.7182 

69 

0.8643 

9 

8 

3 

0.5045 

IS 
15 

0.5844 

24 
23 

•  7113 

69 
68 

0.8634 

9 

7 

24 

4 

0.5060 

0.5867 

•  7045 

0.8625 

6 

I 

a.  4 

5 

0.507S 

15 

0.5890 

23 

.6977 

68 

0.8616 

y 

5 

a 

4-8 

6 

0.5090 

15 

O.S9I4 

24 

.6909 

68 

0.8607 

9 

4 

3 

7-2 

7 

0.5105 

0.5938 

.6842 

0.8599 

3 

| 

12.  0 

8 

0.5120 

15 

0.5961 

23 

•  6775 

67 

0.8590 

9 

a 

6 

14-4 

9 

0.5135 

15 

0.5985 

24 

.6709 

66 

0.8581 

y 

i 

7 

16.8 

31.0 

0.5150 

0.6009 

.6643 

66 

0.8572 

9 

59.0 

Q 

19.2 

21.6 

i 

0.5165 

0.6032 

•  6577 

0.8563 

9 

a 
3 

0.5180 
0.5I9S 

15 
IS 

0.6056 
0.6080 

24 
24 

.6512 
•  6447 

65 
65 

ftA 

0.8554 
0.8545 

y 

9 

8 
7 

I 

25 

2.5 

4 

0.5210 

0.6104 

.6383 

0.8536 

6 

a 

S.o 

5 

0.5225 

IS 

0.6128 

24 

•  6319 

64 

0.8526 

5 

3 

7-5 

6 

0.5240 

IS 
15 

0.6152 

24 
24 

•  6255 

64 
64 

0.8517 

y 

9 

4 

4 
5 

10.  0 
13.5 

7 

0.5255 

0.6176 

.6191 

0.8508 

3 

6 

15.0 

8 

0.5270 

15 

0.6200 

24 

.6128 

63 

0.8499 

y 

a 

7 

17.5 

9 

0.5284 

14 

0.6224 

24 

.6066 

62 
fi-* 

0.8490 

y 

i 

8 

20.  0 

32.0 

0.5299 

0.6249 

.6003 

62 

0.8480 

58.0 

i 

3 
3 

0.5314 
0.5329 
0.5344 

IS 
IS 
14 

0.6273 
0.6297 
0.6322 

24 
25 

24 

•  5941 
.5880 
.5818 

61 
62 
61 

0.8471 
0.8462 
0.8453 

9 
9 
10 

9 
8 

7 

I 

2 

26 

2.6 
5-2 

4 

0.5358 

0.6346 

•  5757 

0.8443 

6 

3 

7-8 

5 
6 

0.5373 
0.5388 

IS 

IS 
14 

0.6371 
0-6395 

25 

24 
25 

.5697 
.5637 

60 
60 
60 

0.8434 
0.8425 

y 

9 

10 

5 
4 

4 

I 

10.4 
13-0 
15-6 

7 

0.5402 

0.6420 

.5577 

0.8415 

3 

7 

18.2 

8 

0.5417 

IS 

0.6445 

25 

•  5517 

60 

0.8406 

y 

a 

8 

20.8 

9 

0.5432 

IS 

0.6469 

24 

•  5458 

59 

0.8396 

i 

y 

23.4 

33.0 

0.5446 

0.6494 

•  5399 

0.8387 

57.0 

i 

0.5461 

0.6519 

•  5340 

0.8377 

9 

15 

a 
3 

0.5476 
0.5490 

IS 
14 
IS 

0.6544 
0.6569 

25 
25 
25 

.5282 
•  5224 

58 
58 
58 

0.8368 
0.8358 

y 

10 
10 

8 
7 

a 
3 

IS 
3-0 
4-5 

4 

0.5505 

0.6594 

.5166 

0.8348 

6 

4 

6.0 

5 
6 

0.5519 
0.5534 

14 
IS 
14 

0.6619 
0.6644 

25 
25 
25 

.5108 
•  SCSI 

58 
57 
57 

0.8339 
0.8329 

y 

10 

9 

5 
4 

s 

6 

7 

7-5 
9-o 
10.  s 

7 

0.5548 

0.6669 

•  4994 

0.8320 

3 

8 

za.o 

8 

0.5563 

15 

0.6694 

25 

•  4938 

56 

0.8310 

a 

9 

13-5 

9 

0.5577 

14 

0.6720 

.4882 

So 

-6 

0.8300 

i 

34.0 

0.5592 

0.6745 

26 

.4826 

rfi 

0.8290 

56.0 

14 

i 
a 
3 

0.5606 
0.5621 
0.5635 

IS 

14 

15 

0.6771 
0.6796 
0.6822 

25 
26 

25 

.4770 
-47IS 
.4659 

55 

56 

54 

0.8281 
0.8271 
0.8261 

10 

10 

10 

9 
8 
7 

i 

2 

3 

4 

1.4 

2.8 

4-2 

5.6 

4 
5 

0.5650 
0.5664 

14 

0.6847 
0.6873 

26 

.4605 
•  4550 

55 

0.8251 
0.8241 

10 

6 
5 

s 

7-o 
8.4 
o  8 

6 

0.5678 

14 

0.6899 

26 

.4496 

54 

0.8231 

4 

§ 

7 

0.5693 

0.6924 

•  4442 

0.8221 

3 

9 

12.6 

8 

0-5707 

14 

0.6950 

.4388 

54 

0.8211 

3 

9 

0.5721 

14 

0.6976 

26 

-4335 

53 

0.8202 

y 

I 

35  0 

0.5736 

0.7002 

1.4281 

0.8192 

55  0 

Cosin 

d. 

Cotan 

d. 

Tan 

d. 

Sin 

d. 

Deg. 

(240) 


TABLE  XXVII.  —  (Continued) 


Deg. 

Sin 

d. 

Tan 

d. 

Cotan 

d. 

Cosin 

d. 

P.P. 

35.0 

0-5736 

0.7002 

26 

1.4281 

0.8192 

55.0 

i 

0.5750 

0.7028 

1.4229 

0.8181 

9 

a 

0.5764 

14 

0.7054 

26 

1.4176 

53 

0.8171 

8 

3 

0-5779 

15 

0.7080 

26 
27 

1.4124 

52 
53 

0.8161 

10 

7 

27 

4 

0.5793 

0.7107 

1.4071 

0.8151 

6 

i 

2.7 

5 
6 

0.5807 
0.5821 

14 
14 

0-7133 
0.7159 

26 
26 

27 

1.4019 
1.3968 

52 
51 
52 

0.8141 
0.8131 

10 
10 

5 

4 

2 
3 

4 

5-4 
8.1 
10.8 

7 

0.5835 

0.7186 

1.3916 

0.8121 

3 

s 

13-5 

8 

0.5850 

15 

0.7212 

26 

1.3865 

51 

0.8111 

2 

6 

16.2 

9 

0.5864 

14 

0.7239 

27 

o(\ 

1.3814 

51 

0.8100 

I 

7 
g 

18.9 

21   6 

36.0 

0.5878 

14 

0.7265 

1.3764 

0.8090 

54.0 

9 

24.3 

i 

0.5892 

14 

0.7292 

I.37I3 

0.8080 

9 

a 
3 

0.5906 
0.5920 

14 
14 

0.7319 
0.7346 

27 
27 

1.3663 
1.3613 

So 
50 
40 

0.8070 
0.8059 

II 

8 
7 

i 

28 

2.8 

4 

0.5934 

0-7373 

1.3564 

0.8049 

6 

2 

5-6 

S 
6 

0.5948 
0.5962 

14 
14 

0.7400 
0.7427 

2? 
2? 

i  35U 
1.3465 

SO 

49 

AQ 

0.8039 
0.8028 

II 

5 

4 

3 

4 
5 

8.4 

II.  2 
I4.O 

7 

0.5976 

0.7454 

1.3416 

0.8018 

3 

6 

16.8 

8 

0.5990 

14 

0.7481 

2? 

1.3367 

49 

0.8007 

2 

7 

19.6 

9 
37.0 

0.6004 

14 
14 

0.7508 

27 
28 

I.33I9 

49 
48 

0.7997 

II 

I 
53.0 

8 
9 

22.4 
25.2 

0.6018 

0.7536 

1.3270 

0.7986 

z 

0.6032 

14 

0.7563 

1.3222 

0.7976 

9 

2 

3 

0.6046 
0.6060 

14 
14 

0.7590 
0.7618 

27 
28 

28 

I.3I7S 
1.3127 

47 
48 
48 

0.7965 
0.79S5 

IO 

II 

8 

7 

i 

2 

2.9 
5-8 

4 

0.6074 

0.7646 

1.3079 

0.7944 

6 

3 

8.7 

S 

0.6088 

14 

0.7673 

27 

1.3032 

47 

0-7934 

5 

4 

II.  6 

6 

0.6101 

13 

14 

0.7701 

28 
28 

1.2985 

47 
47 

0.7923 

II 

4 

i 

17-4 

7 

0.6115 

0.7729 

1.2938 

0.7912 

3 

7 

20.3 

8 

9 

0.6129 
0.6143 

14 
14 

0.7757 
0.7785 

28 

28 

1.2892 
1.2846 

40 
46 

0.7902 
0.7891 

II 

2 
I 

8 
9 

3:? 

38.0 

0.6157 

14 

0.7813 

1.2799 

0.7880 

52.0 

i 

0.6170 

13 

0.7841 

1.2753 

4 

0.7869 

9 

14 

2 

0.6184 

14 

0.7869 

28 

1.2708 

45 

0.7859 

8 

2  8 

3 

0.6198 

14 

0.7898 

29 

1.2662 

46 

0.7848 

7 

3 

4.2 

4 

s 

0.6211 
0.6225 

13 

14 

0.7926 
0.7954 

28 

28 

1.2617 
1.2572 

45 
45 

0.7837 
0.7826 

II 

6 
5 

4 
5 

5.6 

7-0 

6 

0.6239 

14 

0.7983 

29 

1.2527 

45 

0.7815 

4 

7 

9.8 

7 

0.6252 

0.8012 

1.2482 

0.7804 

3 

8 

II.  2 

8 

0.6266 

14 

0.8040 

28 

1-2437 

45 

0.7793 

2 

9 

12.6 

9 

0.6280 

14 

0.8069 

29 

1.2393 

44 

0.7782 

I 

39.0 

0.6293 

13 

0.8098 

29 

1-2349 

0.7771 

51.0 

13 

I 

0.6307 

0.8127 

1.2305 

0.7760 

9 

i 

1:1 

2 

3 

o  .  6320 
0.6334 

13 
14 
J3 

0.8156 
0.8185 

29 
29 

29 

1.2261 
1.2218 

44 
43 
44 

0.7749 
0.7738 

II 
II 

8 
7 

3 

3.9 

r! 

4 

0.6347 

0.8214 

I.  2174 

0.7727 

6 

5 

6.5 

5 
6 

0.6361 
0.6374 

14 
13 

0.8243 
0.8273 

29 

30 

1.2131 
1.2088 

43 
43 

0.7716 
0.7705 

II 

S 
4 

6 

7 
8 

7-8 
9-1 
10.4 

7 

0.6388 

0.8302 

1.2045 

0.7694 

3 

9 

II.  7 

8 

o  .  6401 

13 

0.8332 

30 

1.2002 

43 

0.7683 

2 

9 

0.6414 

13 

0.8361 

29 

I  .  I960 

42 

0.7672 

I 

40  0 

0.6428 

0.8391 

I.I9I8 

0.7660 

5.0  0 

Cosin 

d. 

Cotan 

d. 

Tan 

d. 

Sin 

d. 

Deg 

(241) 


TABLE  XXVII.  —  (Continued) 


Deg. 

Sin 

d. 

Tan 

d. 

Cotan 

d. 

Cosin 

d. 

F 

.P. 

40.0 

0.6428 

0.8391 

1.1918 

0.7660 

50.0 

i 

2 

3 

4 
5 
6 

7 
8 
9 

0.6441 
0.6455 
0.6468 

0.6481 
0.6494 
0.6508 
0.6521 
0.6534 
0.6547 

14 
13 
13 
13 
14 
13 
13 
13 

0.8421 
0.8451 
0.8481 
0.8511 
0.8541 
0.8571 
0.8601 
0.8632 
0.8662 

30 
30 
30 
30 
30 
30 

30 

1.1875 
1-1833 
1.1792 
I.I750 
1.1708 
1.1667 
i  .  1626 
1.1585 
i.  1544 

42 
41 
42 
42 

41 
41 

0.7649 
0.7638 
0.7627 

0.7615 
0.7604 
0.7593 
0.7581 
0.7570 
0.7559 

ii 
ii 

12 
II 
II 
12 
II 
II 

9 
8 
7 
6 
5 
4 
3 

2 
I 

i 

2 

3 
4 
5 
6 
7 
8 

31 

9.3 
12.4 
15.5 
18.6 
21.7 
24.8 

41.0 

0.6561 

0.8693 

1.1504 

0.7547 

49.0 

9 

i 

2 
3 
4 
5 
6 

7 
8 
9 

0.6574 
0.6587 
0.6600 
0.6613 
0.6626 
0.6639 
0.6652 
0.6665 
0.6678 

13 
13 
13 
13 
13 
13 
13 
13 

0.8724 
0.8754 
0.8785 

0.8816 
0.8847 
0.8878 

0.8910 
0.8941 
0.8972 

30 
31 
31 

32 

1.1463 
1.1423 
1.1383 
i  -1343 
1.1303 
i  .  1263 
i  .  1224 
1.1184 
i.  1145 

40 
40 
40 
40 
40 
39 
40 
39 

0.7536 
0.7524 
0.7513 
0.7501 
0.7490 
0.7478 
0.7466 
0.7455 
0-7443 

12 
II 
12 
II 
12 
12 
II 
12 

9 
8 
7 
6 
5 
4 
3 

2 
I 

i 

2 

3 

4 

1 

7 
8 
9 

32 

3-2 
6.4 
9.6 

12.8 

16.0 
19.2 
22.4 
25.6 
28.8 

42.0 

0.6691 

0.9004 

1.1106 

0.7431 

48.0 

i 

2 

3 

4 
5 
6 

7 
8 
9 

0.6704 
0.6717 
0.6730 

0.6743 
0.6756 
0.6769 
0.6782 
0.6794 
0.6807 

13 
13 
13 
13 
13 
13 

12 
13 

0.9036 
0.9067 
0.9099 
0.9131 
0.9163 
0.9195 
0.9228 
0.9260 
0.9293 

32 
32 
32 
32 
33 
32 
33 

1.1067 
i  .  1028 
1.0990 
1.0951 
1.0913 
1.0875 

1.0837 
1.0799 
i  .  0761 

39 
38 
39 
38 
38 
38 
38 
38 

0.7420 
0.7408 
0.7396 
0.7385 
0.7373 
0.7361 

0.7349 
0.7337 
0.7325 

12 
12 
II 
12 
12 
12 
12 
12 

9 
8 
7 
6 
5 
4 
3 

2 
I 

i 

2 
3 
4 
5 
6 

I 

9 

33 

3-3 
6.6 
9-9 
13.2 
16.5 
19.8 

26.4 
29-7 

43.0 

0.6820 

0.0325 

1.0724 

0.7314 

12 

47.0 

i 

2 
3 
4 
5 
6 

7 
8 
9 

0.6833 
0.6845 
0.6858 

0.6871 
0.6884 
0.6896 
0.6909 
0.6921 
0.6934 

12 
13 

13 

13 
12 
13 

12 
13 

0.9358 
0-9391 
0.9424 

0.9457 
0.9490 
0.9523 
0.9556 
0.9590 
0.9623 

33 
33 
33 
33 
33 
33 
34 
33 

1.0686 
1.0649 
i.  0612 

1.0575 
1.0538 
i  .  0501 
1.0464 
1.0428 
1.0392 

37 
37 
37 
37 
37 
37 
36 
36 

0.7302 
0.7290 
0.7278 
0.7266 
0.7254 
0.7242 

0.7230 
0.7218 
0.7206 

12 
12 
12 
12 
12 
12 
12 
12 

9 
8 
7 
6 
5 
4 
3 

2 
I 

i 

2 

3 

4 
5 
6 
7 
8 
9 

34 

3-4 
6.8 

IO.2 

13.6 
17.0 
20.4 
23.8 
27.2 
30.6 

44.0 

0.6947 

0.9657 

1.0355 

0.7193 

12 

46.0 

13 

i 

2 
3 
4 

6 

7 
8 
9 

0.6959 
0.6972 
0.6984 

0.6997 
0.7009 
0.7022 

0.7034 
0.7046 
0.7059 

13 
12 
13 
12 
13 
12 

12 
13 

0.9691 
0.9725 
0-9759 

0.9793 
0.9827 
0.9861 
0.9896 
0.9930 
0.9965 

34 
34 
34 
34 
34 
35 
34 
35 

1.0319 
i  .  0283 
1.0247 

I.  0212 
I.OI76 
I.OI4I 
1.  01  05 

I.OO70 

1.0035 

36 
36 
35 
36 
35 
36 

35 
35 

0.7181 
0.7169 
0.7157 
0.7145 
0.7133 
0.7120 

0.7108 
0.7096 
0.7083 

12 
12 
12 
12 
13 
12 

12 
13 
12 

9 
8 
7 
6 
S 
4 
3 

2 
I 

i 
a 
3 

4 
5 
6 

I 

9 

1.3 

2.6 

3-9 

5-2 

6.5 

7-8 
9-1 
10.4 
n.  7 

45.0 

0.7071 

I.  0000 

I  .  0000 

0.7071 

45.0 

Cosin 

d. 

Cotan 

d. 

Tan 

d. 

Sin 

d. 

Deg. 

(242) 


TABLE  XXVIII.  —  NATURAL  VERSED  SINES  AND  EXTERNAL 
SECANTS 


Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

0.0 

.0000 

.0000 

5.0 

.0038 

.0038 

10.0 

.0152 

.0154 

15.0 

•  0341 

•  0353 

.1 

.0000 

.0000 

.1 

.0040 

.0040 

.j 

.0155 

.0157 

.1 

•  0345 

•  0358 

.2 

.0000 

.0000 

.2 

.0041 

.0041 

.2 

.0158 

.0161 

.2 

•  0350 

.0363 

3 

.0000 

.0000 

3 

.0043 

.0043 

3 

.0161 

.0164 

•  3 

•  0354 

.0367 

.4 

.0000 

oooo 

4 

.0044 

.0045 

.4 

.0164 

.0167 

•  4 

•  0359 

.0372 

•  5 

.0000 

.0000 

•  5 

.0046 

.0046 

•  S 

.0167 

.0170 

•  5 

.0364 

•  0377 

.6 

.0001 

.0001 

.6 

.0048 

.0048 

.6 

.0171 

.0174 

.6 

.0368 

.0382 

.7 

.0001 

.0001 

.7 

.0049 

.0050 

.7 

•  0174 

.0177 

.7 

•  0373 

.0388 

.8 

.0001 

.0001 

.8 

.0051 

.0051 

.8 

•  0177 

.0180 

.8 

•  0378 

•  0393 

.9 

.0001 

.0001 

•  9 

•  0053 

.0053 

•  9 

.0180 

.0184 

•9 

.0383 

.0398 

1.0 

.0002 

.0002 

6.0 

•  0055 

.0055 

11.0 

.0184 

.0187 

16.0 

.0387 

.0403 

.1 

.0002 

.0002 

.1 

.0057 

.0057 

.1 

.0187 

.0191 

.1 

•  0392 

.0408 

.2 

.0002 

.0002 

.2 

.0058 

.0059 

.2 

.0190 

.0194 

.2 

•  0397 

•  0413 

3 

.0003 

.0003 

3 

.0060 

.0061 

3 

.0194 

.0198 

3 

.0402 

.0419 

•  4 

.0003 

.0003 

4 

.0062 

.0063 

•  4 

.0197 

.0201 

•  4 

.0407 

.0424 

•  5 

.0003 

.0003 

•  5 

.0064 

.0065 

•  S 

.0201 

.0205 

•  5 

.0412 

.0429 

.6 

.0004 

.0004 

.6 

.0066 

.0067 

.6 

.0204 

.0209 

.6 

.0417 

•  0435 

.7 

.0004 

.0004 

•  7 

.0068 

.0069 

•  7 

.0208 

.0212 

-7 

.0422 

.0440 

.8 

.0005 

.0005 

.8 

.0070 

.0071 

.8 

.0211 

.O2l6 

.8 

.0427 

.0446 

•  9 

.0005 

.0005 

•9 

.0072 

.0073 

•9 

.0215 

.0220 

•  9 

.0432 

.0451 

2.0 

.0006 

.0006 

7.0 

.0075 

-0075 

12.0 

.0219 

.0223 

17.0 

•  0437 

.0457 

.1 

.0007 

.0007 

,i 

.0077 

.0077 

.1 

.0222 

.O227 

.1 

.0442 

.0463 

.2 

.0007 

.0007 

.2 

.0079 

.0079 

.2 

.0226 

.0231 

.2 

.0447 

.0468 

3 

.0008 

.0008 

3 

.0081 

.0082 

•  3 

.0230 

•0235 

3 

.0452 

.0474 

•4 

.0009 

.0009 

•  4 

.0083 

.0084 

•  4 

.0233 

.0239 

•  4 

.0458 

.0480 

.5 

.0010 

.0010 

5 

.0086 

.0086 

5 

.0237 

.0243 

•  5 

.0463 

.0485 

.6 

.0010 

.0010 

.6 

.0088 

.0089 

.6 

.0241 

.0247 

.6 

.0468 

.0491 

.7 

.OOII 

.0011 

•  7 

.0090 

.0091 

•  7 

.0245 

.0251 

.7 

•  0473 

•  0497 

.8 

.0012 

.0012 

8 

.0093 

.0093 

.8 

.0249 

.0255 

.8 

•  0479 

.0503 

•  9 

.0013 

.0013 

•  9 

.0095 

.0096 

•  9 

.0252 

.0259 

•  9 

.0484 

.0509 

30 

.0014 

.0014 

8.0 

.0097 

.0098 

13.0 

.0256 

.0263 

18.0 

.0489 

.0515 

.1 

.0015 

.0015 

.1 

.0100 

.OIOI 

.1 

.0260 

.0267 

.1 

•  0495 

.0521 

.2 

.0016 

.0016 

.2 

.0102 

.0103 

.2 

.0264 

.0271 

.2 

.0500 

•  0527 

3 

.0017 

.0017 

3 

.OIO5 

.0106 

3 

.0268 

.0276 

•  3 

.0506 

.0533 

•  4 

.0018 

.0018 

.4 

.010? 

.0108 

•  4 

.0272 

.0280 

•  4 

.0511 

.0539 

•  5 

.0019 

.0019 

•  5 

.OIIO 

.0111 

•  5 

.0276 

.0284 

•  5 

.051? 

.0545 

.6 

.0020 

.0020 

.6 

.OI  12 

.0114 

.6 

.0280 

.0288 

.6 

.0522 

•  0551 

.7 

.0021 

.0021 

•  7 

.OII5 

.0116 

•  7 

.0285 

.0293 

.7 

.0528 

.0557 

.8 

.0022 

.O022 

.8 

.0118 

.0119 

.8 

.0289 

.0297 

.8 

•  0534 

.0564 

•  9 

.0023 

.O023 

9 

.OI20 

.0122 

•9 

.0293 

.0302 

•9 

•  0539 

•  0570 

40 

.0024 

.OO24 

9.0 

.0123 

.0125 

14.0 

.0297 

.0306 

19.0 

.0545 

.0576 

.1 

.0026 

.0026 

.1 

.0126 

.0127 

.1 

.0301 

.0311 

.1 

•  0551 

.0583 

.2 

.0027 

.OO27 

.2 

.0129 

.0130 

.2 

.0306 

.0315 

.2 

.0556 

•  0589 

3 

.0028 

.0028 

•3 

.0131 

-0133 

•  3 

.0310 

.0320 

3 

.0562 

•  0595 

.4 

.0030 

.0030 

.4 

•  0134 

.0136 

•  4 

•  0314 

.0324 

•  4 

.0568 

.0602 

•  5 

.0031 

.0031 

.5 

•  0137 

•  0139 

5 

.0319 

•  0329 

•  5 

.0574 

.0608 

.6 

.0032 

.0032 

.6 

.0140 

.0142 

.6 

•  0323 

•  0334 

.6 

.0579 

.0615 

.7 

.0034 

.0034 

.7 

.0143 

.0145 

•  7 

.0327 

.0338 

.7 

.0585 

.0622 

.8 

.0035 

.0035 

.8 

.0146 

.0148 

.8 

•  03,32 

•  0343 

.8 

.0591 

.0628 

•  9 

.0037 

.0037 

•  9 

.0149 

.0151 

•  9 

.0336 

.0348 

.9 

.0597 

.0635 

5.0 

.0038 

.0038 

10.0 

.0152 

.0154 

15.0 

.0341 

-0353 

20.0 

.0603 

.0642 

(243) 


TABLE  XXVIII.  —  NATURAL  VERSED  SINES  AND  EXTERNAL 

SECANTS 


Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

20.0 

.0603 

.0642 

25.0 

•  0937 

.1034 

30.0 

.1340 

•  1547 

35.0 

.1808 

.2208 

.1 

.0609 

.0649 

.1 

.0944 

-1043 

.1 

.1348 

-1559 

.1 

.1819 

.2223 

.2 

.0615 

•  0655 

.2 

.0952 

.1052 

.2 

•  1357 

.1570 

.2 

.1829 

.2238 

•  3 

.0621 

.0662 

3 

•0959 

.1061 

3 

.1366 

.1582 

•  3 

.1839 

•  2253 

4 

.0627 

.0669 

4 

.0967 

.1070 

•  4 

.1375 

•  1594 

.4 

.1849 

.2268 

•  5 

-0633 

.0676 

•  5 

•  0974 

.1079 

•  5 

-1384 

.1606 

•  5 

.1859 

.2283 

.6 

.0639 

.0683 

.6 

.0982 

.1089 

.6 

•  1393 

.1618 

.6 

.1869 

.2299 

.7 

.0646 

.0690 

•  7 

.0989 

.1098 

.7 

.1401 

.1630 

•  7 

.1879 

.2314 

.8 

.0651 

.0697 

.8 

.0997 

.1107 

.8 

.1410 

.1642 

.8 

.1889 

.2329 

-9 

.0658 

•  0704 

•  9 

.1004 

.1117 

•  9 

.1419 

.1654 

•  9 

.1900 

•  2345 

21.0 

.0664 

.0711 

26.0 

.1012 

.1126 

31.0 

.1428 

.1666 

36.0 

.1910 

.2361 

.1 

.0670 

.0719 

.1 

.IO2O 

.1135 

.1 

•  1437 

.1679 

.1 

.1920 

.2376 

.2 

.0677 

.0726 

.2 

.1027 

.1145 

.2 

.1446 

.1691 

.2 

.1930 

.2392 

3 

.0683 

.0733 

•  3 

•1035 

.1155 

•  3 

•  1455 

.1703 

3 

.1941 

.2408 

•  4 

.0689 

.0740 

•  4 

•1043 

.1164 

•  4 

.1464 

.1716 

•  4 

.1951 

.2424 

•  5 

.0696 

.0748 

•  5 

.IO5I 

.1174 

•  5 

.1474 

.1728 

•  5 

.1961 

.2440 

.6 

.0702 

•  0755 

.6 

.1058 

.1184 

.6 

.1483 

.1741 

.6 

.1972 

.2456 

.7 

.0709 

.0763 

.7 

.1066 

.1194 

•  7 

.1492 

•  1753 

.7 

.1982 

.2472 

.8 

.0715 

.0770 

.8 

•  1074 

.1203 

.8 

.1501 

1766 

.8 

•1993 

.2489 

•  9 

.0722 

.0778 

.9 

.1082 

.1213 

•  9 

.1510 

.1779 

•  9 

.2003 

.2505 

22.0 

.0728 

.0785 

27.0 

.1090 

.1223 

32.0 

.1520 

.1792 

37.0 

.2014 

.2521 

.1 

•  0735 

•  0793 

.1 

.1098 

•  1233 

.1 

.1529 

.1805 

.1 

.2024 

.2538 

.2 

.0741 

.0801 

.2 

.1106 

•1243 

.2 

.1538 

.1818 

.2 

.2035 

•  2554 

3 

.0748 

.0808 

3 

.1114 

.1253 

3 

.1547 

.1831 

•  3 

•  2045 

.2571 

.4 

.0755 

.0816 

•  4 

.1122 

.1264 

•  4 

•  1557 

.1844 

•  4 

.2056 

.2588 

•  5 

.0761 

.0824 

•  5 

.1130 

•  1274 

•  5 

.1566 

.1857 

•  5 

.2066 

.2605 

.6 

.0768 

.0832 

.6 

.1138 

.1284 

.6 

.1575 

.1870 

.6 

.2077 

.2622 

.7 

•  0775 

.0840 

.7 

.1146 

.1294 

•  7 

.1585 

.1883 

.7 

.2088 

.2639 

.8 

.0781 

.0848 

.8 

.1154 

.1305 

.8 

•  1594 

.1897 

.8 

.2098 

.2656 

•  9 

.0788 

.0856 

•9 

.1162 

.1315 

.9 

.1604 

.1910 

•  9 

.2109 

.2673 

23.0 

•  0795 

.0864 

28.0 

.1171 

.1326 

33.0 

.1613 

.1924 

38.0 

.2120 

.2690 

.1 

.0802 

.0872 

.1 

.1179 

.1336 

.1 

.1623 

.1937 

.1 

.2131 

.2708 

.2 

.0809 

.0880 

.2 

.1187 

•  1347 

.2 

.1632 

.1951 

.2 

.2141 

.2725 

•  3 

.0816 

.0888 

•  3 

.1195 

•  1357 

•  3 

.1642 

.1964 

•3 

.2152 

•  2742 

.4 

.0822 

.0896 

•  4 

.1204 

.1368 

•  4 

.1652 

.1978 

•  4 

.2163 

.2760 

•  5 

.0829 

.0904 

5 

.1212 

•  1379 

•  5 

.1661 

.1992 

•  5 

•  2174 

.2778 

.6 

.0836 

.0913 

.6 

.I22O 

•  1390 

.6 

.1671 

.2006 

.6 

.2185 

.2796 

.7 

.0843 

.0921 

.7 

.1229 

.1401 

.7 

.1680 

.2020 

•  7 

.2196 

.2813 

.8 

.0850 

.0929 

.8 

•1237 

.1412 

.8 

.1690 

•2034 

.8 

.2207 

.2831 

•  9 

.0857 

.0938 

•  9 

•  1245 

.1423 

.9 

.1700 

.2048 

•  9 

.2218 

.2849 

24.0 

.0865 

.0946 

29.0 

.1254 

.1434 

34.0 

.1710 

.2062 

39.0 

.2229 

.2868 

.1 

.0872 

.0955 

.1 

.1262 

.1445 

.1 

.1719 

.2076 

.1 

.2240 

.2886 

.2 

.0879 

•  0963 

.2 

.1271 

-1456 

.2 

.1729 

.2091 

.2 

.2251 

.2904 

3 

.0886 

.0972 

3 

.1279 

.1467 

•  3 

•  1739 

.2IO5 

3 

.2262 

.2923 

.4 

.0893 

.0981 

•  4 

.1288 

.1478 

•  4 

•  1749 

.2120 

•  4 

•  2273 

.2941 

•  5 

.0900 

.0989 

•  5 

.1296 

.1490 

•  5 

•  1759 

•  2134 

•  5 

.2284 

.2960 

.6 

.0908 

.0998 

.6 

.1305 

.1501 

.6 

.1769 

•2149 

.6 

.2295 

•  2978 

.7 

.0915 

.1007 

.7 

-I3I4 

.1512 

.7 

.1779 

.2163 

•  7 

.2306 

.2997 

.8 

.0922 

.1016 

.8 

.1322 

-1524 

.8 

.1789 

.2178 

.8 

.2317 

.3016 

•  9 

.0930 

.1025 

.9 

.1331 

-1535 

•9 

.1798 

.2193 

•  9 

.2328 

•  3035 

25  0 

•  0937 

•  1034 

SO  0 

-1340 

.1547 

35.0 

.1808 

.2208 

40  0 

•  2340 

.3054 

(244) 


TABLE  XXVIII.  —  NATURAL  VERSED  SINES  AND  EXTERNAL 

SECANTS 


Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

40.0 
.1 

.2 

•3 

•4 
•  5 
.6 

.7 
.8 
•  9 
41.0 
.1 

.2 

3 

•  4 

!e 
.7 

.8 
.9 
42.0 

.1 

.2 

•3 

•4 

!e 

.7 
.8 
•  9 
43.0 
.1 

.2 

•3 

•  4 

!e 
.7 

.8 
•  9 
44.0 
.1 

.2 

•3 
•4 
•  5 
.6 

.7 
.8 
•  9 
46  0 

.2340 

•  3054 

45  0 

.1 

.2 
3 

•  4 
•  5 
.6 

•  7 
.8 
•  9 
46.0 
.1 

.2 

•3 

•  4 
•  5 
.6 

'.8 
•9 
47.0 
.1 

.2 

•3 

•  4 
•  5 
.6 

.7 
.8 
•  9 
48.0 

.1 

.2 
•3 

•  4 

.6 

.7 
.8 
•9 
49.0 
.1 

.2 
•3 

•4 
•  5 
.6 

.7 
.8 
•  9 
50.0 

.2929 

.4142 

50.0 

.1 

.2 

•3 

•  4 
•  5 
.6 

•  7 
.8 
•  9 
51.0 
.1 

.2 

•3 
4 
•  5 
.6 

•  7 
.8 
•9 
52.0 

.1 

.2 

3 

•  4 
•  5 
.6 

.7 
.8 
•  9 
53.0 
.1 

.2 

3 

•  4 

.6 

.7 
.8 
•9 
54.0 
.1 

.2 

•3 

•4 

'.6 

.7 
.8 
•  9 
55.0 

•  3572 

•  5557 

55.0 
.1 

.2 
•3 

•  4 
•  5 
.6 

•  7 
.8 
•  9 
56.0 
.1 

.2 

3 

•  4 
5 
.6 

•  7 
.8 
•  9 
57.0 

.1 

.2 
3 
•  4 
5 
.6 

•  7 
.8 
•  9 
58.0 
.1 

.2 

3 

•4 

.6 

.7 
.8 
•  9 
59.0 
.1 

.2 

•3 

•  4 
•  5 
.6 

.7 
.8 
•  9 
60.0 

.4264 

•  7434 

•  2351 
.2362 
•  2373 
•  2385 
.2396 
.2407 
.2419 
.2430 
.2441 

•  3073 
•  3093 
.3102 

•  3131 
•  3151 
•  3171 
•  3190 
.3210 
•  3230 

.2941 
•  2954 
.2966 

.2978 
.2991 
•  3003 
.3016 
.3028 
•  3041 

.4167 
.4192 
.4217 

.4242 
.4267 
.4293 
•  4318 
•  4344 
•  4370 

•  3586 
•  3599 
.3612 

.3626 
•  3639 
.3653 
.3666 
.3680 
•3693 

•  5590 
.5622 
.5655 
.5688 
•  5721 
•  5755 
•  5788 
.5822 
-5856 

.4279 
•  4293 
•  4307 
•  4322 
.4336 
•  4350 
.4365 
•  4379 
•  4394 

•  7478 
.7522 
•  7566 
.7610 
.7655 
.7700 

•  7745 
•  7791 
.7837 

.2453 

•  3251 

•  3053 

•  4396 

•  3707 

.5890 

.4408 

.7883 

.2464 
.2476 
.2487 

.2499 
.2510 
.2522 

•  2534 
.2545 
.2557 

.3270 
•  3291 
•3311 

•  3331 
•  3352 
•  3373 
•  3393 
-34I4 
•  3435 

.3066 
•  3079 
•3091 
.3104 
.3116 
•  3129 
.3142 
•  3155 
•  3167 

.4422 
•  4448 
•  4474 
•  4501 
•  4527 
•  4554 
•  4S8i 
.4608 
•  4635 

•  3720 
•  3734 
•  3748 
.376l 
•  3775 
.3789 
.3802 
.3816 
•  3830 

•  5925 
•  5959 
•  5994 
.6029 
.6064 
.6099 

.6i35 
.6171 
.6207 

•  4423 

•  4437 
•  4452 
.4466 
.4481 
•  4495 
•  4510 
•  4524 
•  4539 

.7929 
.7976 
.8023 
.8070 
.8118 
.8166 
.8214 
.8263 
.8312 

.2569 

-3456 

.3180 

.4663 

.3843 

.6243 

•  4554 

.8361 

.2580 
.2592 
.2604 
.2615 
.2627 
•  2639 
.2651 
.2663 
.2675 

•  3478 
•3499 
•  3520 

•  3542 
.3563 
.3585 
•  3607 
.3629 
•  3651 

.3193 
.3206 
.3218 

•  3231 

.3244 
•  3257 
.3270 
•  3283 
-3296 

.4690 
.4718 
.4746 

•  4774 
.4802 
.4830 

.4859 
.4887 
•  4916 

.3857 
•  3871 
.3885 

.3899 
.3912 
.3926 
•  3940 
•  3954 
-3968 

.6279 
.6316 
.6353 
•  6390 
.6427 
.6464 
.6502 
.6540 
-6578 

•  4568 
•  4583 
•  4598 
.4612 
.4627 
.4642 

•  4656 
.4671 
.4686 

.8410 
.8460 
.8510 
.8561 
.8612 
.8663 

.8714 
.8766 
.8818 

.2686 

.3673 

.3309 

•  4945 

.3982 

.6616 

•  4701 

.8871 

.2698 
.2710 
.2722 

•  2734 
.2746 
.2758 
.2770 
.2782 
•  2794 

.3696 
•  3718 
•  3741 
.3763 
•  3786 
•3809 
•  3832 
.3855 
.3878 

•  3322 
.3335 
.3348 
.336l 
•  3374 
.3387 
•  3400 
•  3413 
.3426 

•  4974 
•  5003 
.5032 
.5062 
.5092 
.5121 

.5151 
.5182 
.5212 

•3996 
.4010 
.4024 
.4038 
•  4052 
.4066 
.4080 
.4094 
.4108 

•  6655 
.6694 
.6733 
.6772 
.6812 
.6852 
.6892 
.6942 
.6972 

•  47i6 
•  4730 
•  4745 
.4760 
•  4775 
•  4790 
•  4805 
.4820 
.4835 

.8924 
•  8977 
-903I 
.9084 
•  9139 
.9194 
.9249 
•  9304 
.936o 

.2807 

.3902 

•  3439 

•  5243 

.4122 

•  7013 

•  4850 

.9416 

.2819 
.2831 
•  2843 

.2855 
.2868 
.2880 
.2892 
.2904 
.2917 

.3925 
•3949 
•  3972 

•3996 
.4020 
.4044 
.4069 
.4093 
.4118 

•  3453 
•  3466 
•3479 
•  3492 
.3506 
.3519 
•  3532 
•  3545 
•  3559 

•  5273 
•  5304 
•  5335 
•  5366 
•  5398 
.5429 
.5461 
•  5493 
•  5525 

.4136 
.4150 
.4165 

•  4179 
.4193 
.4207 

.4221 
.4236 
.4250 

•  7054 
.7095 
•  7137 

.7179 
.7221 
.7263 

•  7305 
•  7348 
•  7391 

.4865 
.4880 
.4895 
.4910 
•  4925 
.4940 

.4955 
•  4970 
.4985 

•  9473 
•  9530 
.9587 
.9645 
•  9703 
.9762 
.9821 
.9880 
-9940 

.2929 

.4142 

•  3572 

•  5557 

.4264 

•  7434 

.5000 

I.OOOO 

(245) 


TABLE  XXVIII.  —  NATURAL  VERSED  SINES  AND  EXTERNAL 
SECANTS 


Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

60.0 

.1 

.2 

•3 

•4 
•  5 
.6 

•  7 
.8 
•9 
61.0 
.1 

.2 
•  3 
•4 
•  5 
.6 

.7 
.8 
•  9 
62.0 
.1 

.2 
•3 

•  4 

!e 
.7 

.8 
•9 
63.0 
.1 

.2 

•  3 
•  4 
•  5 
.6 

•  7 
.8 
•  9 
64.0 
.1 

.2 

•  3 
•4 
•  5 
.6 

.7 
.8 
•  9 
65.0 

.5000 

I.  0000 

65.0 

.1 

.2 
•  3 

•  4 

'.6 

•  7 
.8 
•  9 
66.0 
.1 

.2 

•  3 

•4 
•  5 
.6 

.7 
.8 
•9 
67.0 
.1 

.2 

•  3 

•  4 

'.6 

.7 
.8 
•  9 
68.0 
.1 

.2 

•  3 

•4 

'.6 

.7 
.8 
•9 
69.0 
.1 

.2 

•3 

•  4 
•  5 
.6 

.7 
.8 
•9 
70.0 

•  5774 

1.3662 

70.0 
.1 

.2 

•  3 

•  4 
•  5 
.6 

•  7 
.8 
•  9 
71.0 
.1 

.2 
.3 

•  4 
•  5 
.6 

.7 
.8 
•9 
72.0 

.1 

.2 

•  3 

4 
•  5 
.6 

.7 
.8 
•9 
73.0 
.1 

.2 

3 

•  4 
•  5 
.6 

•  7 
.8 
•9 
74.0 
.1 

.2 

3 

•  4 
•  5 
.6 

.7 
.8 
9 
75  0 

.6580 

1.9238 

•  5015 
.5030 
.5045 
.5061 
•  5076 
.5091 
.5106 
.5121 
•  5137 

.0061 
.0122 
.0183 
.0245 
1.0308 
.0371 

.0434 
.0498 
.0562 

•  5790 
•  5805 
.5821 

.583? 
.5853 
.5869 
.5885 
•  5901 
.5917 

•  3751 
.3841 
•  3931 
.4022 
1.4114 
.4207 

•  4300 
•  4395 
.449° 

.6596 
.6613 
.6629 

.6645 
.6662 
.6678 

.6695 
.6711 
.6728 

•  9379 
•  9521 
.9665 
.9811 
1.9957 
2.0106 

.0256 
.0406 
.0561 

.5152 

1.0627 

•  5933 

•  4586 

.6744 

2.0716 

•  5167 
.5182 
•5198 

.5213 
.5228 
.5244 
.5259 
•  5274 
.5290 

.0692 
.0757 
.0824 

.0890 
1.0957 
.1025 

.1093 
.1162 
.1231 

•  5949 
.5965 
.5981 

•  5997 
.6013 
.6029 
.6045 
.6061 
.6077 

.4683 
.4780 
.4879 
.4978 
1.5078 
.5180 
.5282 
.5384 
.5488 

.6761 
•  6777 
.6794 
.6810 
.6827 
.6844 
.6860 
.6877 
.6893 

.0872 
.1030 
.1190 
.1352 
2.1515 
.1681 

.1848 
.2017 
.2188 

.5305 

.1301 

.6093 

1-5593 

.6910 

2  .  2361 

.5321 
.5336 
•5352 
.5367 
.5383 
•  5398 
.5414 
•  5429 
•  5445 

.1371 
.1441 
.1513 
.1584 
1.1657 
.1730 
.1803 
.1877 
.1952 

.6109 
.6125 
.6141 

.6157 
.6173 
.6189 

.6205 
.6222 
.6238 

.5699 
•  5805 
•  5913 
.6022 
1.6131 
.6242 

.6354 
.6466 
.6580 

.6926 
.6943 
.6960 

.6976 
.6993 
.7010 

.7026 
.7043 
.7060 

•2535 
.2712 
.2891 
.3072 
2.3255 
•3440 
.3628 
•3817 
.4009 

.5460 

i  .  2027 

.6254 

1-6695 

.7076 

2.4203 

.5476 
.5491 
•  5507 
•  5522 
•  5538 
•  5554 
.5569 
.5585 
.5601 

.2103 
.2179 
.2256 

•  2333 
1.2412 
.2490 

.2570 
.2650 
.2730 

.6270 
.6286 
.6303 
.6319 
.6335 
.6351 
.6367 
.6384 
.6400 

.6811 
.6927 
.7046 

.7165 
1.7285 
.7407 
.7529 
.7653 
.7778 

.7093 
.7110 
.7126 

•  7143 
.7160 
•  7177 

.7193 
.7210 
.7227 

•  4399 
•  4598 
•  4789 
.5003 
2.5209 
•  5418 
.5629 
.5843 
.6060 

.5616 

1.2812 

.6416 

.7904 

.7244 

2.6280 

.5632 
.5648 
.5663 

.5679 
.5695 
•  5711 
.5726 
•-5742 
•  5758 

.2894 
.2976 
.3060 

.3144 
1.3228 
•3314 
.3400 
.3486 
•  3574 

.6433 
.6449 
.6465 
.6482 
.6498 
•  6514 
.6531 
.6547 
.6563 

.8032 
.8161 
.8291 
.8422 
1.8554 
.8688 

.8824 
.8960 
.9099 

.7260 
.7277 
.7294 

.7311 

.7328 
•  7344 
.7361 
-7378 
•  7395 

.6502 
.6728 
.6955 
.7186 
2.7420 
.7657 

.7897 
.8140 
.8387 

•  5774 

1.3662 

.6580 

1.9238 

•  7412 

2.8637 

(246) 


TABLE  XXVIII.  —  NATURAL  VERSED  SINES  AND  EXTERNAL 
SECANTS 


Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

Angle 

Vers 

Exsec 

75.0 
.1 

.2 

•  3 

.4 
•  5 
.6 

.7 
.8 
•  9 
76.0 
.1 

.2 
•  3 
•  4 
.5 
.6 

.7 
.8 
•  9 
77.0 
.1 

.2 
•3 
.4 
•  5 
.6 

.7 
.8 
-9 
78.0 
.1 

.2 

•3 
•  4 
.5 
.6 

.7 
.8 
•  9 
79.0 
.1 

.2 
.3 
•  4 
•  5 
.6 

.7 
.8 
•  9 
80  0 

.7412 

2.8637 

80.0 
.1 

.2 
•3 
•  4 

!e 
j 

•9 
81.0 
.1 

.2 
•  3 

•4 
•  5 
.6 

.7 
.8 
•9 
82.0 

.1 

.2 
•  3 

M 
•  5 
.6 

.8 
•9 
83.0 
.1 

.2 

•3 

•4 
•  5 
.6 

•  7 
.8 
•  9 
84.0 
.1 

.2 

•3 
•4 

.6 

.8 
•9 
85.0 

.8264 

4-7588 

85.0 
.1 

.2 

•3 

•4 
•  5 
.6 

•  7 
.8 
•  9 
86.0 
.1 

.2 
•3 
•4 
•  5 
.6 

.7 
.8 
•  9 
87.0 
.1 

.2 

•3 

•4 
.5 
.6 

.7 
.8 
•  9 
88.0 
.1 

.2 

•3 

•4 

!e 
.7 

.8 
•  9 
89.0 
.1 

.2 
•3 
•4 
•  3 
.6 

•  7 
.8 
•9 
90.0 

.9128 

10.4737 

.7429 
.7446 
.7462 

•  7479 
.7496 
.7513 
•  7530 
•  7547 
.7564 

.8890 
.9147 
.9408 

.9672 
2.9939 
3.0211 

.0486 
.0765 
.1048 

.8281 
.8298 
.8315 
.8332 
.8350 
.8367 

.8384 
.8401 
.8418 

.8164 
•  8751 
•  9351 
.9963 
5.0589 
.1227 

.1880 
.2546 
.3228 

.9146 
•  9i63 
.9181 

.9198 
•9215 
.9233 
•  9250 
.9268 
.9285 

•  7073 
.9506 
11.2043 
.4690 
H.7455 
12.0346 

•  3371 
.6541 
•  9865 

.7581 

3.1336 

.8436 

5.3925 

•9302 

13.3356 

.7598 
.76iS 
.7632 

.7649 
.7666 
.7683 
.7700 
.7716 
•  7733 

.1627 
.1923 
.2223 

.2527 
3.2837 
.3150 

.3469 
•  3792 
.4121 

.8453 
.8470 
.8487 

.8505 
.8522 
.8539 
.8556 
.8574 
.8591 

.4637 
.5366 
.6111 

.6874 
5.7655 
.8454 
.9273 

6.0II2 

.0972 

.9320 
•9337 
•9355 
•  9372 
•  9390 
.9407 

.9424 
•  9442 
•  9459 

.7026 
14.0889 
.496i 
.9260 
15.3804 
.8616 
16.3720 
.9142 
17.4915 

•  7750 

3-4454 

.8608 

6.1853 

•  9477 

18.1073 

.7767 
.7785 
.7802 

.7819 
.7836 
.7853 
.7870 
.7887 
.7904 

•  4793 
.5137 
.5486 

.5841 
3.6202 
.6569 
.6942 
•  7320 
.7706 

.8626 
.8643 
.8660 

.8677 
.8695 
.8712 

.8729 
•8747 
.8764 

•  2757 
.3684 
.4635 
.5611 
6.6613 
.7642 
.8700 
.9787 
7-0905 

•  9494 
•9512 
.9529 
.9546 
.9564 
.9581 

•  9599 
.9616 
.9634 

.7656 
19.4709 
20.2285 
21.0444 

21  .  9256 
22.8802 
23.9179 
25.0499 
26.2898 

•  7921 

3-8097 

.8781 

7-2055 

.9651 

27.6537 

.7938 
•  7955 
•  7972 

.7989 
.8006 
.8023 
.8041 
.8058 
.8075 

.8496 
.8901 
•9313 
•9732 
4-0159 
•  0593 
.1034 
.1484 
.1942 

.8799 
.8816 
.8833 
.8851 
.8868 
.8885 

.8903 
.8920 
•  8937 

.3238 
•  4457 
•  5711 
.7004 
7.8337 
•  97ii 
8.1129 
•  2593 
.4105 

.9668 
.9686 
.9703 
.9721 
.9738 
•  9756 
•  9773 
•9791 
.9808 

29  .  1612 

30.8362 
32.7083 

34.8145 
37.2016 

39.9296 

43.0775 
46.7500 
51.0903 

.8092 

4.2408 

.8955 

8.5668 

.9825 

56.2987 

.8109 
.8126 
.8143 
.8160 
.8178 
.8195 
.8212 
.8229 
.8246 

.2883 
.3367 
.3860 

.4362 
4-4874 
.5396 
.5928 
.6470 
.7023 

.8972 
.8989 
.9007 
.9024 
.9042 
•9059 
.9076 
.9094 
.9111 

•  7283 
.8955 
9.0685 

.2477 
9-4334 
.6261 

.8260 
10.0336 
•  2493 

.9843 
.9860 
.9878 
•  9895 
•  9913 
•9930 
.9948 
.9965 
.9983 

62.6646 

70.6221 
80.8532 

94-4947 
H3.5930 
142.2406 
189.9868 
285.4795 
571.9581 

.8264 

4-7588 

.9128 

10.4737 

I.  0000 

00 

(247) 


248 


RAILROAD   FIELD   MANUAL 


TABLE  XXIX 


Seconds  in  decimals  of  a  degree 

Sec. 

Degree 

Sec. 

Degree 

Sec. 

Degree 

Sec. 

Degree 

Sec. 

Degree 

Sec. 

Degree 

i 

0.00028 

II 

0.00306 

21 

0.00584 

3i 

0.00862 

4i 

0.01139 

5i 

0.01417 

2 

0.00056 

12 

0.00334 

22 

0.00612 

32 

0.00890 

42 

0.01167 

52 

0.01445 

i 

0.00083 

13 

0.00361 

23 

0.00639 

33 

0.00917 

43 

0.01195 

53 

0.01473 

4 

O.OOIII 

14 

0.00389 

24 

0.00667 

34 

0.00945 

44 

O.OI222 

54 

0.01500 

5 

0.00139 

IS 

0.00417 

25 

0.00695 

35 

0.00973 

45 

0.01250 

55 

0.01528 

6 

0.00167 

16 

0.00445 

26 

o  .  00723 

36 

O.OIOOO 

46 

0.01278 

56 

0.01556 

7 

0.00195 

17 

0.00473 

27 

0.00751 

37 

0.01028 

47 

0.01306 

57 

0.01584 

8 

0.00222 

18 

0.00500 

28 

0.00778 

38 

0.01056 

48 

0-01334 

58 

0.01612 

9 

o  .  00250 

19 

0.00528 

29 

0.00806 

39 

0.01083 

49 

0.01361 

59 

0.01639 

10 

O.OO278 

20 

0.00556 

30 

0.00834 

40 

O.OIIII 

So 

0.01389 

60 

0.01667 

TABLE  XXX 


Minutes  in  decimals  of  a  degree 

Min. 

Degree 

Min. 

Degree 

Min. 

Degree 

Min. 

Degree 

Min. 

Degree 

Min. 

Degree 

i 

0.01667 

II 

0.18333 

21 

0.35000 

31 

0.51667 

4i 

0.68333 

5i 

0.85000 

2 

0.03333 

12 

0.2OOOO 

22 

0.36667 

32 

0.53333 

42 

0.70000 

52 

0.86667 

3 

0.05000 

13 

.21667 

23 

0.38333 

33 

0.55000 

43 

0.71667 

53 

0.88333 

4 

0.06667 

14 

•23333 

24 

0.40000 

34 

0.56667 

44 

0.73333 

54 

0.90000 

5 

0.08333 

IS 

.25000 

25 

0.41667 

35 

0.58333 

45 

0.75000 

55 

0.91667 

6 

O.IOOOO 

16 

.26667 

26 

0.43333 

36 

0.60000 

46 

0.76667 

56 

0.93333 

7 

0.11667 

17 

.28333 

27 

0.45000 

37 

0.61667 

47 

0.78333 

57 

0.95000 

8 

0.13333 

18 

.30000 

28 

0.46667 

38 

0.63333 

48 

0.80000 

58 

0.96667 

9 

0.15000 

19 

.31667 

29 

0.48333 

39 

0.65000 

49 

0.81667 

59 

0.98333 

10 

0.16667 

20 

•33333 

30 

0.50000 

40 

0.66667 

50 

0.83333 

60 

I.OOOOC 

From  Roberts'  "  Track  Formulae  and  Tables." 


CHAPTER   IV 
LOCATION  THEORIES  AND  TABLES 

FOR  problems  relating  to  improvements  of  existing  lines  exact  data 
and  volumes  of  discussion  of  methods  will  be  available.  The  methods 
here  suggested  are  for  use  in  locating  new  lines  for  which  precise  data 
respecting  motive  power,  business,  or  expense  are  indeterminate. 
Most  of  the  problems  will  relate  to  saving  in  operation  of  freight  trains. 
A  single  locomotive  may  be  assumed,  since  in  the  solution  of  problems 
the  results  will  be  practically  the  same  relatively  for  any  probable  differ- 
ences in  locomotives.  It  must  be  remembered  that  not  all  of  the  trains 
will  be  affected  by  probable  changes  in  ruling  grades;  the  engineer 
must  use  his  judgment  in  determining  what  trains  will  be  affected.  All 
trains  must  be  considered  in  estimating  the  cost  of  distance,  rise  and  fall, 
and  curvature.  The  formulas  given  in  what  follows  are  based  on  the 
full  discussion  of  the  subjects  in  the  author's  "Elements  of  Railroad 
Engineering." 

Tractive  Effort.  —  For  approximate  computations  the  tractive  effort 
of  a  locomotive  may  be  assumed  to  be 

~        146  # 

Tb  = — -<q — pounds, 

or  Tc  =     D    pounds, 

W 

or  Ta  — pounds  if  W  is  pounds, 

4-25 

in  which  H  is  the  square  feet  of  heating  surface. 
5  is  the  speed  in  miles  per  hour. 
P  is  the  mean  effective  pressure  in  the  cylinders. 
d   is  the  diameter  of  the  piston. 
L  is  the  length  of  the  stroke. 
D  is  the  diameter  of  the  drive  wheels. 
W  is  the  weight  on  the  drive  wheels. 

Tb  is  to  be  used  for  speeds  above  that  for  which  Tb  =  Tc  when  P  is 
85  per  cent  of  the  working  boiler  pressure,  and  is  known  as  the  boiler 

249 


250  RAILROAD  FIELD  MANUAL 

tractive  effort;  Ta  is  used  only  in  case  it  is  less  than  Tc  for  P  =  85  per 
cent  of  the  boiler  pressure.  It  is  the  tractive  effort  of  adhesion  and  all 
that  the  locomotive  can  exert  under  normal  conditions  regardless  of 
the  values  of  Tb  and  Tc.  Tc  is  called  the  cylinder  tractive  effort. 

W 
Ta  has  been  known  to  be  as  high  as  — ,  with  sand  on  the  track,  and 

W 
it  is  probably  as  low  as  —  under  unfavorable  conditions  of  track. 

5 

Theoretic  values  of  Tb  for  a  particular  consolidation  locomotive  are 
tabulated  in  Table  XXXIII. 

Resistance.  —  Resistance  to  motion  on  a  straight  level  track  varies 
with  speed  and  weight  per  car  of  train;  it  may  be  taken  from  Table 
XXXII.  Grade  resistance  or  acceleration  is  given  by  Rg  =  20  r,  in 
which  Rg  is  resistance  in  pounds  per  ton  and  r  is  the  rate  per  cent  of  grade 
expressed  as  a  whole  or  mixed  number;  thus  for  a  2  per  cent  grade  r  is 
2.0,  etc.  Curve  resistance  in  pounds  per  ton  varies  with  the  degree 
of  curve,  somewhat  with  speed,  being  less  as  the  speed  is  greater,  and 
with  the  rigid  wheel  base  of  the  car  or  locomotive.  It  may  be  averaged 
for  a  train  at 

Rc  =  0.4  +  0.35  D, 

in  which  Rc  is  curve  resistance  in  pounds  per  ton  and  D  is  the  degree 
of  curve.  This  is  an  empirical  equation  that  does  not  vanish  when 
D  is  o  as  it  should  to  be  mathematically  correct.  Ruling  grades  or 
others  likely  ever  to  become  ruling  because  of  the  curves  on  them  should 
be  reduced  or  "compensated"  in  rate  per  cent  through  all  curves  as 
follows:  For  i°  curves  reduce  0.04  per  cent;  for  curves  from  2°  to  4° 
reduce  0.03  D  per  cent;  for  curves  of  5°  and  over  reduce  0.025  ^  Per 
cent.  Greater  reductions  will  do  no  harm  unless  they  make  a  steeper 
ruling  grade  necessary. 

To  Find  the  Maximum  Load  a  Locomotive  can  Haul  on  a  Given 
Grade  at  a  Given  Speed.  —  From  Table  XXXII  find  the  train  resistance 
for  an  assumed  or  known  car  weight  at  the  given  speed;  add  the  grade 
resistance  =  20  r,  and  divide  the  tractive  effort  for  the  given  speed 
by  the  sum ;  subtract  the  weight  of  engine  and  tender.  The  values  for 
a  particular  consolidation  engine  are  tabulated  in  Table  XXXIV. 

Pusher  Grade. —  To  find  the  grade  up  which  two  similar  locomotives 
can  haul  the  load  that  one  can  haul  on  a  given  grade.  If  X  be  the  rate 
of  grade  sought, 


LOCATION  THEORIES  AND   TABLES  251 

in  which  Rt  is  train  resistance  in  pounds  per  ton,  T  is  the  tractive  effort 
of  one  locomotive,  W  is  the  weight  of  the  train  and  E  the  weight  of 
one  locomotive  and  tender  both  in  tons.  If  there  are  to  be  three 
locomotives  the  corresponding  pusher  grade  is 

2-857^-*, 


20 

To  Find  the  Length  of  Up  Grade  Required  to  Reduce  the  Speed  from 
Si  to  S2  Miles  an  Hour  for  a  Given  Locomotive  and  Train.  —  This 
is  the  so-called  momentum  or  velocity  grade  problem  and  finds  the 
length  of  grade  steeper  than  the  ruling  grade  that  can  still  be  operated 
if  a  sufficient  velocity  of  approach  may  be  had. 

Let  r  be  the  rate  of  the  grade  steeper  than  that  for  which  the  loco- 
motive is  loaded.  Find  the  tractive  effort  for  the  average  speed;  add 
the  weight  of  the  train  and  locomotive  for  gross  load  W  in  tons;  find 
the  train  resistance  Rt  for  the  train  at  the  average  speed;  find  the 
quantity 


find  the  velocity  heads  for  the  speeds  Si  and  52  from  Table  XXXI,  then 

difference  in  velocity  heads 
L  stations  = — = — , 

V  is  the  virtual  grade,  or  grade  that  the  locomotive  can  work  at  the 
given  speed  with  the  given  load.  If  the  steep  grade  differs  only  a  little 
from  the  ruling  grade  for  the  given  £2,  the  result  is  inaccurate  but  errs 
on  the  safe  side,  giving  a  grade  somewhat  shorter  than  true  theory 
indicates. 

Grades  for  Unbalanced  Traffic.  —  If  traffic  is  pretty  certain  to  be 
permanently  unbalanced  with  respect  to  direction  of  haul  the  grade 
against  the  lighter  traffic  may  be  steeper  than  that  against  the  heavier 
traffic  if  economy  of  construction  will  result.  The  same  number  of 
engines  and  cars  must  go  both  ways,  hence  the  lighter  traffic  trains 
will  have  a  higher  resistance  per  ton  because  the  average  car  weight 
will  be  less.  Having  the  ruling  grade  against  the  heavy  traffic  deter- 
mined, the  corresponding  grade  for  a  traffic  in  the  opposite  direction  is 
found  as  follows: 

Find  the  load  that  the  assumed  or  known  locomotive  can  haul  be- 
hind the  tender  at  a  speed  of  about  ten  miles  an  hour  on  the  ruling 
grade  against  the  heavy  traffic,  using  an  assumed  or  known  car  weight 
to  determine  train  resistance.  If  there  is  much  variation  in  the  traffic 


252  RAILROAD   FIELD   MANUAL 

subtract  the  weight  of  the  cars  (taken  at  about  18  tons  per  car  for  pre- 
liminary purposes)  from  the  load,  reduce  the  remaining  live  or  freight 
load  by  the  assumed  percentage  of  unbalancing,  add  the  car  weights 
and  get  the  new  total  load  and  average  car  weight.  Find  the  train 
resistance  for  the  new  car  weight.  If  Rt  be  that  resistance,  T  the 
tractive  effort  of  the  locomotive,  E  the  weight  of  engine  and  tender 
and  L  the  load  behind  the  tender,  then  the  grade,  G,  against  the  lighter 
traffic  may  be 


The  caboose  or  way  car  has  not  been  considered.  For  a  greater  degree 
of  precision  than  such  problems  generally  warrant  its  weight  should 
be  included  with  the  engine  weight  E. 

Elements  for  Estimating.  —  i .  Distance.  —  To  estimate  the  cost  of 
operating  extra  distance  or  the  saving  due  to  reducing  distance  assume 
a  probable  average  train  mile  cost  and  assume  a  number  of  trains  per 
day  over  the  distance  under  consideration.  All  trains  going  both  ways 
are  to  be  included.  Then  if  C  be  the  train  mile  cost  in  dollars,  M  the 
miles  of  extra  distance  under  consideration,  and  N  the  number  of 
daily  trains,  the  annual  cost  of  operating  the  M  miles,  or  the  annual 
saving  by  omitting  M  miles,  is  given  approximately  by 
K  =  156C-M-N 

for  moderate  changes  in  distance. 

The  limit  of  justifiable  expenditure  to  reduce  the  distance  in  miles 

g 

is  — ,  where  r  is  the  going  rate  of  interest  which  should  be  taken  some- 
what higher  than  the  nominal  rate  specified  in  the  company's  bonds. 
In  the  formula  it  should  be  used  as  a  decimal,  thus  8  per  cent  =  0.08. 
For  large  changes  in  long  lines  the  coefficient  may  be  increased  up  to, 
say,  315  for  a  change  involving  the  addition  of  a  whole  division. 

The  average  train  mile  cost  for  the  United  States  is  not  far  from  $1.55 
in  1914.  The  figures  for  the  year  have  not  been  computed  at  this 
writing.  The  cost  has  been  increasing  for  a  number  of  years,  but  recent 
economies  have  checked  this  increase  somewhat.  In  1908  the  average 
cost  was  about  $1.47.  The  Interstate  Commerce  Commission  divides 
the  country  into  three  great  districts  for  reporting  savings  and  expenses, 
the  Eastern,  Southern,  and  Western.  The  Eastern  district  comprises 
that  portion  of  the  country  bounded  on  the  west  by  the  northern  and 
western  shores  of  Lake  Michigan  to  Chicago,  thence  by  a  line  to  Peoria, 
thence  to  East  St.  Louis,  thence  down  the  Mississippi  River  to  the 


LOCATION  THEORIES  AND   TABLES 


253 


mouth  of  the  Ohio  River;  and  on  the  south  by  the  Ohio  River  from 
its  mouth  to  Parkersburg,  West  Virginia,  thence  by  a  line  to  the  south- 
western corner  of  Maryland,  thence  by  the  Potomac  River  to  its  mouth. 
The  Southern  district  comprises  the  territory  south  of  the  Eastern 
district  and  east  of  the  Mississippi  River.  The  Western  district  in- 
cludes the  remainder  of  the  United  States,  exclusive  of  Alaska  and  insu- 
lar possessions. 

The  Commission  also  divides  the  railroads  into  three  classes: 

I.  Roads  with  annual  gross  operating  revenues  of  $1,000,000  or 
more. 

II.  Roads  with  annual  gross  operating  revenues  of  $100,000  or  more 
but  less  than  $1,000,000. 

III.  Roads  with  annual  gross  operating  revenues  of  less  than  $100,000. 
Average  train  mile  costs  for  the  three  classes  in  the  three  districts 

may  be  taken  for  purposes  of  estimating  as  follows  (1914): 


District 

Class  I 

Class  II 

Class  III 

Eastern  
Southern  
Western     

$i.'6o 
1.38 
I  59 

$1.19 
I.  IS 
i  52 

$1.02 

I.IO 

I  45 

2.  Rise  and  Fall.  —  Rise  and  fall  between  any  two  points  is  the  total 
vertical  feet  of  rising  grade  with  its  corresponding  vertical  feet  of  fall. 
If  the  two  points  are  at  different  levels  it  requires  a  round  trip  to  realize 
the  rise  and  fall  due  to  this  difference.  In  calculating  the  cost  of  rise 
and  fall  as  between  two  lines,  only  the  cost  of  the  difference  in  rise  and 
fall  is  of  consequence  and  hence  the  following  rule  is  satisfactory  though 
inaccurate  for  a  train  going  one  way. 

To  find  the  rise  and  fall  between  two  points  add  all  vertical  feet  of 
rising  grades  and  all  vertical  feet  of  falling  grades  and  divide  by  two. 

Three  classes  of  rise  and  fall  are  recognized: 

Class  A.  Rise  and  fall  of  small  amounts  on  light  grades  apparently 
not  felt  by  the  locomotive,  requiring  no  apparent  change  in  effort,  only 
varying  the  speed  a  little. 

Class  B.  Rise  and  fall  requiring  the  full  power  of  the  locomotive 
in  the  ascent,  the  shutting  off  of  steam  in  the  descent,  but  no  use  of 
brakes. 

Class  C.  Rise  and  fall  requiring  the  whole  power  of  the  locomotive 
in  the  ascent  and  the  use  of  brakes  and  sometimes  of  sand  on  the  de- 
scent. 


254 


RAILROAD   FIELD  MANUAL 


If  Cbe  the  train  mile  cost,  N  the  number ,of  daily  trains  (all  trains 
both  ways)  and  /  the  number  of  feet  of  rise  and  fall,  the  annual  cost 
for  operation  may  be  estimated  as  follows  —  the  result  being  in  dollars. 

Class  A.     K!  =  0.25  f-C-N. 
Class  B.     Ki  =  i.2f-C-N. 

Class  C.     Ki  =  /  •  C  -  N  X  the  factor  of  the  following 
table. 


Grade..  . 

0.4 
and 

o  5 

o  67 

I   0 

1.5 

2  0 

2  5 

3  ° 

3  5 

4  ° 

under 

Cost  factor  

2.4 

2.9 

3-6 

4.2 

4-6 

4-8 

4-9 

S.o 

5.05 

S.I 

The  limit  of  justifiable  expenditure  to  reduce  the  rise  and  fall  by  / 
js- 

feet  is  — ,  where  r  is  the  going  rate  of  interest  which  should  be  some- 
what larger  than  the  rate  of  the  company's  bonds,  and  in  the  formula 
is  to  be  expressed  as  a  decimal,  i.e.,  8  per  cent  =  0.08. 

3.  Curvature.  —  If  C  be  the  train  mile  cost  and  N  the  number  of 
daily  trains  (all  trains  both  ways)  the  annual  operating  cost  saved  by 
eliminating  D  degrees  of  curvature  is  found  as  follows,  the  result  being 
in  dollars: 

K,  =  DC  (0.11^  +  2.55), 

and  the  limit  of  justifiable  expenditure  to  eliminate  D°  of  curvature 

•jr 
is  — -,  in  which  r  is  the  going  rate  of  interest  expressed  as  a  decimal  and 

should  be  somewhat  larger  than  that  carried  by  the  company's  bonds. 

4.  Ruling  Grade.  —  This  is  the  most  important  of  the  four  elements 
of  location.     The  value  of  reducing  the  ruling  grade  from  one  rate  to 
another  is  found  by  finding  the  saving  in  train  miles  due  to  the  larger 
loads  possible  on  the  lighter  grades  and  is  assumed  to  be  approximately 
proportional  to  the  reduction  in  number  of  train  miles.     The  ruling 
grade  determines  the  weight  of  train  for  the  whole  operating  division 
on  which  the  grade  occurs.     The  relative  number  of  trains  on  two 
different  ruling  grades  are  assumed  to  be  inversely  as  the  loads  behind 
the  tender.     To  find  the  load  behind  the  tender  see  page  259.     If  W 
be  the  train  weight  for  ruling  grade  g  and  W  be  the  train  weight  for 
ruling  grade  g'  and  if  N'  be  the  number  of  daily  trains  one  way  to  do  a 


LOCATION  THEORIES  AND  TABLES  255 

given  business  on  g',  the  number  of  trains  to  do  the  same  business  on  g 
will  be 

TT/y 

N  =  —  Nf 
W* 

If  g'  is  steeper  than  g,  the  saving  in  daily  trains  one  way  will  be  N'  —  Nf 
and  the  total  train  miles  saved  will  be  2  (AT  —  N)  L,  L  being  the 
length  of  the  division  in  miles.  Having  found  this,  substitute  in  the 
following  formula  for  annual  saving  due  to  reduction  in  ruling  grade 
from  g'  to  g,  C  being  the  train  mile  cost  on  g'. 

(W  —W      \ 
0.43  (Nf  -N)-  ^-^-  N). 

The  N's  of  the  foregoing  discussion  include  only  those  full  weight 
trains  affected  by  the  change.  If  the  grade  reduction  is  obtained  at 
the  expense  of  distance  the  extra  distance  should  be  figured  against  the 
improvement  considering  all  trains  to  be  run  on  the  g  grade  and  a  train 

mile  cost  somewhat  larger  than  C,  say  f  I  H ==-,  j  C,  which  supposes 

that  about  half  the  total  trains  may  be  affected.  Precision  is  im- 
possible. If  rise  and  fall  is  reduced  by  the  change  the  reduction  should 
be  credited  to  the  change  considering  all  trains  for  the  g'  grade  at  a  train 
mile  cost  of  C. 

Table  XXXV  gives  the  relative  number  of  trains  for  a  consolidation 
locomotive  for  various  grades.  To  use  it  for  a  reduction  from  an 
0.8  per  cent  grade  to  a  0.6  per  cent  grade,  there  being  10  daily  trains 
on  the  0.8  per  cent  grade,  divide  the  tabular  quantity  under  12  miles 
opposite  0.8  by  that  opposite  0.6  and  multiply  by  10.  In  any  problem 
the  maximum  hauling  capacity  would  probably  be  considered  and 
hence  the  lower  speeds.  For  fast  freights  slightly  higher  speeds  may 
be  considered.  The  limit  of  justifiable  expenditure  to  reduce  the  ruling 

grade  of  the  division  from  g'  to  g  is  — ,  in  which  r  is  the  going  interest 

rate  expressed  as  a  decimal  and  should  be  somewhat  larger  than  the 
nominal  rate  carried  by  the  company's  bonds. 

Cost  of  Pusher  Service.  —  When  helper  engines  must  be  maintained 
at  intermediate  points  on  a  line  the  annual  cost  in  dollars  may  be 
estimated  as  follows  if  the  helpers  can  be  kept  busy: 

K<  =  i55-N'M, 

in  which  N  is  the  number  of  trains  helped  daily  and  M  is  the  length 
of  the  pusher  incline  in  miles.  If  the  helper  engine  is  not  kept  busy, 
say,  making  100  miles  a  day,  the  part  of  100  miles  not  run  may  be 
estimated  to  cost  half  as  much  per  mile  as  the  miles  that  are  run. 


TABLE  XXXI.  —  VELOCITY  HEADS  IN  FEET  FOR  SPEED  IN  MILES 

PER  HOUR 

Formula:  h  =  0.035  sz' 


Speed 

0.0 

O.I 

0.2 

0-3 

0.4 

o.S 

0.6 

0.7 

0.8 

0.9 

0 

o.oo 

o.oo 

O.OO 

o.oo 

O.OI 

O.OI 

O.OI 

0.02 

O.O2 

0.03 

i 

0.03 

0.04 

0.05 

0.06 

0.07 

0.08 

0.09 

O.IO 

O.II 

0.13 

2 

0.14 

0.15 

0.17 

0.19 

0.2O 

O.22 

0.24 

0.26 

0.2? 

0.29 

3 

0.31 

0.34 

0.36 

0.38 

0.40 

0.43 

0.45 

0.48 

0.51 

0.53 

4 

0.56 

o.59 

0.62 

0.65 

0.68 

0.71 

0.74 

0-77 

0.81 

0.84 

5 

0.87 

0.91 

0.95 

0.98 

1.02 

1.  06 

I.IO 

1.14 

1.18 

1.22 

6 

1.26 

1.30 

1-35 

1.39 

1-43 

MB 

1.52 

1-57 

1.62 

1.67 

7 

1.72 

1.76 

1.81 

1.87 

1.92 

1.97 

2.02 

2.08 

2.13 

2.18 

8 

2.24 

2.30 

2.35 

2.41 

2.47 

2.53 

2.59 

2.65 

2.71 

2.77 

9 

2.84 

2.90 

2.96 

3-03 

3-09 

3-16 

3-23 

3-29 

3-36 

3-43 

10 

3-50 

3-57 

3-64 

3-71 

3-79 

3-86 

3-93 

4.01 

4-08 

4-16 

ii 

4-24 

4.3i 

4-39 

4-47 

4-55 

4-63 

4-71 

4-79 

4-87 

4-96 

12 

5-04 

5-12 

5-21 

5-29 

5-38 

5-47 

5-56 

5.65 

5-73 

5-82 

13 

5-91 

6.01 

6.10 

6.19 

6.28 

6.38 

6.47 

6.57 

6.66 

6.76 

14 

6.86 

6.96 

7.06 

7.16 

7.26 

7-36 

7.46 

7-56 

7-67 

7-77 

IS 

7.8? 

7-98 

8.09 

8.19 

8.30 

8.41 

8.52 

8.63 

8-74 

8.85 

16 

8.96 

9-07 

9.18 

9-30 

9.41 

9-53 

9.64 

9-76 

9.88 

10.  OO 

17 

10.  II 

10.23 

10.35 

10.47 

10.  60 

10.72 

10.84 

10.97 

11.09 

II.  21 

18 

11-34 

11.47 

H.59 

11.72 

11.85 

11.98 

12.  II 

12.24 

12.37 

12.50 

19 

12.64 

12.77 

12.90 

13-04 

13-17 

13.31 

13-45 

13-58 

13.72 

13.86 

20 

14.00 

14.14 

14.28 

14.42 

14-57 

14-71 

14-85 

15.00 

15.14 

15.29 

21 

lS-44 

15.58 

15-73 

15.88 

16.03 

16.18 

16.33 

16.48 

16.63 

16.79 

22 

16.94 

17.10 

17.25 

17.41 

17.56 

17.72 

17.88 

18.03 

18.19 

18.35 

23 

18.52 

18.68 

18.84 

19.00 

19.17 

19-33 

19.50 

19.66 

19.82 

19.99 

24 

20.16 

20.33 

20.50 

20.67 

20.84 

21.01 

21.18 

21.35 

21.53 

21.70 

25 

21.88 

22.05 

22.22 

22.40 

22.58 

22.76 

22-94 

23.12 

23-30 

23.48 

26 

23.66 

23.84 

24.03 

24.21 

24.40 

24.58 

24.77 

24-95 

25.14 

25-33 

27 

25.52 

25.70 

25.90 

26.09 

26.28 

26.47 

26.66 

26.86 

27.05 

27.25 

28 

27-44 

27.64 

27.83 

28.03 

28.23 

28.43 

28.63 

28.83 

29.03 

29-23 

29 

29.44 

29-64 

29.84 

30-05 

30.25 

30.46 

30.67 

30.88 

31-08 

31.29 

30 

3L50 

3L7I 

31.92 

32.13 

32.35 

32.56 

32.78 

32.98 

33-20 

33-42 

31 

33.64 

33-85 

34.07 

34-29 

34-51 

34-73 

34-96 

35-18 

35-40 

35-62 

32 

35.84 

36.06 

36.29 

36.52 

36.74 

36.97 

37-19 

37-42 

37-65 

37-88 

33 

38.ll 

38.34 

38.58 

38-81 

39-05 

39-27 

39-51 

39-75 

39-98 

40.22 

34 

40.46 

40.70 

40-94 

41.18 

41.42 

41.66 

41.90 

42.14 

42.38 

42.63 

35 

42.87 

43-12 

43-37 

43-61 

43-86 

44-11 

44.36 

44-61 

44-86 

45-11 

36 

45.36 

45.6i 

45-87 

46.12 

46.38 

46.63 

46.88 

47-14 

47-40 

47-66 

37 

47-91 

48.18 

48.43 

48.70 

48.96 

49-22 

49-48 

49-74 

50.01 

50.28 

38 

50.54 

50.81 

51.08 

51-34 

51.61 

51-88 

52.16 

52-42 

52.69 

52.96 

39 

53-24 

53-51 

53  78 

54.o6 

54-34 

54.6i 

54-89 

55.17 

55-44 

55-72 

0.0 

I.O 

2.0 

30 

4.0 

So 

6.0 

7.0 

8.0 

9.0 

40 

56.00 

58.84 

61.74 

64.72 

67-76 

70.88 

74.06 

77-32 

80.64 

84.03 

50 

87.50 

91-03 

94.64 

98-31 

102.06 

105-77 

109.75 

"3.72 

117.74 

121.83 

60 

126.00 

130.23 

134-54 

138.92 

143.36 

147-87 

152.45 

I57-II 

161.84 

166.63 

70 

171.50 

176.45 

181.44 

186.52 

191-65 

196.88 

202.16 

207.52 

212.94 

218.42 

80 

224.00 

229.60 

235-33 

241  .  10 

246.95 

257-88 

258.84 

264.91 

271.04 

277.22 

90 

283.50 

289.82 

296.23 

302.70 

309-25 

315.86 

322.55 

329-31 

336.15 

343-05 

100 

350.00 

Note.  —  For  the  table  the  theoretical  heads  have  been  increased  4.63  per  cent 
for  the  energy  of  the  rotating  wheels. 

(256) 


LOCATION  THEORIES  AND   TABLES 


257 


TABLE  XXXI I.  — TRAIN  RESISTANCE  AT  DIFFERENT  SPEEDS  AND 
FOR  TRAINS  OF  VARIOUS  AVERAGE  CAR  WEIGHTS 


Speed, 
miles 

Train  resistance,  pounds  per  ton  * 

Speed, 
miles 

per 

15 

20 

25 

30 

35 

40 

45 

So 

55 

60 

65 

70 

75 

per 

hour 

tons 

tons 

tons 

tons 

tons 

tons 

tons 

tons 

tons 

tons 

tons 

tons 

tons 

hour 

5 

7.6 

6.8 

6.0 

5-4 

4-8 

4-4 

4.0 

3-7 

3-5 

33 

3-2 

3i 

3-0 

5 

6 

7-7 

6-9 

6.1 

5-5 

4-9 

4-4 

4-1 

3-8 

3-5 

33 

3-2 

3-1 

3-0 

6 

7 

7.8 

7-0 

6.2 

5.5 

5-0 

4-5 

4-1 

3-8 

3-6 

3-4 

3-2 

3-1 

3-1 

7 

8 

8.0 

7-1 

6.3 

5-6 

S.o 

4-6 

4.2 

3-9 

3-6 

3-4 

3.3 

3-2 

31 

8 

9 

8.1 

7-2 

6-4 

5-7 

5-1 

4-6 

4.2 

3-9 

3-6 

3-4 

3.3 

3-2 

31 

9 

10 

8.2 

7-3 

6.5 

5.8 

5.2 

4-7 

4-3 

4-0 

3-7 

3-5 

3.3 

3-2 

3-2 

zo 

ii 

8.3 

7-4 

6.6 

5-9 

5-3 

4.8 

4-3 

4.0 

3-7 

3-5 

3-4 

3-3 

3-2 

zz 

12 

8.4 

7-5 

6.7 

6.0 

5-4 

4-8 

4-4 

4.0 

3-8 

3-6 

3-4 

3-3 

3-3 

12 

13 

8.6 

7-6 

6.8 

6.1 

5-5 

4-9 

4-5 

4-1 

3-8 

3-6 

3-5 

3-4 

3-3 

13 

14 

8.7 

7-8 

6-9 

6.2 

55 

S.o 

4-5 

4-2 

3-9 

3-7 

3-5 

3-4 

3-4 

14 

15 

8.8 

7-9 

7-0 

6.3 

5.6 

5-1 

4-6 

4-2 

3-9 

3-7 

3-6 

3-5 

3-4 

IS 

16 

9.0 

8.0 

7-1 

6-4 

5-7 

5-1 

4-7 

4-3 

4.0 

3-8 

3-6 

3-5 

3-5 

z6 

17 

9-1 

8.1 

7-2 

6.5 

5-8 

5-2 

4-8 

4-4 

4.1 

3-9 

3-7 

3-6 

3-5 

17 

18 

9-3 

8.3 

7-4 

6.6 

5-9 

5-3 

4.8 

4-5 

4-1 

3-9 

3-7 

3-7 

3-6 

18 

19 

9-4 

8.4 

7-5 

6.7 

6.0 

5-4 

4-9 

4-5 

4.2 

4.0 

3-8 

3-7 

3-6 

19 

20 

9.6 

8.5 

7-6 

6.8 

6.1 

5-5 

5-0 

4.6 

4-3 

4-0 

3-9 

3-8 

3-7 

20 

21 

9-7 

8.7 

7-7 

6.9 

6.2 

5-6 

5-1 

4-7 

4-3 

4.1 

3-9 

3-9 

3-8 

2Z 

22 

9-9 

8.8 

9r\ 

7-9 
8.0 

7.0 

7T 

6-3 
6.4 

5-7 
5-8 

5-2 
57 

4-8 

4-4 

4-2 

4.0 

3-9 

3-8 

22 

23 

24 

IO.2 

•U 

8.1 

80 

•  A 

7-3 

7      A 

6^6 

6  7 

5-9 
6  o 

•O 

5-4 

S{- 

4-9 

4.6 

4-3 

4-2 

4-1 

4-0 

34 

25 

26 

IO-4 

10.5 

9-4 

•3 

8.4 

•4 
7-5 

u./ 

6.8 

6.1 

•o 

5-6 

S-i 

4-8 

4-5 

4-3 

4-2 

4-0 
4-1 

26 

27 

28 

10  7 

9-6 

9*7 

8.5 

8  7 

7-7 
7  8 

6-9 

7.0 

6.2 

5-7 

c    8 

5-2 
57 

4-8 
A  a 

4-6 

4-4 

4-3 

4-2 

27 

28 

29 

II.  I 

•  / 

9-9 

o.  / 

8.8 

9A 

/  *° 

7-9 

8  o 

7-1 

6.5 
6  6 

o.o 

5-9 

•O 

5-4 

4*  y 
S.o 

4-8 

4.6 

4-5 

4-4 

39 

3° 
31 

11.3 
II.  4 

10.2 

•O 

8.2 

7-3 
7-4 

6.7 

6.1 

5-6 

5-2 

S.o 

4-8 

4-6 

4-5 
4-5 

30 

31 

32 

ii.  6 

10.4 

9-3 

8.3 

7-5 

6.8 

6.2 

5-8 

5.3 

S.o 

4-9 

4-7 

4.6 

33 

33 

ii.  8 

10.  S 

9-4 

8.5 

7-6 

7.0 

6.3 

5-9 

5.4 

5-2 

S.o 

4-8 

4-7 

33 

34 

12.0 

10.7 

9-6 

8.6 

7-8 

7-i 

6.5 

6.0 

5.5 

5-3 

5-1 

4-9 

4-8 

34 

35 

12.3 

10.9 

9-7 

8.8 

7-9 

7-2 

6.6 

6.1 

5.7 

5-4 

5-2 

S.o 

4-9 

35 

36 

12.5 

ii.  i 

9-9 

8.9 

8.0 

7-4 

6.7 

6.2 

5-8 

S-S 

5-3 

S-i 

5-0 

36 

37 

12.7 

II.  2 

IO.O 

9-0 

8.2 

7-5 

6-9 

6-4 

5-9 

5-6 

5-4 

52 

5-1 

37 

38 

12.9 

II.  4 

IO.2 

9-2 

8.3 

7-6 

7-0 

6.5 

6.0 

5-7 

5-5 

5-3 

5-2 

38 

39 

13.1 

ii.  6 

10.4 

9-4 

8.5 

7.8 

7-1 

6.6 

6.2 

5.8 

5.6 

5-4 

S3 

39 

40 

13.4 

ii.  8 

10.6 

9-5 

8.6 

7-9 

7-3 

6.8 

6.3 

6.0 

5-7 

5-6 

5-5 

40 

*  Column  headings  indicate  the  average  car  weights. 


This  table  from  experiments  of  Professor  Edward  C.  Schmidt  of  the  University  of 
Illinois.    See  Transactions  of  the  American  Society  of  Mechanical  Engineers  for  1910, 


258 


RAILROAD   FIELD  MANUAL 


TABLE  XXXIII 

TRACTIVE  EFFORT  IN  POUNDS  OF  THE  CONSOLIDATION  LOCOMOTIVE, 
HAVING  THE  CHARACTERISTICS  GIVEN  BELOW,  FOR  DIFFERENT  SPEEDS. 
NEAREST  50  POUNDS 


Speed 

0.0 

10.  0 

20.0 

30.0 

0.0 

50,000 

28,000 

18,650 

o.S 

50,000 

27,350 

18,350 

x.o 

50,000 

26,700 

18,050 

I.S 

48,700 

26,050 

17,800 

2.0 

46,700 

25,450 

17,500 

25 

44,800 

24,900 

17,250 

3<> 

43,100 

24,350 

16,950 

35 

09 

41,500 

23,850 

16,700 

4-0 

1 

40,000 

23,350 

16,500 

45 

g 

38,650 

22,850 

16,250 

5-0 

Q 

37,350 

22,4OO 

16,000 

55 

8 

36,150 

21,950 

15,800 

6.0 

v> 

35,000 

21,550 

15,550 

6.5 

33,950 

21,150 

15,350 

7.0 

32,950 

20,750 

15,150 

7.5 

32,000 

20,350 

14,950 

8.0 

31,100 

20,000 

14,750 

8.5 

30,300 

19,650 

14,550 

9.0 

29,500 

19,300 

14,350 

9-5 

28,750 

19,000 

14,200 

Consolidation  locomotive. 

Weight  on  drivers:  210,000  pounds. 

Weight  of  engine  and  tender:  400,000  pounds. 

Cylinders:  28"  diam.  by  32"  stroke. 

Heating  surface:  3837  sq.  ft. 

Diameter  drive  wheels:  63". 

Boiler  working  pressure:  163  pounds. 

For  this  locomotive: 

Te  =  55,174  pounds  (say  55,000  pounds); 

To,  =  49,412  pounds  (say  50,000  pounds); 

Tt  =  50,000  pounds  at  1 1. 2  mi./hr.,  and  as 
To  limits  the  effort,  this  will  be 
taken  as  constant  and  equal  to 
50,000  pounds  at  speeds  below  IX 
mi./hr. 


LOCATION  THEORIES  AND  TABLES 


259 


TABLE  XXXIV 

NET  LOADS  IN  TONS  OF  2000  POUNDS  BEHIND  THE  TENDER  OF  THE 
CONSOLIDATION  LOCOMOTIVE  OF  TABLE  XXXIII,  ON  GIVEN  GRADES  AT 
GIVEN  SPEEDS 


*\"  Speed 

Grade" 

Under 
II  mi 

15 

30 

35 

30 

35 

40 

o.oo 

11430 

79i8 

5400 

3873 

2908 

2224 

I?l8 

.05 

9234 

6468 

446? 

3246 

2464 

1905 

1487 

.10 

7736 

5458 

3800 

2787 

2131 

1660 

1305 

.15 

6650 

4714 

3300 

2435 

1872 

1467 

"59 

.30 

5825 

4142 

2911 

2158 

1665 

1310 

1039 

.35 

5177 

3690 

2600 

1934 

1495 

"79 

938 

•30 

46SS 

3323 

2346 

1748 

1354 

1070 

853 

35 

4225 

3019 

2134 

1592 

1235 

977 

779 

40 

3866 

2764 

1954 

1459 

1132 

896 

715 

•45 

3S6o 

2546 

1800 

1345 

1043 

826 

659 

•So 

3297 

2358 

1667 

1245 

966 

764 

609 

•55 

3068 

2194 

1550 

1158 

897 

709 

565 

.60 

2868 

2050 

1447 

1080 

836 

660 

525 

.65 

2691 

1922 

1356 

IOII 

782 

616 

490 

.70 

2533 

1808 

1274 

949 

733 

577 

457 

•75 

2391 

1706 

1200 

893 

688 

541 

428 

.80 

2263 

1613 

1  133 

842 

648 

508 

401 

.85 

2148 

1529 

1073 

795 

6" 

478 

376 

-90 

2042 

1453 

1017 

753 

577 

450 

353 

•95 

1946 

1382 

967 

714 

546 

425 

332 

1.  00 

1858 

1318 

920 

678 

517 

401 

3X3 

05 

1776 

1259 

877 

645 

491 

380 

295 

.10 

1702 

1204 

837 

6i5 

466 

359 

278 

•  IS 

1632 

1153 

800 

586 

443 

341 

262 

.30 

1567 

1106 

765 

559 

422 

323 

247 

.35 

1507 

1062 

733 

534 

402 

306 

233 

•30 

1450 

1020 

703 

5ii 

383 

291 

220 

•35 

1398 

982 

675 

489 

365 

276 

208 

.40 

1348 

946 

649 

469 

348 

262 

197 

•45 

1302 

911 

624 

449 

333 

249 

186 

•  50 

1258 

879 

600 

431 

3i8 

237 

175 

•  55 

1217 

849 

578 

414 

304 

226 

1  66 

.60 

1178 

820 

557 

397 

291 

214 

156 

.65 

1141 

793 

537 

382 

278 

204 

147 

.70 

1106 

768 

5i8 

367 

266 

194 

139 

•75 

1072 

743 

500 

353 

255 

185 

131 

.80 

1041 

720 

483 

340 

244 

176 

123 

.85 

IOII 

698 

467 

327 

234 

167 

"6 

•  90 

982 

677 

451 

315 

224 

159 

109 

•  95 

955 

657 

436 

303 

214 

151 

102 

3.00 

929 

637 

422 

292 

205 

143 

96 

The  average  car  weight  for  this  table  Is  45  tons. 


TABLE  XXXV.  —  RELATIVE  NUMBER  OF  TRAINS  TO  DO  THE  SAME 
BUSINESS  TONNAGE  ON  DIFFERENT  GRADES,  FOR  DIFFERENT  SPEEDS. 
COMPUTED  FROM  TABLE  XXXIV 


^-•v^Speed 
Grade^^ 

Under 
ii  mi. 

15 

20 

25 

30 

35 

40 

0.00 

0.34 

0.49 

0.72 

.00 

1-33 

•  74 

2.25 

0.05 

0.42 

0.60 

.87 

•  19 

1-57 

•03 

2.60 

O.IO 

0.50 

0.71 

.02 

•  39 

1.81 

-33 

2.96 

0.15 

0.58 

0.82 

•  17 

•59 

2.07 

.64 

3  34 

O.2O 

0.66 

0.93 

33 

•79 

2.32 

•95 

3.72 

0.25 

0.75 

1.05 

•49 

.00 

2-59 

3.29 

4.12 

0.30 

0.83 

1.16 

-65 

.21 

2.86 

3-6i 

4-53 

0-35 

0.92 

1.28 

.81 

•  43 

3.13 

3.96 

4-96 

0.40 

.00 

1.40 

•98 

•  65 

3-42 

4-31 

5-41 

0-45 

.09 

1.52 

-15 

.87 

3-71 

4.68 

5.87 

0.50 

-17 

1.64 

•  32 

3-  II 

4.00 

5.o6 

6.35 

0.55 

.26 

1.76 

•49 

3-34 

4-31 

5-45 

6.84 

0.60 

•  35 

1.89 

2.67 

3-58 

4.62 

5.86 

7.36 

0.65 

•44 

2.01 

2.85 

3.82 

4-94 

6.28 

7-89 

0.70 

•  53 

2.14 

3  03 

4.07 

5.27 

6.70 

8.46 

0.75 

.62 

2.27 

3-22 

4-33 

5.62 

7.15 

9  03 

0.80 

•  71 

2.40 

3-41 

4-59 

5-97 

7-61 

9.64 

0.85 

.80 

2.53 

3.6o 

4.86 

6.33 

8.09 

10.28 

0.90 

•  89 

2.66 

3.8o 

S.I3 

6.70 

8.59 

10.95 

•  95 

•99 

2.80 

4.00 

5-41 

7-o8 

9.10 

11.64 

.00 

2.08 

2-93 

4.20 

5-70 

7.48 

9.64 

12.35 

•  05 

2.18 

3.07 

4-41 

5-99 

7--  87 

10.17 

13.10 

.10 

2.27 

3-21 

4.62 

6.29 

8.30 

10.77 

13.91 

•  IS 

•  37 

3-35 

4-83 

6.60 

8-73 

11-34 

14.76 

.20 

•  47 

3-50 

5-05 

6.92 

9.16 

11.97 

15.65 

25 

•  57 

3-64 

5-27 

7.24 

9.62 

12.63 

16-59 

30 

•  67 

3-79 

S-So 

7-57 

10.09 

13-29 

17-57 

35 

•  77 

3-94 

5-73 

7-91 

10.59 

14.01 

18.59 

40 

2.87 

4-09 

5.96 

8.24 

n.  ii 

14.76 

19.63 

•45 

2.97 

4-24 

6.20 

8.61 

ii.  61 

15-53 

20.79 

50 

3-07 

4-40 

6.44 

8.97 

12.  16 

16.31 

22.09 

-55 

3.18 

4-55 

6.69 

9-34 

12.72 

17.11 

23.29 

.60 

3-28 

4-71 

6-94 

9-74 

13-29 

18.07 

24-78 

.65 

3-39 

4-87 

7.20 

IO.I2 

13.91 

18-95 

26.30 

70 

3-SO 

5-03 

7.46. 

10.53 

14-53 

19-93 

27.82 

•  75 

3-6l 

5-20 

7-73 

10-95 

15.16 

20.90 

29.51 

.80 

3-71 

5.37 

8.00 

11-37 

15.84 

21.97 

31-43 

.85 

3-82 

5-54 

8.28 

11.82 

16.52 

23.15 

33-33 

90 

3-94 

S-7I 

8.57 

12.27 

17.26 

24-32 

35-47 

•  95 

4-05 

5-88 

8.87 

12.76 

18.07 

25.60 

37.90 

.00 

4.16 

6.07 

9.16 

13-24 

18.86 

27.04 

40.27 

TABLE  XXXVI.  —  PUSHER  GRADES 

The  tabular  quantities  are  pusher  grades  for  the  through  grades 
indicated  at  the  side  and  top  of  table.  Computed  for  the  Consolida- 
tion Engine  of  Table  XXXIII. 


Through 
grade 

0.0 

O.I 

0.2 

0-3 

0.4 

o.S 

0.6 

0.7 

0.8 

0.9 

0.0 
I.O 
2.O 

0.187 
!.889 
3-359 

0-369 
2.045 

0.548 
2.2OO 

0.725 
2-353 

0.899 
2.502 

1.070 
2.650 

1.238 
2.796 

1.404 
2-939 

1-569 
3.082 

1.730 

3-222 

(260) 


TABLE  XXXVII.  —  GRADES  AND  GRADE  ANGLES 


Feet 

Feet 

Incli- 

Feet 

Feet 

Incli- 

Feet 

Feet 

Incli- 

Feet 

Feet 

Incli- 

per 

sta- 
tion 

per 
mile 

nation, 
itfeg. 

per 
sta- 
tion 

per 
mile 

nation, 
deg. 

per 
sta- 
tion 

per 
mile 

nation, 
deg. 

per 
sta- 
tion 

per 
mile 

nation, 
deg. 

00 

.000 

.000 

50 

26.400 

.286 

.00 

52.800 

•  573 

So 

79.200 

"~859~ 

OI 

.528 

.006 

Si 

26.928 

.292 

.01 

53.328 

•  579 

•  Si 

79.728 

.865 

02 

1.056 

.Oil 

52 

27.456 

.298 

.02 

53.856 

.584 

52 

80.256 

.871 

03 

1.584 

.017 

53 

27.984 

•  304 

03 

54.384 

•  590 

53 

80.784 

.877 

04 

2,112 

.023 

54 

28.512 

.309 

04 

54-912 

-596 

-54 

81.312 

.882 

05 

2640 

.029 

55 

29.040 

.315 

•  05 

55-440 

.601 

-55 

81.840 

.888 

06 

3:168 

•  034 

56 

29.568 

.321 

.06 

55-968 

.607 

-56 

82.368 

.894 

07 

3696 

.040 

57 

30.096 

•  327 

.07 

56.496 

.613 

57 

82.896 

-899 

08 

4.224 

.046 

58 

30.624 

•  332 

.08 

57-024 

.619 

-58 

83.424 

•  90S 

09 

4752 

.052 

59 

31-152 

.338 

.09 

57-552 

.624 

-59 

83.952 

.9" 

10 

5,280 

.057 

60 

31.680 

•  344 

.10 

58.080 

.630 

.60 

84.480 

.917 

II 

5,8o8 

.063 

61 

32.208 

•349 

.11 

58.608 

.636 

.61 

85.008 

.922 

12 

6.336 

.069 

62 

32.736 

•  355 

.12 

59-136 

.642 

.62 

85.536 

.928 

13 

6864 

.074 

63 

33.264 

.361 

13 

59-664 

.648 

-63 

86.064 

•  934 

14 

7392 

.080 

64 

33-792 

.367 

•  14 

60.192 

.653 

-64 

86.592 

•  939 

IS 

7.920 

.086 

65 

34-320 

•  372 

•  IS 

60.720 

.659 

-65 

87.120 

•  945 

16 

8.448 

.092 

66 

34.848 

•378 

.16 

61.248 

.665 

.66 

87.648 

•  951 

17 

8.976 

.098 

67 

35.376 

.384 

.17 

61.776 

.670 

.67 

88.176 

•  957 

18 

9-504 

.103 

68 

35.904 

•  390 

.18 

62.304 

.676 

.68 

88.704 

.962 

19 

10.032 

.109 

69 

36.432 

•  395 

.19 

62.832 

.682 

.69 

89.232 

.968 

20 

10.560 

.115 

70 

36.960 

.401 

.20 

63.360 

.688 

.70 

89.760 

•  974 

21 

ii.  088 

.120 

7i 

37-488 

.407 

.21 

63.888 

.693 

•  71 

90.288 

.980 

22 

11.616 

.126 

72 

38.016 

.412 

.22 

64.416 

.699 

-72 

90.816 

.985 

23 

12.144 

.132 

73 

38.544 

.418 

23 

64.944 

•  70S 

73 

91-344 

.991 

24 

12.672 

.138 

74 

39-072 

•  424 

24 

65.472 

.710 

-74 

91.872 

,997 

25 

13.200 

•143 

75 

39-600 

•  430 

25 

66.000 

.716 

-75 

92.400 

.002 

26 

13.728 

.149 

76 

40.128 

.436 

.26 

66.528 

.722 

.76 

92.928 

.008 

27 

14.256 

.155 

77 

40.656 

.441 

27 

67.056 

.728 

•  77 

93.456 

.014 

28 

14-784 

.160 

78 

41  .  184 

•  447 

.28 

67.584 

•  733 

.78 

93.984 

.020 

29 

15.312 

.166 

79 

41.712 

•  452 

.29 

68.112 

•  739 

•  79 

94-512 

.026 

30 

15.840 

.172 

80 

42.240 

-458 

30 

68.640 

•  745 

.80 

95.040 

.031 

31 

16.368 

.178 

81 

42.768 

.464 

'31 

69.168 

•  751 

.81 

95.568 

.037 

32 

16.896 

.183 

82 

43-296 

.470 

32 

69.696 

•  756 

.82 

96.096 

•  043 

33 

17.424 

.189 

83 

43-824 

.476 

33 

70.224 

.762 

-83 

96.624 

.048 

34 

17-952 

•  195 

84 

44-352 

.481 

34 

70.752 

.768 

.84 

97-152 

.054 

35 

18.480 

.200 

85 

44.880 

.487 

•  35 

71.280 

•  773 

.85 

97.68o 

.060 

36 

19.008 

.206 

86 

45.408 

•  493 

.36 

71.808 

•  779 

.86 

98.208 

.066 

37 

19.536 

.212 

87 

45.936 

•  498 

37 

72.336 

.785 

.87 

98.736 

.071 

38 

20.064 

.218 

88 

46.464 

.504 

.38 

72.864 

•  791 

.88 

99.264 

.077 

39 

20.592 

.223 

89 

46.992 

•  510 

39 

73-392 

.796 

-89 

99.792 

.083 

40 

21  .  120 

.229 

90 

47-520 

.516 

40 

73-920 

.802 

90 

100.320 

.089 

4i 

21.648 

.235 

9i 

48.048 

.521 

•  41 

74.448 

.808 

9i 

100.848 

.094 

42 

22.176 

.240 

92 

48.576 

•  527 

42 

74.976 

.814 

92 

101  .  376 

.100 

43 

22  .  704 

.246 

93 

49-104 

•  533 

43 

75.504 

.8I9 

93 

101.904 

.106 

44 

23.232 

.252 

94 

49.632 

•  539 

•44 

76.032 

.825 

94 

102.432 

.ill 

45 

23.760 

.258 

95 

50.160 

.544 

•45 

76.560 

.831 

•  95 

IO2  .  960 

.117 

46 

24.288 

.264 

96 

50.688 

.550 

.46 

77.088 

.836 

-96 

103.488 

.123 

47 

24.816 

.269 

97 

51.216 

.556 

•47 

77.616 

.842 

-97 

IO4.OI6 

.129 

48 

25.344 

-275 

98 

51-744 

.561 

•  48 

78.144 

.848 

98 

104.544 

.134 

49 

25.872 

.281 

99 

52.272 

.567 

•  49 

78.672 

.854 

•  99 

105.072 

.140 

5° 

26.400 

.286 

1.  00 

52.800 

•  573 

So 

79-200 

.859 

.00 

105.600 

.146 

(261) 


CHAPTER  V 
ESTIMATING  AND  CONSTRUCTION  TABLES 

TABLE  XXXVIII 

Relative  prices  in  place  that  can  be  paid  for  articles  for  the  same 
purpose  lasting  N  and  N'  years.  The  article  lasting  N  years  is 
assumed  to  cost  $1.00  or  one  unit.  Interest  4  per  cent. 

Example.  —  If  a  lasts  10  years  and  costs  50  cents,  there  may  be 
paid  for  b  lasting  7  years  50  X  0.74  =  37  cents. 


\       N 

N     / 

Amount 

\^ 

5 

6 

7 

8 

9 

IO 

II 

12 

13 

14 

/ 

$i.oo  at 

N' 

/    N' 

comp'd  int.. 

5 

I.OO 

~s 

0-74 

0.66 

0.60 

0.55 

0-51 

0.47 

o.45 

0.42 

5 

.21665 

6 

1.18 

I.OO 

0.87 

0.78 

0.70 

0.65 

0.60 

0.56 

0.52 

0.50 

6 

.26532 

7 

1.35 

1.  14 

I.OO 

0.89 

0.81 

0.74 

0.69 

0.64 

0.60 

0.57 

7 

•31593 

8 

1.51 

1.28 

1.  12 

I.OO 

0.91 

0.83 

0.77 

0.72 

0.67 

0.64 

8 

.36857 

9 

1.67 

1.42 

1.24 

1.  10 

I.OO 

0.92 

0.85 

0.79 

0.74 

0.70 

9 

.42331 

10 

1.82 

1-55 

1.35 

1.20 

1.09 

I.OO 

0.93 

0.86 

0.81 

0-77 

10 

.48024 

ii 

1.97 

1.67 

1.46 

1.30 

1.18 

1.  08 

I.OO 

0.93 

0.88 

0.83 

ii 

•53945 

12 

2.  II 

1.79 

1.56 

1-39 

1.26 

1.16 

1.07 

I.OO 

0.94 

0.89 

12 

.60103 

13 

2.43 

1.90 

1.66 

1.48 

1-34 

1.23 

1.  14 

1.  06 

I.OO 

0.95 

13 

.66507 

14 

2.37 

2.01 

1.76 

1-57 

1.42 

1.30 

1.  21 

1.  13 

1.  06 

I.OO 

14 

.73167 

IS 

2.50 

2.12 

1.85 

1.65 

1.50 

1.37 

1.27 

1.18 

I.  II 

1.05 

15 

.80094 

16 

2.62 

2.22 

1.94 

1-73 

1.57 

1.44 

1.33 

1.24 

1.  17 

1.  10 

16 

•87297 

17 

2.73 

2.32 

2.03 

1.81 

1.64 

1.50 

1.39 

1.30 

1.22 

I.  IS 

17 

.94790 

18 

2.84 

2.41 

2.  II 

1.88 

•1.70 

.56 

1.44 

•  35 

1.27 

1.20 

18 

2.02581 

19 

2.95 

2.50 

2.19 

1.95 

1.77 

.62 

1.50 

.40 

1.32 

1.24 

19 

2.10685 

20 

3-05 

2.59 

2.26 

2.  02 

1.83 

.68 

1.55 

•  45 

1.36 

1.29 

20 

2.19112 

21 

3-15 

2.68 

2.34 

2.08 

1.89 

•  73 

1.  60 

•  49 

1.40 

1-33 

21 

2.27876 

22 

3-25 

2.76 

2.41 

2.15 

1-94 

.78 

1.65 

•  54 

1.45 

1-37 

22 

2.36991 

23 

3-34 

2.83 

2.48 

2.21 

2.0O 

.83 

1.70 

.58 

1.49 

1.41 

23 

2.46471 

24 

3-42 

2.91 

2.54 

2.26 

2.05 

.88 

1.74 

.62 

1.53 

1.44 

24 

2.56330 

25 

3  Si 

2.C)8 

2.60 

2.32 

2.10 

-93 

1.78 

.66 

1.56 

1.48 

25 

2.66583 

262 


ESTIMATING  AND   CONSTRUCTION  TABLES 


263 


TABLE  XXXVIII.  —  (Continued) 


>\ 

IS 

16 

17 

18 

19 

20 

21 

22 

33 

24 

35 

!% 

5~~ 

0.40 

0.38 

0.37 

0.35 

0.34 

0.33 

0.32 

0.31 

0.30 

0.29 

0.28 

5 

6 

0-47 

0.45 

0-43 

0.41 

0.40 

0.39 

0-37 

0.36 

0.35 

0.34 

0.34 

6 

7 

0.54 

0.52 

0.49 

0.47 

0.46 

0.44 

0.43 

0.42 

0.40 

0.39 

0.38 

7 

8 

0.61 

0.58 

0.55 

0.53 

0.51 

0.50 

0.48 

0.47 

0-45 

0.44 

0.43 

8 

9 

0.67 

0.64 

0.61 

0.59 

0.57 

0.55 

0.53 

0.51 

0.50 

0.49 

0.48 

9 

10 

c.73 

0.70 

0.67 

0.64 

0.62 

0.60 

0.58 

0.56 

0.55 

0.53 

0.52 

10 

ii 

Q.79 

0.75 

0.72 

0.69 

0.67 

0.64 

0.62 

0.61 

0.59 

0.57 

0.56 

ii 

12 

0.84 

0.81 

0.77 

0.74 

0.71 

0.69 

0.67 

0.65 

0.63 

0.62 

0.60 

12 

13 

0.90 

0.86 

0.82 

0.79 

0.76 

0.73 

0.71 

0.69 

0.67 

0.65 

0.64 

13 

14 

0-95 

0.91 

0.87 

0.83 

0.80 

0.78 

0.75 

0.73 

0.71 

0.69 

0.68 

14 

IS 

.00 

0-95 

•  91 

0.88 

0.85 

0.82 

0.79 

0-77 

0.75 

0.73 

0.71 

IS 

16 

.05 

.00 

.96 

0.92 

0.89 

0.86 

0.83 

0.81 

0.78 

0.76 

0.75 

16 

17 

•  09 

•  04 

00 

0.96 

0.93 

0.90 

0.87 

0.84 

0.82 

0.80 

0.78 

17 

18 

.14 

•  09 

.04 

I.OO 

0.96 

0-93 

0.90 

0.88 

0.85 

0.83 

0.81 

18 

19 

.18 

.13 

.08 

1.04 

I.OO 

0-97 

0.94 

0.91 

0.88 

0.86 

0.84 

19 

20 

.22 

•  17 

.12 

1.07 

1.03 

I.OO 

0.97 

0.94 

0.91 

0.89 

0.87 

20 

21 

.26 

.20 

•IS 

.11 

.07 

.03 

.00 

0.97 

0.94 

0.92 

0.90 

21 

22 

•30 

.24 

•19 

•  14 

.10 

.06 

•  03 

I.OO 

0.97 

0.95 

0.92 

22 

33 

•  34 

.27 

.22 

•  17 

•  13 

.09 

.06 

1.03 

I.OO 

0.97 

0.95 

23 

24 

•  37 

•  31 

.25 

.20 

.16 

.12 

.08 

1.  06 

1.03 

I.OO 

0.98 

24 

35 

•  41 

•  34 

.28 

.23 

19 

•      15 

.11 

1.  08 

1.05 

1.02 

I.OO 

35 

TABLE  XXXIX 

Relative  prices  in  place  that  can  be  paid  for  articles  for  the  same 
purpose  lasting  N  and  N'  years.  The  article  lasting  N  years  is  as- 
sumed to  cost  $1.00  or  one  unit.  Interest  5  per  cent. 

Example.  —  If  a  lasts  10  years  and  costs  60  cents,  there  may  be  paid 
for  b  lasting  12  years,  60  X  1.15  =  79  cents. 


\       N 

N     / 

Amount 

N. 

5 

6 

7 

8 

9 

10 

ii 

12 

13 

14 

/ 

fi.oo  at 

N'   \ 

/     N' 

comp'd  int. 

5 

I.OO 

~ 

0.75 

0.67 

0.61 

0.56 

0.52 

0.49 

0.46 

o.44 

5 

.27628 

6 

1.  17 

I.OO 

0.88 

0-79 

0.71 

0.66 

0.61 

0.57 

0.54 

0.51 

6 

.34009 

7 

1-34 

1.  14 

I.OO 

0.90 

0.81 

0.75 

0.70 

0.65 

0.62 

0.58 

7 

.40710 

8 

1.49 

.27 

1.  12 

I.OO 

0.91 

0.84 

0.78 

0.73 

0.69 

.65 

8 

•47745 

9 

1.64 

.40 

1.23 

I.IO 

I.OO 

0.92 

0.86 

0.80 

0.76 

•  72 

9 

.55132 

10 

1.78 

.52 

1-33 

1.19 

1.09 

I.OO 

0-93 

0.87 

0.82 

•  78 

10 

.62889 

ii 

1.92 

.64 

1.44 

1.29 

1.  17 

1.  08 

I.OO 

o.94 

0.88 

.84 

ii 

.71034 

12 

2.05 

•  75 

1-53 

1-37 

1.25 

I.  IS 

1.07 

I.OO 

0.94 

.90 

12 

•79585 

13 

2.17 

1.85 

1.62 

1-45 

1.32 

1.22 

1.  13 

1.  06 

I.OO 

•  95 

13 

.88564 

14 

2.29 

1-95 

I.7I 

1.53 

1.39 

1.28 

1.  19 

1.  12 

1.05 

00 

14 

•97993 

IS 

2.40 

2.04 

1.79 

1.61 

1.46 

1.34 

1.25 

1.  17 

I.IO 

.05 

IS 

.07892 

16 

2.50 

2.14 

1.87 

1.68 

1.52 

1.40 

1.30 

1.22 

I.  IS 

•  09 

16 

.18287 

17 

2.60 

2.22 

1-95 

1-74 

1-59 

1.46 

1.36 

1.27 

1.20 

•  14 

17 

2.29202 

18 

2.70 

2.30 

2.02 

1.81 

1.64 

I.  Si 

1.41 

1.32 

1.24 

.18 

18 

2.40662 

19 

2.79 

2.38 

2.09 

1.87 

1.70 

1.56 

1.45 

1.36 

1.29 

.22 

19 

2.52695 

20 

2.88 

2.46 

2.15 

1-93 

1-75 

1.61 

I.  SO 

I.4I 

1.33 

.25 

20 

2.65330 

21 

2.96 

2.53 

2.22 

1.98 

1.  80 

1.66 

1.54 

1-45 

1.36 

•29 

21 

2.78596 

22 

3-04 

2.59 

2.2? 

2.04 

1.85 

1.70 

1.58 

1-49 

1.40 

•  33 

22 

2.92526 

23 

3-12 

2.66 

2.33 

2.09 

1.90 

1-75 

1.62 

1-52 

1-44 

.36 

23 

3.07152 

24 

3.19 

2.72 

2.38 

2.13 

1.94 

1-79 

1.66 

1.56 

1-47 

-39 

24 

3-22510 

25 

3.26 

2.78 

2.44 

2.18 

1.98 

1.83 

1.70 

1.59 

1.50 

.42 

25 

3-38635 

TABLE  XXXIX.  —  (Continued) 


\  N 

AT'\ 

IS 

16 

17 

18 

19 

20 

21 

22 

23 

24 

25 

N  / 
/W 

5 

0.42 

0.40 

0.38 

0.37 

0.36 

0.35 

0.34 

0.33 

0.32 

0.31 

0.31 

5 

6 

o.49 

0.47 

0.45 

o.43 

0.42 

0.41 

0.40 

0.39 

0.38 

0.37 

0.36 

6 

7 

0.56 

0.53 

0.51 

0.49 

0.48 

0.46 

0.45 

0.44 

0.43 

0.42 

0.41 

7 

8 

0.62 

0.60 

o.57 

0-55 

0.53 

0.52 

0.50 

0.49 

0.48 

0.47 

0.46 

8 

9 

0.68 

0.66 

0.63 

0.61 

0.59 

0-57 

0.55 

0-54 

o.53 

0.52 

0.50 

9 

10 

0.74 

0.71 

0.68 

0.66 

0.64 

0.62 

0.60 

0.59 

0.57 

0.56 

o.SS 

10 

ii 

0.80 

0.77 

0.74 

0.71 

0.69 

0.67 

0.65 

0.63 

0.62 

0.60 

0.59 

ii 

12 

0.85 

0.82 

0.79 

0.76 

o.73 

0.71 

0.69 

0.67 

0.66 

0.64 

0.63 

12 

13 

0.90 

0.87 

0.83 

0.80 

0.78 

0.75 

0-73 

0.71 

0.70 

0.68 

0.67 

13 

14 

0.95 

0.91 

0.88 

0.85 

0.82 

0-79 

0.77 

0.75 

0.73 

0.72 

0.70 

14 

IS 

I.OO 

0.96 

0.92 

0.89 

0.86 

0.83 

0.81 

0.79 

0.77 

0.75 

0.74 

IS 

16 

1.04 

I.OO 

0.96 

0.93 

0.90 

0.87 

0.85 

0.82 

0.8o 

0.79 

0.77 

16 

17 

1.09 

1.04 

.00 

0.96 

0.93 

0.90 

0.88 

0.86 

0.84 

0.82 

0.80 

17 

18 

1.13 

1.  08 

.04 

I.OO 

0.97 

0-94 

0.91 

0.89 

0.87 

0.85 

0.83 

18 

19 

1.16 

1.  12 

.07 

1.03 

I.OO 

0.97 

0.94 

0.92 

0.90 

0.88 

0.86 

19 

20 

1.20 

I.  IS 

.11 

1.07 

1.03 

I.OO 

0-97 

0.95 

0.92 

0.90 

0.88 

20 

21 

1.24 

1.18 

•  14 

I.IO 

1.  06 

1.03 

I.OO 

0-97 

0.95 

0.93 

0.91 

21 

22 

1.27 

1.  21 

•  17 

1.  13 

1.09 

1.  06 

1.03 

I.OO 

0.98 

0.95 

0.93 

22 

23 

1.30 

1.24 

1.  20 

I.  IS 

1.  12 

1.  08 

1.05 

1.02 

I.OO 

0.98 

0.96 

23 

24 

1-33 

1.27 

1.22 

1.18 

1.  14 

I.  II 

i.  08 

i.  05 

1.  02 

I.OO 

0.98 

24 

25 

1-36 

1-30 

1.25 

1.  21 

1.  17 

1.  13 

I.IO 

1.07 

1.04 

1.  02 

I.OO 

25 

(264) 


ESTIMATING  AND   CONSTRUCTION  TABLES          265 

Volumes  of  Triangular  Prisms.  —  Table  XL.     In  railroad  earth-work 
the  volume  of  a  given  length  of  cut  or  fill  is  given  by  the  average  end 

area  method  as  /  X  — — - — •  in  which  /  is  the  length,  usually  100  feet, 
and  AI  and  A2  are  the  cross-section  areas  at  the  two  ends.  This  is 
equivalent  to  -  AI  +  -  A2  and  Table  XL  is  made  on  this  basis  with  100 

for  /.  Hence  the  volumes  are  for  5O-foot  lengths  and  are  to  be  used 
twice,  once  on  one  side  of  a  station  section  for  the  part  of  the  station 


FIG.  25. 

volume  on  that  side,  and  once  on  the  other  side  as  part  of  the  station 
volume  on  that  side. 

The  commonest  formula  for  the  cross-section  area  of  a  3-level  section 

is  A  =  -D  +-  (hi  +  fh).     This  is  equivalent  to  the  area  of  two 
triangles  of  bases  c  and  -  and  altitudes  D  and  hi  +  h2  or  it  may  be  taken 

as  three  triangles  of  bases  D  and  —  and  altitudes  c,  hi  and  hz. 
Whence  the  volume  in  cubic  yards  for  a  5O-foot  length  is 

•  ^=50/7  +  50  ( 


-  5?  «*+  <*•  +  *•>. 

D  is  the  sum  of  the  slope  stake  distances.     The  table  is  made  to  give 
the  quantity  f  f  •  x  •  y,  in  which  x  is  the  base  or  altitude  and  y  is  the 
altitude  or  base  of  the  triangular  base  or  end  of  a  triangular  prism. 
In  using  the  table  for  such  work  the  x  numbers  at  the  side  of  the  page 

should  be  used  for  heights  c  and  —  and  the  y  numbers  at  the  top  for  D 
and  hi  +  h%.    The  quantities  are  given  for  only  whole  numbers  of  y 


266  RAILROAD   FIELD  MANUAL 

from  i  to  9  inclusive,  but  are  given  to  hundredths  so  that  for  y  =  50  or 
70,  etc.,  ten  times  the  tabular  values  for  5  or  7,  etc.,  are  taken  and 
for  y  =  0.5  and  0.7,  etc.,  one-tenth  the  tabular  values  for  5  and  7  are  taken. 
Example.  —  The  cross-section  notes  of  two  stations  show 


Sta. 
762 

763 

L 
-3.6 

C 

R 
-5-3 

13-6 
-4.8 

4.2 

-5-7 

15-3 
16.4 

14.8 

the  minus  sign  indicating  a  cut.     The  volume  between  stations  762  and 
763  is  had  from  the  tables  as  follows: 

For  762.     D  =  13.6  +  15.3  =  28.9,  done  mentally, 
c  =  4.2, 

w 
w  =  20,     —  =  10, 

At  +  fa  =  8.9. 

From  Table  XL  opposite  x  =  4.2  under  2  take  10  X    7.78  =  77.8 

under  8  1X31.11  =31.11 

under  9          ^  X  35-OO  =    3.5 

j  =  10  .'.  opposite  x  =  10.0     under  8  take    i  X  74.00  =  74.00 

under  9          ^  X  83.33  =    8.33 

Total          194.8  =  194.8 
For  763.     D  =  14.8  +  16.4  =  31.2. 

c  =  5-7, 

w 

W  =20,         -  =  10, 

hi  -f  fa  =  n.2. 

Opposite  x  =  5.7  take  10  X  15.83  =  158.3 

i  X    5-28  =     5.3 

&  X  10.56  =      I.I 

!  =  "• 

.'.  opposite  *  =  10  take  10  X    9.72  =  97.2 

i  X    9-72  =     9.7 

&  X  1944  =      1-9 

Total  273.5  273.5 

Total  for  sta.  468.3 

If  the  length  between  two  sections  is  50  feet,  take  |  the  result  from 
the  tables;  if  40  feet,  take  &  the  result,  and  so  on.     For  a  single  right 


ESTIMATING  AND   CONSTRUCTION  TABLES          267 

prism  of  any  length  take  that  portion  of  the  tabular  quantity  that  the 
length  is  of  50. 

Prismoidal  Correction.  —  Table  XLI.  To  get  the  volume  of  a  station 
of  earthwork  by  the  prismoidal  formula,  get  it  by  the  average  end  area 
method  and  subtract  the  prismoidal  correction.  That  is,  get  the  vol- 
ume from  Table  XL,  and  subtract  the  correction  of  Table  XLI.  The 
correction  is  for  full  stations  of  100  feet;  for  shorter  lengths  use  pro- 
portional parts  of  the  tabular  quantities.  The  arguments  of  the  table 
Ci  —  Co  and  D\  —  D0  are  the  differences  in  center  heights  and  total 
widths  respectively  of  the  two  end  sections. 

Level  Section  Volumes.  —  Table  XLI  I.  This  table  is  used  only  in 
preliminary  estimates  and  gives  the  volumes  in  cubic  yards  for  100- 
foot  lengths  for  varying  center  heights.  Its  use  will  be  evident. 


TABLE  XL.  —  VOLUMES  OF  TRIANGULAR  PRISMS  50  FEET  IN 
LENGTH 


Y  / 

N. 

I 

2 

3 

4 

S 

6 

7 

8 

9 

X 

'  X 

.1 

.09 

•19 

.28 

•  37 

.46 

•  56 

.65 

•  74 

.83 

.1 

.2 

•19 

•  37 

.56 

•  74 

•  93 

i.  ii 

1.30 

1.48 

1.67 

.2 

3 

.28 

•  56 

.83 

I.  II 

1-39 

1.67 

1-94 

2.22 

2.50 

•  3 

•4 

•  37 

•  74 

.11 

1.48 

1.85 

2.22 

2.59 

2.96 

333 

•  4 

•  5 

.46 

•93 

•  39 

1.85 

2.31 

2.78 

3.24 

3-70 

4.17 

-5 

.6 

•  56 

I.  ii 

.67 

2.22 

2.78 

3-33 

3-89 

4-44 

5-00 

.6 

•  7 

.65 

•  30 

•94 

2.59 

3-24 

3-89 

4-54 

5-19 

5.83 

-7 

.8 

•  74 

.48 

.22 

2.96 

3-70 

4-44 

5-19 

5-93 

6.67 

.8 

•  9 

.83 

.67 

•50 

3  33 

4-17 

5.00 

5-83 

6.67 

7-50 

.9 

1.0 

•93 

.85 

2.78 

3  70 

4.63 

5.56 

6.48 

7-41 

8-33 

1.0 

.1 

1.  02 

.04 

3-06 

4-07 

5-09 

6.  ii 

7-13 

8.  is 

9-17 

.1 

.2 

I.  ii 

.22 

3  33 

4-44 

5.56 

6.67 

7-78 

8.89 

IO.OO 

.2 

•3 

1.20 

•  41 

3.6l 

4.81 

6.02 

7.22 

8.43 

9-63 

10.83 

3 

.4 

1.30 

•  59 

3-89 

S-I9 

6.48 

7-78 

9-07 

10.37 

11.67 

-4 

•  5 

1-39 

•  78 

4.17 

5-56 

6.94 

8-33 

9-72 

ii.  ii 

12.50 

-5 

.6 

1.48 

2.96 

4-44 

5-93 

7.41 

8.89 

10.37 

11.85 

13.33 

.6 

.7 

1-57 

3-15 

4-72 

6.30 

7.87 

9-44 

11.02 

12.59 

14.17 

-7 

.8 

1.67 

3-33 

5-00 

6.6? 

8.33 

IO.OO 

11.67 

13-33 

15.00 

.8 

•  9 

1.76 

3  52 

5-28 

7.04 

8.80 

10.56 

12.31 

14.07 

15.83 

•9 

2.0 

1.85 

3-70 

5-56 

7-41 

9-26 

II.  II 

12.96 

14.81 

16.67 

2.0 

.1 

1.94 

3-89 

5-83 

7-78 

9-72 

11.67 

I3.6l 

15.56 

17.50 

.1 

.2 

2.04 

4.07 

6.H 

8.15 

10.19 

12.22 

14.26 

16.30 

18.33 

.2 

•3 

2.13 

4.26 

6.39 

8.52 

10.65 

12.78 

14.91 

17.04 

19.17 

3 

•  4 

2.22 

4-44 

6.67 

8.89 

II.  II 

13-33 

15.56 

17.78 

20.00 

.4 

5 

2.31 

4-63 

6-94 

9-26 

H-57 

13.89 

16.20 

18.52 

20.83 

-5 

.6 

2.41 

4.81 

7.22 

9.63 

12.04 

14.44 

16.85 

19.26 

21.67 

.6 

•  7 

2.50 

5.00 

7.50 

IO.OO 

12.50 

15-00 

17.50 

20.00 

22.50 

•  7 

.8 

2.59 

5-19 

7-78 

10.37 

12.96 

15-56 

18.15 

20.74 

23-33 

.8 

•9 

2.69 

5-37 

8.06 

10.74 

13-43 

16.11 

18.80 

21.48 

24.17 

•  9 

3.0 

2.78 

5-56 

8.33 

II.  II 

13-89 

16.67 

19.44 

22.22 

25.OO 

3.0 

.1 

2.87 

5-74 

8.61 

11.48 

14-35 

17.22 

20.09 

22.96 

25.83 

.1 

.2 

2.96 

5-93 

8.89 

11.85 

14-81 

17.78 

20.74 

23.70 

26.67 

.2 

3 

3-06 

6.  ii 

9-17 

12.22 

15.28 

18.33 

21.39 

24.44 

27.50 

3 

.4 

3-iS 

6.30 

9-44 

12.59 

15-74 

18.89 

22.04 

25.19 

28.33 

•  4 

•  5 

3-24 

6.48 

9-72 

12.96 

16.20 

19-44 

22.69 

25-93 

29.17 

•  5 

.6 

3-33 

6.67 

10.00 

13-33 

16.67 

20.00 

23-33 

26.67 

30.00 

.6 

•  7 

3-43 

6.85 

10.28 

13.70 

17.13 

20.56 

23.98 

27.41 

30.83 

.7 

.8 

3-52 

7.04 

10.56 

14.07 

17-59 

21.  II 

24-63 

28.15 

31.67 

.8 

•9 

3-61 

7.22 

10.83 

14-44 

18.06 

21.67 

25.28 

28.89 

32.50 

.9 

4.0 

3.70 

7-41 

II.  II 

I4.8I 

18.52 

22.22 

25-93 

29.63 

33  33 

4.0 

.1 

3-80 

7-59 

11-39 

15-19 

18.98 

22.78 

26.57 

30.37 

34-17 

.1 

.2 

3-89 

7-78 

11.67 

15.56 

19-44 

23-33 

27.22 

31-  II 

35-00 

.2 

3 

3-98 

7-96 

11.94 

15-93 

19.91 

23-89 

27.87 

31.85 

35-83 

3 

•  4 

4.07 

8.15 

12.22 

16.30 

20.37 

24-44 

28.52 

32.59 

36.67 

•  4 

•  5 

4-17 

8.33 

12.50 

16.67 

20.83 

25.00 

29-17 

33  33 

37.50 

•  5 

.6 

4.26 

8.52 

12.78 

17.04 

21.30 

25.56 

29.81 

34-07 

38.33 

.6 

•  7 

4-35 

8.70 

13.06 

I7-4I 

21.76 

26.11 

30.46 

34-81 

39-17 

•  7 

.8 

4-44 

8.89 

13  33 

17.78 

22.22 

26.67 

31.11 

35.56 

40.00 

.8 

.9 

4-54 

9-07 

13.61 

18.15 

22.69 

27.22 

3I.76 

36.30 

40.83 

•  9 

50 

4-63 

9.26 

13.89 

18.52 

23.15 

27.78 

32.41 

37-04 

41-67 

5.0 

(268) 


TABLE  XL.  —  (Continued] 


\  Y 

F   / 

\ 

I 

2 

3 

4 

5 

6 

7 

8 

9 

/ 

x\ 

/  x 

5.1 

4-72 

9-44 

14.17 

18.89 

23.61 

28.33 

33.o6 

37.78 

42.50 

51 

.2 

4.81 

9-63 

14-44 

19.26 

24.07 

28.89 

33-70 

38.52 

43-33 

.2 

3 

4-91 

9-8i 

14.72 

19.63 

24-54 

29-44 

34-35 

39-26 

44-17 

•  3 

•  4 

S.oo 

10.  OO 

15.00 

20.00 

25.00 

30.00 

35.00 

40.00 

45-00 

•  4 

5 

5-09 

10.19 

15.28 

20.37 

25.46 

30.56 

35.65 

40.74 

45.83 

•  5 

.6 

5.19 

10.37 

15.56 

20.74 

25-93 

31.11 

36.30 

41-48 

46.67 

.6 

•  7 

5.28 

10.56 

15.83 

21.  II 

26.39 

31.67 

36.94 

42.22 

47-50 

•  7 

.8 

5-37 

10.74 

i6.ii 

21.48 

26.85 

32.22 

37-59 

42.96 

48.33 

.8 

•  9 

5.46 

10.93 

16.39 

21.85 

27.31 

32.78 

38.24 

43-70 

49-17 

•  9 

6.0 

5.56 

ii.  n 

16.67 

22.22 

27.78 

33-33 

38.89 

44-44 

50.00 

6.0 

.1 

5.65 

11.30 

16.94 

22.59 

28.24 

33.89 

39-54 

45.19 

50.83 

.1 

.2 

5-74 

11.48 

17.22 

22.96 

28.70 

34-44 

40.19 

45-93 

51.67 

.2 

3 

5.83 

11.67 

17.50 

23-33 

29.17' 

35-00 

40.83 

46.67 

52.50 

3 

•4 

5-93 

11.85 

17.78 

23.70 

29.63 

35.56 

4L48 

47-41 

53-33 

4 

•  5 

6.02 

12.04 

18.06 

24.07 

30.09 

36.11 

42.13 

48.15 

54-17 

•  5 

.6 

6.  II 

12.22 

18.33 

24.44 

30.56 

36.67 

42.78 

48.89 

55-00 

.6 

•  7 

6.  20 

12.41 

18.61 

24.81 

31.02 

37-22 

43-43 

49.63 

55.83 

•  7 

.8 

6.30 

12.59 

18.89 

25.19 

31.48 

37.78 

44.07 

50.37 

56.67 

.8 

•  9 

6.39 

12.78 

19-17 

25.56 

31-94 

38.33 

44-72 

51.  ii 

57-50 

•9 

70 

6.48 

12.96 

19.44 

25-93 

32.41 

38.89 

45.37 

51.85 

58.33 

7.0 

! 

6.  57 

13-15 

19.72 

26.30 

32.87 

39.44 

46.02 

52.59 

59-17 

.1 

.2 

6.67 

13  33 

20.00 

26.67 

33  33 

40.00 

46.67 

53  33 

60.00 

.2 

3 

6.76 

13-52 

20.28 

27.04 

33-80 

40.56 

47-31 

54-07 

60.83 

3 

-4 

6.85 

13-70 

20.56 

27.41 

34-26 

41.11 

47.96 

54-81 

61.67 

•  4 

•  5 

6.94 

13.89 

20.83 

27.78 

34.72 

41.67 

48.61 

55.56 

62.50 

-5 

.6 

7-04 

14.07 

21.  II 

28.15 

35-19 

42.22 

49-26 

56.30 

63.33 

.6 

-7 

7-13 

14.26 

21-39 

28.52 

35.65 

42.78 

49-91 

57-04 

64.17 

.7 

.8 

7.22 

14.44 

21.67 

28.89 

36.li 

43.33 

50.56 

57-78 

65.00 

.8 

•  9 

7-31 

14-63 

21.94 

29.26 

36-57 

43.89 

51.20 

58.52 

65.83 

•  9 

8.0 

7-41 

14.81 

22.22 

29.63 

37-04 

44-44 

51.85 

59-26 

66.67 

8.0 

.1 

7-50 

15-00 

22.50 

30.00 

37-50 

45-00 

52.50 

60.00 

67-50 

.1 

.2 

7-59 

15.19 

22.78 

30.37 

37.96 

45.56 

53.15 

60.74 

68.33 

.2 

3 

7.69 

15-37 

23.06 

30.74 

38.43 

46.11 

53.80 

61.48 

69.17 

3 

•  4 

7.78 

15.56 

23-33 

31.  II 

38.89 

46.67 

54.44 

62.22 

70.00 

•  4 

•  5 

7-87 

15.74 

23.6l 

31.48 

39-35 

47-22 

55.09 

62.96 

70.83 

5 

.6 

7.96 

15-93 

23.89 

31.85 

39-81 

47.78 

55.74 

63.70 

71.67 

.6 

•  7 

8.06 

16.11 

24.17 

32.22 

40.28 

48.33 

56.39 

64.44 

72.50 

-7 

.8 

8.15 

16.30 

24.44 

32.59 

40-74 

48.89 

57.04 

65.19 

73-33 

.8 

•  9 

8.24 

16.48 

24.72 

32.96 

41.20 

49.44 

57.69 

65.93 

74-17 

-9 

9.0 

8.33 

16.67 

25.OO 

33-33 

41-67 

50.00 

58.33 

66.67 

75-00 

9.0 

.1 

8.43 

16.85 

25.28 

33-70 

42.13 

50.56 

58.98 

67.41 

75.83 

.1 

.2 

8.52 

17.04 

25.56 

34-07 

42.59 

Si.  ii 

59.63 

68.15 

76.67 

.2 

•3 

8.6l 

17.22 

25.83 

34-44 

43-06 

5I-67 

60.28 

68.89 

77-50 

•  3 

•4 

8.70 

17.41 

26.11 

34-81 

43-52 

52.22 

60.93 

69-63 

78-33 

•4 

•  5 

8.80 

17-59 

26.39 

35-19 

43-98 

52.78 

6l.57 

70.37 

79-17 

•  5 

.6 

8.89 

17.78 

26.67 

35.56 

44-44 

53-33 

62.22 

71.  n 

80.00 

.6 

•  7 

8.98 

17.96 

26.94 

35-93 

44-91 

53.89 

62.87 

71.85 

80.83 

-7 

.8 

9.07 

18.15 

27.22 

36.30 

45-37 

54-44 

63.52 

72.59 

81.67 

.8 

-9 

9.17 

18.33 

27.50 

36.67 

45.83 

55-00 

64.17 

73-33 

82.50 

-9 

10.0 

9.26 

18.52 

27.78 

37-04 

46.30 

55-56 

64.81 

74-07 

83.33 

10.0 

(269) 


TABLE  XL.  —  (Continued) 


\  Y 

Y   / 

\ 

i 

2 

3 

4 

S 

6 

7 

8 

9 

/ 

x\ 

'  X 

10.1 

9  35 

18.70 

28.06 

37-41 

46.76 

56.11 

65.46 

74.81 

84.17 

10.1 

.2 

9-44 

18.89 

28.33 

37.78 

47-22 

56.67 

66.11 

75-56 

85.00 

.2 

3 

9-54 

I9-07 

28.61 

38.15 

47-69 

57-22 

66.76 

76.30 

85-83 

3 

.4 

9.63 

19.26 

28.89 

38.52 

48.15 

57.78 

67.41 

77.04 

86.67 

-4 

•  5 

9-72 

19-44 

29.17 

38.89 

48.61 

58.33 

68.06 

77-78 

87-50 

-5 

.6 

9-81 

I9.63 

29.44 

39-26 

49-07 

58.89 

68.70 

78-52 

88.33 

.6 

.7 

9.91 

I9.8I 

29.72 

39-63 

49-54 

59.44 

69.35 

79  26 

89-17 

7 

.8 

10.00 

20.00 

30.00 

40.00 

50.00 

60.00 

70.00 

80.00 

90.00 

.8 

•9 

10.09 

2O.I9 

30.28 

40-37 

50.46 

60.56 

70.65 

80.74 

90.83 

•9 

11.0 

10.19 

20.37 

30.56 

40-74 

50.93 

6i.n 

71-30 

81.48 

91.67 

11.0 

.1 

10.28 

20.56 

30.83 

41.11 

51-39 

61.67 

71-94 

82.22 

92-50 

.1 

.2 

10.37 

20.74 

31.  II 

41.48 

51.85 

62.22 

72-59 

82.96 

93-33 

.2 

3 

10.46 

20.93 

31-39 

41.85 

52.31 

62.78 

73-24 

83-70 

94-17 

3 

•  4 

10.56 

21.  II 

31.67 

42.22 

52.78 

63.33 

73-89 

84-44 

95.00 

-4 

•  5 

10.65 

21.30 

31-94 

42-59 

53-24 

63-89 

74-54 

85-19 

95-83 

5 

.6 

10.74 

21.48 

32.22 

42.96 

53-70 

64.44 

75-19 

85.93 

96.67 

.6 

•  7 

10.83 

21.6? 

32.50 

43-33 

54-17 

65.00 

75.83 

86.67 

97-50 

-7 

.8 

10.93 

21.85 

32.78 

43-70 

54.63 

65.56 

76.48 

87-41 

98-33 

.8 

•  9 

11.02 

22.04 

33.06 

44-07 

55-09 

66.11 

77-13 

88.15 

99-17 

-9 

12.0 

II.  II 

22.22 

33  33 

44-44 

55.56 

66.67 

77-78 

88.89 

100.00 

12.0 

.1 

11.20 

22.41 

33.6i 

44-81 

56.02 

67.22 

78-43 

89-63 

100.83 

.1 

.2 

11.30 

22.59 

33.89 

45.19 

56.48 

67.78 

79-07 

90-37 

101.67 

.2 

•  3 

".39 

22.78 

34-17 

45.56 

56.94 

68.33 

79-72 

9I.II 

102.50 

3 

•4 

11.48 

22.96 

34-44 

45-93 

57-41 

68.89 

80.37 

91.85 

103-33 

4 

•  5 

11-57 

23.15 

34-72 

46.30 

57.87 

69.44 

81.02 

92.59 

104.17 

-5 

.6 

11.67 

23-33 

35-00 

46.67 

58.33 

70.00 

81.67 

93  33 

105.00 

.6 

.7 

11.76 

23.52 

35-28 

47-04 

58.80 

70.56 

82.31 

94.07 

105.83 

.7 

.8 

11.85 

23.70 

35-56 

47-41 

59-26 

71.11 

82.96 

94-81 

106.67 

.8 

•  9 

11.94 

23.89 

35-83 

47-78 

59-72 

71.67 

83-61 

95-56 

107.50 

•  9 

13.0 

12.04 

24-07 

36.11 

48.15 

60.19 

72.22 

84.26 

96.30 

108.33 

13.0 

.1 

12.13 

24.26 

36-39 

48.52 

60.65 

72.78 

84.91 

97-04 

109.17 

.1 

.2 

12.22 

24.44 

36.67 

48.89 

61.11 

73-33 

85-56 

97.78 

IIO.OO 

.2 

,    -3 

12.31 

24.63 

36.94 

49-26 

6i.57 

73.89 

86.20 

98.52 

110.83 

3 

•4 

12.41 

24.81 

37-22 

49.63 

62.04 

74-44 

86.85 

99-26 

111.67 

•  4 

.5 

12.50 

25.OO 

37.50 

50.00 

62.50 

75-00 

87-50 

100.00 

112.50 

5 

.6 

12.59 

25.19 

37.78 

50.37 

62.96 

75-56 

88.15 

100.74 

113.33 

.6 

•  7 

12.69 

25-37 

38.06 

50.74 

63.43 

76.11 

88.80 

101.48 

114.17 

•  7 

.8 

!2.78 

25.56 

38.33 

Si-  ii 

63.89 

76.67 

89-44 

102.22 

115.00 

.8 

-9 

12.87 

25-74 

38.61 

51.48 

64-35 

77-22 

90.09 

102.96 

US  83 

•  9 

14  0 

12.96 

25-93 

38.89 

51.85 

64.81 

77.78 

90-74 

103.70 

116.67 

14.0 

.1 

13.06 

26.11 

39.17 

52.22 

65.28 

78.32 

91-39 

104.44 

117-50 

.1 

.2 

13-15 

26.30 

39.44 

52.59 

65.74 

78.89 

92.04 

105.19 

"8.33 

.2 

•  3 

13.24 

26.48 

39.72 

52.96 

66.20 

79-44 

92.69 

105-93 

119.17 

3 

•4 

13-33 

26.67 

40.00 

53-33 

66.67 

80.00 

93-33 

I06.67 

120.00 

•4 

•  5 

13-43 

26.85 

40.28 

53-70 

67-13 

80.56 

93-98 

107.41 

120.83 

•  5 

.6 

13.52 

27-04 

40.56 

54-07 

67.59 

81.11 

94.63 

108.15 

121.67 

.6 

•  7 

I3.6I 

27.22 

40.83 

54-44 

68.06 

81.67 

95.28 

108.89 

122.50 

•  7 

.8 

13.70 

27.41 

41.11 

54-81 

68.52 

82.22 

95-93 

109.63 

123  33 

.8 

•  9 

13-80 

27-59 

41.39 

55-19 

68.98 

82.78 

96.57 

H0.37 

124.17 

-9 

15.0 

13.89 

27-78 

41.67 

55-56 

69.44 

83.33 

97.22 

III.  II 

125.00 

15.0 

(270) 


TABLE  XL.  —  (Continued) 


\  Y 

X" 

\ 

X 

2 

3 

4 

5 

6 

7 

8 

9 

x\ 

15.1 

13.98 

27.96 

41-94 

55-93 

69.91 

83-89 

97-87 

111.85 

125.83 

15.1 

.2 

14-07 

28.15 

42.22 

56.30 

70.37 

84.44 

98.52 

112.59 

126.67 

.2 

3 

14.17 

28.33 

42.50 

56.67 

70.83 

85.00 

99-17 

"3-33 

127.50 

3 

.4 

14.26 

28.52 

42.78 

57-04 

71-30 

85.56 

99-81 

114.07 

128.33 

•4 

5 

14.35 

28.70 

43.o6 

57-41 

71.76 

86.11 

100.46 

114.81 

129.17 

•  5 

.6 

14.44 

28.89 

43-33 

57.78 

72.22 

86.67 

IOI.II 

115.56 

130.00 

.6 

-7 

14.54 

29.07 

43.61 

58.15 

72.69 

87.22 

101.76 

116.30 

130.83 

•  7 

.8 

14.63 

29.26 

43-89 

58.52 

73-15 

87.78 

102.41 

117.04 

131.67 

.8 

9 

14.72 

29.44 

44-17 

58.89 

73.6i 

88.33 

103.06 

117.78 

132.50 

•  9 

16.0 

14.81 

29.63 

44-44 

59-26 

74-07 

88.89 

103.70 

118.52 

133-33 

16.0 

.1 

14.91 

29.81 

44.72 

59.63 

74-54 

89.44 

104.35 

119.26 

134-17 

.1 

.2 

15.00 

3O.OO 

45-00 

60.00 

75-00 

90.00 

105.00 

120.00 

135-00 

.2 

3 

15.09 

30.19 

45-28 

60.37 

75.46 

90.56 

105.65 

120.74 

135-83 

•3 

•  4 

15.19 

30.37 

45.56 

60.74 

75-93 

91.11 

106.30 

121.48 

136.67 

•  4 

•  5 

15.28 

30.56 

45.83 

61.11 

76.39 

91.67 

106.94 

122.22 

137-50 

•  5 

.6 

15.37 

30.74 

46.11 

61.48 

76.85 

92.22 

107.59 

122.96 

138.33 

.6 

•  7 

15.46 

30.93 

46.39 

61.85 

77-31 

92.78 

108.24 

123.70 

139-17 

•  7 

.8 

15.56 

31.11 

46.67 

62.22 

77-78 

93  33 

108.89 

124-44 

140.00 

.8 

•9 

15.65 

31.30 

46.94 

62.59 

78.24 

93.89 

109.54 

125.19 

140.83 

•9 

17.0 

15.74 

31-48 

47-22 

62.96 

78.70 

94-44 

110.19 

125-93 

141-67 

17.0 

.1 

15.83 

31.67 

47.50 

63-33 

79-17 

95-00 

110.83 

126.67 

142.50 

.1 

.2 

15.93 

31.85 

47.78 

63.70 

79.63 

95.56 

111.48 

127-41 

143-33 

.2 

3 

16.02 

32.04 

48.06 

64.07 

80.09 

96.11 

112.13 

128.15 

144.17 

3 

•  4 

i6.n 

32.22 

48.33 

64.44 

80.56 

96.67 

112.78 

128.89 

145.00 

•  4 

•  S 

16.20 

32.41 

48.61 

64.81 

81.02 

97-22 

113-43 

129.63 

145.83 

•  5 

.6 

16.30 

32-59 

48.89 

65-19 

81.48 

97.78 

114.07 

130.37 

146.67 

.6 

•  7 

16.39 

32-78 

49.17 

65.56 

81.94 

98.33 

114.72 

I3I.II 

147-50 

•  7 

.8 

16.48 

32.96 

49.44 

65.93 

82.41 

98.89 

115.37 

131.85 

148.33 

.8 

9 

16.57 

33-15 

49.72 

66.30 

82.87 

99-44 

116.02 

132.59 

149-17 

•  9 

18.0 

16.67 

33-33 

50.00 

66.67 

83.33 

IOO.OO 

116.67 

133  33 

150.00 

18.0 

.1 

16.76 

33-52 

50.28 

67.04 

83.80 

100.56 

117.31 

134.07 

150.83 

.1 

.2 

16.85 

33-70 

50.56 

67-41 

84.26 

IOI.II 

117.96 

I34.8I 

151-67 

.2 

3 

16.94 

33-89 

50.83 

67.78 

84.72 

101.67 

118.61 

135.56 

152.50 

3 

•4 

17.04 

34-07 

51-  II 

68.15 

85.19 

IO2.22 

119.26 

136.30 

153-33 

•4 

5 

17-13 

34.26 

51-39 

68.52 

85.65 

102.78 

119.91 

137-04 

154-17 

•  5 

.6 

17.22 

34-44 

51-67 

68.89 

86.ii 

103-33 

120.56 

137.78 

155.00 

.6 

•  7 

I7.3I 

34.63 

51-94 

69.26 

86.57 

103.89 

121.20 

138.52 

155.83 

.7 

.8 

17.41 

34-81 

52.22 

69-63 

87.04 

104.44 

121.85 

139.26 

156.67 

.8 

9 

17-50 

35-00 

52-50 

70.00 

87.50 

IO5.OO 

122.50 

140.00 

157.50 

•  9 

19.0 

17-59 

35-19 

52.78 

70.37 

87-96 

105.56 

123.15 

140.74 

158.33 

19.0 

.1 

17.69 

35-37 

53-o6 

70.74 

88.43 

106.11 

123.80 

141.48 

159-17 

.1 

.2 

17.78 

35-56 

53-33 

71.  II 

88.89 

106.67 

124-44 

142.22 

160.00 

.2 

3 

17.87 

35-74 

53.6l 

71.48 

89-35 

107.22 

125.09 

142.96 

160.83 

3 

•4 

17.96 

35-93 

53.89 

71.85 

89.81 

107.78 

125-74 

143.70 

161.67 

•  4 

•  S 

18.06 

36.11 

54-17 

72.22 

90.28 

108.33 

126.39 

144-44 

162  .  50 

•  5 

.6 

18.15 

36.30 

54-44 

72.59 

90-74 

108.89 

127.04 

145.19 

163-33 

.6 

.7 

18.24 

36.48 

54-72 

72.96 

91.20 

109.44 

127.69 

145-93 

164.17 

•  7 

.8 

18.33 

36.67 

55-00 

73-33 

91.67 

110.00 

128.33 

146.67 

165.00 

.8 

•  9 

18.43 

36.85 

55-28 

73-70 

92.13 

110.56 

128.98 

147.41 

165.83 

•  9 

20.0 

18.52 

37-04 

55-56 

74.07 

92.59 

III.  II 

129.63 

148.15 

166.67 

20.0 

(271) 


TABLE  XL.  —  (Continued) 


\  F 

Y  / 

A 

I 

2 

3 

4 

5 

6 

7 

8 

9 

/x 

20.1 

18.61 

37-22 

55.83 

74-44 

93-06 

111.67 

130.28 

148.89 

167.50 

20  1 

.2 

18.70 

37.41 

56.11 

74-81 

93-52 

112.22 

130.93 

149-63 

168.33 

.2 

•3 

18.80 

37.59 

56.39 

75-19 

93-98 

112.78 

I3L57 

150.37 

169.17 

3 

•  4 

18.89 

37.78 

56.67 

75.56 

94-44 

113-33 

132.22 

151.11 

170.00 

•  4 

-5 

18.98 

37.96 

56.94 

75-93 

94-91 

113.89 

132.87 

151.85 

170.83 

•  5 

.6 

19.07 

38.15 

57-22 

76.30 

95-37 

114.44 

133.52 

152.59 

171.67 

.6 

.7 

19-17 

38.33 

57.50 

76.67 

95.83 

II5.OO 

134.17 

153-33 

172.50 

.7 

.8 

19.26 

38.52 

57.78 

77-04 

96.30 

115.56 

134-81 

154-07 

173-33 

.8 

•  9 

19-35 

38.70 

58.06 

77-41 

96.76 

116.11 

135.46 

154-81 

174-17 

•  9 

21.0 

19-44 

38.89 

58.33 

77-78 

97-22 

116.67 

136.11 

155.56 

175.00 

21.0 

.1 

19-54 

39.07 

58.61 

78.15 

97.69 

117.22 

136.76 

156.30 

175.83 

.1 

.2 

19-63 

39.26 

58.89 

78.52 

98.15 

II7-78 

I37-4I 

157-04 

176.67 

.2 

•  3 

19.72 

39-44 

59.17 

78-89 

98.61 

118.33 

138.06 

157.78 

177-50 

3 

•  4 

19.81 

39.63 

59-44 

79-26 

99-07 

118.89 

138.70 

158.52 

178.33 

•  4 

•  5 

19-91 

39-Si 

59-72 

79.63 

99-54 

119-44 

139-35 

159-26 

I79-I7 

•  5 

.6 

20.00 

40.00 

60.00 

80.00 

IOO.OO 

120.  OO 

140.00 

160.00 

180.00 

.6 

.7 

20.09 

40.19 

60.28 

80.37 

100.46 

I2O.56 

140.65 

160.74 

180.83 

•  7 

.8 

20.19 

40.37 

60.56 

80.74 

100.93 

121.  II 

141.30 

161.48 

181.67 

.8 

•  9 

20.28 

40.56 

60.83 

81.11 

101.39 

121.67 

141.94 

162.22 

182.50 

•  9 

22.0 

20.37 

40.74 

6i.n 

81.48 

101.85 

122.22 

142.59 

162.96 

183-33 

22.0 

.1 

20.46 

40-93 

6i.39 

81.85 

102.31 

122.78 

143-24 

163.70 

184.17 

.1 

.2 

20.56 

41.11 

61.67 

82.22 

102.78 

123.33 

143-89 

164.44 

185.00 

.2 

3 

20.65 

41-30 

6i.94 

82.59 

103.24 

123.89 

144-54 

165.19 

185.83 

3 

•4 

20.74 

41.48 

62.22 

82.96 

103.70 

124.44 

145.19 

165.93 

186.67 

•  4 

5 

20.83 

41.67 

62.50 

83.33 

104.17 

125.00 

145.83 

166.67 

187.50 

-5 

.6 

20.93 

41.85 

62.78 

83-70 

104.63 

125.56 

146.48 

167.41 

188.33 

.6 

.7 

21.  02 

42.04 

63.06 

84-07 

105.09 

126.11 

147.13 

168.15 

189.17 

•  7 

.8 

21.  II 

42.22 

63.33 

84-44 

105.56 

126.67 

147.78 

168.89 

190.00 

.8 

•  9 

21.20 

42.41 

63-61 

84.81 

106.02 

127.22 

148.43 

169.63 

190.83 

•  9 

23.0 

2I.3O 

42.59 

63.89 

85.19 

106.48 

127.78 

149.07 

170.37 

191-67 

23.0 

.1 

21.39 

42.78 

64.17 

85.56 

106.94 

128.33 

149.72 

171.11 

192.50 

.1 

.2 

21.48 

42.96 

64.44 

85-93 

107.41 

128.89 

150.37 

171.85 

193-33 

.2 

•  3 

21.57 

43-15 

64.72 

86.30 

107.87 

129.44 

151.02 

172-59 

194-17 

3 

•  4 

21.67 

43-33 

65.00 

86.67 

108.33 

I3O.OO 

151.67 

173.33 

195.00 

•  4 

•  5 

21.76 

43-52 

65-28 

87.04 

108.80 

130.56 

152.31 

174.07 

195.83 

•  5 

.6 

21.85 

43-70 

65-56 

87.41 

109.26 

I3I.II 

152.96 

174.81 

196.67 

.6 

.7 

21-94 

43-89 

65.83 

87.78 

109.72 

131.67 

I53.6i 

175.56 

197.50 

.7 

.8 

22.04 

44.07 

66.11 

88.15 

110.19 

132.22 

154-26 

176.30 

198.33 

.8 

9 

22.13 

44.26 

66.39 

88.52 

110.65 

132.78 

I54.9I 

177.04 

199-17 

•  9 

24.0 

22.22 

44-44 

66.67 

88.89 

in.  II 

133-33 

155.56 

177.78 

200.00 

24.0 

.1 

22.31 

44.63 

66.94 

89.26 

in-  57 

133.89 

156.20 

178.52 

200.83 

.1 

.2 

22.41 

44-81 

67.22 

89.63 

112.04 

134.44 

156.85 

179-26 

201.67 

.2 

3 

22.50 

45.00 

67.50 

90.00 

112.50 

135-00 

157.50 

180.00 

202  .  SO 

3 

•  4 

22.59 

45-19 

67-78 

90.37 

112.96 

135.56 

158.15 

180.74 

203.33 

-4 

•  S 

22.69 

45-37 

68.06 

90.74 

113-43 

136.11 

158.80 

181  .  48 

204.17 

•  5 

.6 

22.78 

45.56 

68.33 

91.11 

113-89 

136.67 

159-44 

182.22 

2O5.OO 

.6 

•  7 

22.87 

45-74 

68.  61 

91.48 

114-35 

137-22 

160.09 

182.96 

205.83 

-7 

.8 

22.96 

45-93 

68.89 

91-85 

114.81 

137.78 

160.74 

183-70 

206.67 

.8 

9 

23.06 

46.11 

69.17 

92.22 

115.28 

138.33 

161.39 

184.44 

207.50 

•  9 

25.0 

23.15 

46.30 

69.44 

92-59 

115-74 

138.89 

162  .  04 

185.19 

208.33 

25  0 

(272) 


TABLE  XL.  — (Continued) 


X 

I 

2 

3 

4 

5 

6 

7 

8 

9 

A 

25.1 

23.24 

46.48 

69.72 

92.96 

116.20 

139-44 

162.69 

185.93 

209.17 

25.1 

.2 

23  33 

46.67 

70.00 

93-33 

116.67 

140.00 

163.33 

186.67 

210.00 

.2 

•3 

23-43 

46.85 

70.28 

93-70 

117.13 

140.56 

163.98 

187.41 

210.83 

3 

.4 

23.52 

47.04 

70.56 

94-07 

117-59 

141.11 

164.63 

188.15 

211.67 

•4 

•  5 

23.61 

47-22 

70.83 

94-44 

118.06 

141.67 

165.28 

188.89 

212.50 

-5 

.6 

23.70 

47.41 

7I.II 

94.81 

118.52 

142.22 

165.93 

189.63 

213-33 

.6 

•  7 

23.80 

47-59 

71-39 

95.19 

118.98 

142.78 

166.57 

190.37 

214.17 

.7 

.8 

23-89 

47-78 

71.67 

95.56 

119-44 

143-33 

Il6?.22 

191.11 

2I5.OO 

.8 

•  9 

23.98 

47.96 

71-99 

95-93 

119.91 

143-89 

167.87 

191-85 

215.83 

•  9 

26.0 

24.07 

48.15 

72.22 

96.30 

120.37 

144.44 

168.52 

192.59 

216.67 

26.0 

.1 

24.17 

48-33 

72.50 

96.67 

120.83 

145.00 

169.17 

193.33 

217.50 

.1 

.2 

24.26 

48.52 

72.78 

97-04 

121.30 

145.56 

169.81 

194.07 

218.33 

.2 

3 

24-35 

48.70 

73.06 

97-41 

121.76 

146.11 

170.46 

194-81 

219.17 

3 

.4 

24-44 

48.89 

73-33 

97-78 

122.22 

146.67 

I7I.II 

195.56 

220.00 

•  4 

•  S 

24-54 

49-07 

73-6i 

98.15 

122.69 

147-22 

171.76 

196.30 

220.83 

•  5 

.6 

24-63 

49-26 

73-89 

98.52 

123.15 

147-78 

172.41 

197.04 

221.67 

.6 

.7 

24.72 

49-44 

74-17 

98.89 

I23.6I 

148.33 

173.06 

197.78 

222.50 

•  7 

.8 

24.81 

49-63 

74-44 

99-26 

124.07 

148.89 

173.70 

198.52 

223-33 

.8 

•  9 

24.91 

49-Si 

74.72 

99.63 

124-54 

149-44 

174.35 

199-26 

224.17 

•9 

27.0 

25.00 

50.00 

75.oo 

100.00 

125.00 

150.00 

175.00 

200.00 

225.00 

27.0 

j 

25.09 

50-19 

75-28 

100.37 

125.46 

150.56 

175.65 

200.74 

225.83 

.1 

.2 

25.19 

50.37 

75.56 

100.74 

125-93 

151.11 

176.30 

201.48 

226.67 

.2 

3 

25.28 

50.56 

75.83 

IOI.II 

126.39 

151.67 

176.94 

202.22 

227.50 

•  3 

•  4 

25-37 

50.74 

76.11 

101.48 

126.85 

152.22 

177-59 

202  .  96 

228.33 

•  4 

•  5 

25-46 

50-93 

76.39 

101.85 

127.31 

152.78 

178.24 

203.70 

229.17 

•  5 

.6 

25.56 

Si-il 

76.67 

102.22 

127.78 

153-33 

178.89 

204.44 

230.00 

.6 

•  7 

25.65 

51.30 

76.94 

102.59 

128.24 

153-89 

179-54 

205.19 

230.83 

-7 

.8 

25.74 

51.48 

77.22 

102.96 

128.70 

154-44 

180.19 

205-93 

231.67 

.8 

•  9 

25-83 

51-67 

77-50 

103.33 

129.17 

155-00 

180.83 

206.67 

232.50 

-9 

28.0 

25-93 

51-85 

77.78 

103.70 

129.63 

155.56 

181.48 

207.41 

233-33 

28.0 

.1 

26.02 

52.04 

78.06 

104.07 

130.09 

156.11 

182.13 

208.15 

234.17 

.1 

.2 

26.11 

52.22 

78.33 

104.44 

130.56 

156.67 

182  .  78 

208.89 

235-00 

.2 

3 

26.20 

52.41 

78.61 

I04.8I 

I3I.O2 

157-22 

183.43 

209.63 

235.83 

•  3 

•  4 

26.30 

52-59 

78.89 

105.19 

131.48 

157.78 

184-07 

210.37 

236.67 

-4 

•  5 

26.39 

52.78 

79-17 

105.56 

131-94 

158.33 

184.72 

211.  II 

237.50 

-5 

.6 

26.48 

52.96 

79-44 

105-93 

132.41 

158.89 

185-37 

211.85 

238-33 

.6 

.7 

26.57 

53-15 

79.72 

I06.30 

132.87 

159-44 

186.02 

212.59 

239.17 

-7 

.8 

26.67 

53-33 

80.00 

106.67 

133  33 

160.00 

186.67 

213.33 

240.00 

.8 

9 

26.76 

53-52 

80.28 

107.04 

I33.8o 

160.56 

187.31 

214.07 

240.83 

-9 

29.0 

26.85 

53-70 

80.56 

107.41 

I34.26 

i6i.n 

187.96 

214.81 

241.67 

29.0 

.1 

26.94 

53.89 

80.83 

107.78 

134.72 

161.67 

188.61 

215.56 

242.50 

.1 

.2 

27.04 

54.07 

81.11 

108.15 

135.19 

162.22 

189.26 

216.30 

243-33 

.2 

3 

27-13 

54-26 

81.39 

108.52 

135.65 

162.78 

189.91 

217.04 

244.17 

-3 

•  4 

27.22 

54-44 

81.67 

108.89 

136.11 

163.33 

190.56 

217.78 

245.00 

-4 

•  5 

27-31 

54-63 

81.94 

109.26 

136.57 

163.89 

I9I.2O 

218.52 

245.83 

5 

.6 

27.41 

54-81 

82.22 

109.63 

137.04 

164.44 

191.85 

219.26 

246.67 

.6 

•  7 

27.50 

55-00 

82.50 

IIO.OO 

137.50 

165.00 

192.50 

220.00 

247.50 

.7 

.8 

27-59 

55-19 

82.78 

110.37 

137.96 

165.56 

193.15 

220.74 

248.33 

.8 

•  9 

27.69 

55-37 

83.06 

110.74 

138.43 

i66.ii 

193.80 

221  .  48 

249.17 

•  9 

30.0 

27-78 

55-56 

83.33 

III.  II 

138.89 

166.67 

194-44 

222  .  22 

25O.OO 

30  0 

(273) 


TABLE  XL.  —  (Continued) 


\  Y 

Y  / 

\ 

I 

2 

3 

4 

5 

6 

7 

8 

9 

/ 

x  \ 

'  X 

30.1 

27.87 

55-74 

83-61 

111.48 

139-35 

167.22 

195.09 

222.96 

250.83 

30.1 

.2 

27.96 

55-93 

83.89 

111.85 

I39.8i 

167.78 

195-74 

223.70 

251.67 

.2 

3 

28.06 

56.11 

84.17 

112.22 

140.28 

168.33 

196.39 

224.44 

252.50 

3 

.4 

28.15 

56.30 

84.44 

112.59 

140.74 

168.89 

197.04 

225.19 

253-33 

-4 

•  5 

28.24 

56.48 

84.72 

112.96 

141.20 

169.44 

197.69 

225.93 

254.17 

.5 

.6 

28.33 

56.67 

85.00 

113-33 

141.67 

170.00 

198.33 

226.67 

255.00 

.6 

.7 

28.43 

56.85 

85.28 

113.70 

142.13 

170.56 

198.98 

227.41 

255.83 

-7 

.8 

28.52 

57-04 

85-56 

114.07 

142.59 

171.11 

199.63 

228.15 

256.67 

.8 

•9 

28.61 

57-22 

85.83 

114-44 

143.06 

171.67 

200.28 

228.89 

257.50 

9 

31.0 

28.70 

57.41 

86.11 

114.81 

143.52 

172.22 

200.93 

229.63 

258.33 

31.0 

.1 

28.80 

57.59 

86.39 

115.19 

143.98 

172.78 

201.57 

230.37 

259-17 

.! 

.2 

28.89 

57.78 

86.67 

115.56 

144-44 

173-33 

202  .  22 

231.11 

260.00 

.2 

•3 

28.98 

57.96 

86.94 

115-93 

144.91 

173-89 

202.87 

231.85 

260.83 

3 

.4 

29.07 

58.15 

87.22 

II6.30 

145-37 

174-44 

203-52 

232.59 

261.67 

-4 

•  5 

29.17 

58.33 

87.50 

116.67 

145.83 

175.00 

204.17 

233-33 

262  .  50 

•  5 

.6 

29.26 

58.52 

87.78 

117.04 

146.30 

175.56 

204.81 

234-07 

263.33 

.6 

-7 

29.35 

58.70 

88.06 

II7-4I 

146.76 

176.11 

205.46 

234-81 

264.17 

-7 

.8 

29-44 

58.89 

88.33 

117.78 

147.22 

176.67 

206.  II 

235.56 

265.00 

.8 

•9 

29-54 

59.07 

88.61 

II8.I5 

147.69 

177.22 

206.76 

236.30 

265.83 

•9 

32.0 

29.63 

59.26 

88.89 

118.52 

148.15 

177.78 

207.41 

237.04 

266.67 

32.0 

.1 

29.72 

59-44 

89.17 

118.89 

148.61 

178.33 

208.06 

237.78 

267.50 

.1 

.2 

29.81 

59.63 

89-44 

119.26 

149-07 

178.89 

2O8.70 

238.52 

268.33 

.2 

•  3 

29.91 

59-81 

89.72 

119.63 

149-54 

179-44 

209.35 

239-26 

269.17 

3 

•4 

30.00 

60.00 

90.00 

120.00 

150.00 

180.00 

210.00 

240.00 

270.00 

•  4 

•  5 

30.09 

60.19 

90.28 

I2O.37 

150.46 

180.56 

210.65 

240.74 

270.83 

•  5 

.6 

30.19 

60.37 

90.56 

I2O.74 

150.93 

i8l.il 

211.30 

241-48 

271-67 

.6 

.7 

30.28 

60.56 

90.83 

121.  II 

151-39 

181  .  67 

211.94 

242  .  22 

272.50 

.7 

.8 

30.37 

60.74 

9I.II 

121.48 

151  85 

182.22 

212.59 

242.96 

273-33 

.8 

•9 

30.46 

60.93 

91-39 

121.85 

152.31 

182.78 

213.24 

243-70 

274.17 

•  9 

33.0 

30.56 

6i.n 

91.67 

122  .  22 

152.78 

183.33 

213.89 

244-44 

275-00 

33  0 

.1 

30.65 

61.30 

91.94 

122.59 

153.24 

183.89 

214.54 

245.19 

275-83 

.1 

.2 

30.74 

61.48 

92.22 

122.96 

153.70 

184.44 

215.19 

245-93 

276.67 

.2 

3 

30.83 

61.67 

92.50 

123-33 

I54-I7 

185.00 

215.83 

246.67 

277-50 

3 

•  4 

30.93 

61.85 

92.78 

123.70 

154.63 

185.56 

216.48 

247.41 

278.33 

•  4 

-5 

31.02 

62.04 

93.o6 

124  .  07 

155.09 

i86.il 

217.13 

248.15 

279-17 

-5 

.6 

31.11 

62.22 

93-33 

124-44 

155.56 

186.67 

217.78 

248.89 

280.00 

.6 

•  7 

31.20 

62.41 

93-61 

124.81 

156.02 

187.22 

218.43 

249.63 

280.83 

.7 

.8 

31.30 

62.59 

93.89 

125.19 

156.48 

187.78 

219.07 

250.37 

281.67 

.8 

.9 

31-39 

62.78 

94.17 

125.56 

156.94 

188.33 

219.72 

251.11 

282  .  50 

•  9 

34.0 

31.48 

62.96 

94-44 

125-93 

I57.4I 

188.89 

220.37 

251.85 

283.33 

34.0 

.1 

31-57 

63.15 

94-72 

126.30 

157.87 

189.44 

221.02 

252.59 

284.17 

.1 

.2 

31-67 

63.33 

95-00 

126.67 

158.33 

190.00 

221.67 

253-33 

285.00 

.2 

•3 

31.76 

63-52 

95.28 

127.04 

158.80 

190.56 

222.31 

254.07 

285.83 

3 

•4 

31.85 

63.70 

95.56 

127.41 

159-26 

191.11 

222.96 

254.81 

286.67 

•  4 

•  5 

31-94 

63.89 

95.83 

127.78 

159-72 

191-67 

223.61 

255.56 

287.50 

5 

.6 

32.04 

64.07 

96.11 

128.15 

160.19 

192  .  22 

224.26 

256.30 

288.33 

.6 

•  7 

32.13 

64.26 

96.39 

128.52 

160.65 

192.78 

224.91 

257-04 

289.17 

•  7 

.8 

32.22 

64.44 

96.67 

128.89 

i6i.n 

193-33 

225.56 

257.78 

290.00 

.8 

.9 

32.31 

64.63 

96.94 

129.26 

i6i.57 

193.89 

226.20 

258.52 

290.83 

.9 

35.0 

32.41 

64.81 

97.22 

129.63 

162  .  04 

194.44 

226.85 

259.26 

291.67 

35.0 

(274) 


TABLE  XL.  —  (Continued) 


\  ¥ 

F  / 

\ 

A.   V 

i 

2 

3 

4 

5 

6 

7 

8 

9 

/x 

35.1 

32.50 

65.00 

97-50 

130.00 

162.50 

195.00 

227.50 

260.00 

292.50 

35.1 

.2 

32.59 

65.19 

97-78 

130.37 

162.96 

195.56 

228.15 

260.74 

293  33 

.2 

3 

32.69 

65.37 

98.06 

130.74 

163.43 

196.11 

228.80 

261.48 

294.17 

•3 

•4 

32.78 

65.56 

98.33 

131.11 

163.89 

196.67 

229.44 

262.22 

295.00 

•4 

•  5 

32.87 

65.74 

98.61 

131.48 

164.35 

197-22 

230.09 

262.96 

295.83 

•  5 

.6 

32.96 

65.93 

98.89 

131-85 

164.81 

197.78 

230.74 

263.70 

296.67 

.6 

•  7 

33-06 

66.11 

99-17 

132  .  22 

165.28 

198.33 

231.39 

264.44 

297.50 

.7 

.8 

33-15 

66.30 

99-44 

132.59 

165.74 

198.89 

232.04 

265.19 

298.33 

.8 

-9 

33  24 

66.48 

99-72 

132.96 

166.20 

199.44 

232.69 

265.93 

299.17 

•  9 

36.0 

33  33 

66.67 

IOO.OO 

133-33 

166.67 

200.00 

233  33 

266.67 

300.00 

36.0 

.1 

33-43 

66.85 

100.28 

133.70 

167.13 

200.56 

233.98 

267.41 

300.83 

.x 

.2 

33.52 

67.04 

100.56 

134-07 

167.59 

2OI.II 

234.63 

268.15 

301.67 

.  .a 

3 

33.61 

67.22 

100.83 

134-44 

168.06 

201.67 

235.28 

268.89 

302.50 

•3 

•  4 

33-70 

67.41 

IOI.II 

134-81 

168.52 

202.22 

235-93 

269.63 

303.33 

.4 

.5 

33-80 

67-59 

101.39 

135-19 

168.98 

202.78 

236.57 

270.37 

304.17 

•  5 

.6 

33.89 

67-78 

101.67 

135.56 

169-44 

203-33 

237-22 

271.11 

305.00 

.6 

.7 

33-98 

67.96 

101.94 

135-93 

169.91 

203.89 

237.87 

271.85 

305.83 

•  7 

.8 

34-07 

68.15 

102  .  22 

136.30 

170.37 

204-44 

238.52 

272.59 

306.67 

.8 

•9 

34-17 

68.33 

IO2  .  50 

136.67 

170.83 

2O5.OO 

239  I? 

273  33 

307.50 

•  9 

37.0 

34-26 

68.52 

102.78 

I37.04 

171.30 

205.56 

239-81 

274-07 

308.33 

37.0 

.x 

34-35 

68.70 

103.06 

137-41 

171.76 

206.  II 

240.46 

274-81 

309.17 

.1 

.2 

34-44 

68.89 

103-33 

137.78 

172.22 

206.67 

241.11 

275  56 

310.00 

.2 

3 

34-54 

69.07 

IO3.6I 

138.15 

172.69 

207  .  22 

241.76 

276.30 

310.83 

3 

•4 

34.63 

69.26 

103.89 

138.52 

173.15 

207.78 

242.41 

277.04 

311.67 

•4 

•  5 

34-72 

69.44 

104.17 

138.89 

173-61 

208.33 

243  06 

277.78 

312.50 

•  5 

.6 

34-81 

69.63 

104.44 

139.26 

174-07 

208.89 

243.70 

278.52 

313.33 

.6 

7 

34-91 

69.81 

104.72 

139.63 

174-54 

209.44 

244-35 

279.26 

314.17 

.7 

.8 

35-00 

70.00 

I05.OO 

140.00 

175.00 

•210.00 

245-00 

280.00 

315-00 

.8 

.9 

35-09 

70.19 

105.28 

140.37 

175.46 

210.56 

245.65 

280.74 

315.83 

.9 

38.0 

35-19 

70.37 

105.56 

140.74 

175-93 

211.  II 

246.30 

281.48 

316.67 

38.0 

.1 

35-28 

70.56 

105.83 

I4I.II 

176.39 

211.67 

246.94 

282.22 

3I7.50 

.1 

.2 

35-37 

70.74 

io6.ii 

141.48 

176.85 

212.22 

247-59 

282.96 

318.33 

.2 

3 

35.46 

70.93 

106.39 

141.85 

177.31 

212.78 

248.24 

283.70 

319.17 

•3 

•  4 

35.56 

71.11 

106.67 

142.22 

177.78 

213-33 

248.89 

284.44 

320.00 

.4 

5 

35.65 

71-30 

106.94 

142.59 

178.24 

213.89 

249-54 

285.19 

320.83 

-5 

.6 

35-74 

71.48 

107  .  22 

142.96 

178.70 

214.44 

250.19 

285.93 

321.67 

.6 

•  7 

35.83 

71.67 

107.50 

143-33 

179-17 

2I5.OO 

250.83 

286.67 

322.50 

.7 

.8 

35-93 

71-85 

107.78 

143.70 

179.63 

215.56 

251.48 

287.41 

323.33 

.8 

.9 

36.02 

72.04 

108.06 

144-07 

180.09 

2l6.II 

252.13 

288.15 

324.17 

•  9 

39.0 

36.11 

72.22 

108.33 

144-44 

180.56 

216.67 

252.78 

288.89 

325.00 

39.0 

.1 

36.20 

72.41 

108.61 

144-81 

181.02 

217.22 

253-43 

289.63 

325.83 

.1 

.2 

36.30 

72.59 

108.89 

145.19 

181.48 

217.78 

254-07 

290.37 

326.67 

.2 

3 

36.39 

72.78 

109.17 

145.56 

181.94 

218.33 

254-72 

291.11 

327.50 

3 

•4 

36.48 

72.96 

109.44 

145-93 

182.41 

218.89 

255-37 

291.85 

328.33 

•  4 

.5 

36.57 

73-15 

109.72 

146-30 

182.87 

219.44 

256.02 

292.59 

329.17 

•  5 

.6 

36.67 

73-33 

IIO.OO 

146.67 

183.33 

220.00 

256.67 

293-33 

330.00 

.6 

•  7 

36.76 

73-52 

110.28 

147.04 

183.80 

220.56 

257-31 

294.07 

330.83 

.7 

.8 

36.85 

73.70 

110.56 

147-41 

184.26 

221.  II 

257.96 

294.81 

331  67 

.8 

•9 

36.94 

73.89 

110.83 

147.78 

184.72 

221  .  67 

258.61 

295.56 

332.50 

•9 

40.0 

37-04 

74-07 

III.  II 

148.15 

185.19 

222  .  22 

259.26 

296.30 

333-33 

40.0 

(275) 


TABLE  XLI 

Prismoidal  Corrections  to  be  subtracted  from  average  end  area 
volumes  100  feet  long.  D  —  DI  =  difference  in  total  width;  C  —  C\ 
=  difference  in  center  height.  Corrections  in  cubic  yards. 


\D-£>, 

D-DJ 

Ny, 

I 

2 

3 

4 

5 

6 

V 

8 

9 

c-cX 

/C-C, 

.2 

0.06 

O.I2 

0.19 

0.25 

0.31 

0-37 

0.43 

0-49 

0.56 

.2 

•  4 

O.I2 

0.25 

0.37 

o.49 

0.62 

0.74 

0.86 

0-99 

i.  ii 

•  4 

.6 

O.I9 

0.37 

0.56 

0.74 

0.93 

I.  ii 

1.30 

1.48 

1.67 

.6 

.8 

0.25 

0.49 

0-74 

0-99 

1.23 

1.48 

1-73 

1.98 

2.22 

.8 

I.O 

0.31 

0.62 

0,93 

•  23 

1-54 

1.85 

2.16 

2-47 

2.78 

I.O 

.2 

0-37 

0.74 

I.  II 

-48 

1.85 

2.22 

2.59 

2.96 

3-33 

.2 

-4 

0.43 

0.86 

1-30 

•  73 

2.16 

2-59 

3-02 

3.46 

3.89 

•4 

.6 

0.49 

•99 

1.48 

•  98 

2.47 

2.96 

3-46 

3-95 

4-44 

.6 

.8 

0.56 

.11 

1.67 

.22 

2.78 

3-33 

3.89 

4-44 

S.oo 

.8 

2.0 

0.62 

•  23 

1.85 

2-47 

3-09 

3.70 

4.32 

4-94 

5-56 

2.0 

.2 

0.68 

.36 

2.04 

2.72 

3-40 

4-07 

4-75 

5-43 

6.  ii 

.2 

•4 

0.74 

.48 

2.22 

2.96 

3-70 

4-44 

5-19 

5-93 

6.67 

•  4 

.6 

0.80 

.60 

2.41 

3-21 

4.01 

4.81 

5-62 

6.42 

7-22 

.6 

.8 

0.86 

•  73 

2.59 

3.46 

4-32 

5-19 

6.05 

6.91 

7-78 

.8 

3-0 

0.93 

.85 

2.78 

3.70 

4-63 

5-56 

6.48 

7-41 

8.33 

30 

.2 

0.99 

.98 

2.96 

3.95 

4-94 

5-93 

6.91 

7-90 

8.89 

.2 

•4 

1.05 

.10 

3-15 

4.20 

5-25 

6.30 

7-35 

8.40 

9-44 

•  4 

.6 

i.  ii 

.22 

3-33 

4-44 

5-56 

6.67 

7-78 

8.89 

10.00 

.6 

.8 

1.  17 

•  35 

3.52 

4.69 

5-86 

7-04 

8.21 

9-38 

10.56 

.8 

4.0 

1.23 

2.47 

3-70 

4-94 

6.17 

7-41 

8.64 

9.88 

ii.  ii 

4.0 

.2 

1.30 

2.59 

3-89 

5-19 

6.48 

7.78 

9-07 

10.37 

11.67 

.2 

•4 

1.36 

2.72 

4.07 

5-43 

6-79 

8.15 

9-Si 

10.86 

12.22 

•4 

.6 

1.42 

2.84 

4-26 

5-68 

7.10 

8.52 

9-94 

11.36 

12.78 

.6 

.8 

1.48 

2.96 

4-44 

5-93 

7-41 

8.89 

10-37 

11.85 

13-33 

.8 

S.o 

I  -54 

3-09 

4-63 

6.17 

7-72 

9.26 

10.80 

12-35 

13.89 

So 

.2 

1.  60 

3.21 

4.81 

6.42 

8.02 

9-63 

11.23 

12.84 

14.44 

.2 

•4 

1.67 

3-33 

S.oo 

6.67 

8.33 

IO.OO 

11.67 

13-33 

15-00 

•  4 

.6 

1-73 

3.46 

5-19 

6.91 

8.64 

10-37 

12.  IO 

13-83 

15.56 

.6 

.8 

1-79 

3-58 

5-37 

7.16 

8.95 

10.74 

12.53 

14-32 

16.11 

.8 

6.0 

1.85 

3-70 

5-56 

7-41 

9.26 

ii.  ii 

12.96 

14.81 

16.67 

6.0 

.2 

1.91 

3-83 

5-74 

7-65 

9-57 

11.48 

13.40 

15.31 

17.22 

.2 

•4 

1.98 

3-95 

5-93 

7-90 

9.88 

11.85 

13.83 

I5.8o 

17.78 

•  4 

.6 

2.04 

4-07 

6.  ii 

8.15 

10.19 

12.22 

14.26 

16.30 

18-33 

.6 

.8 

2.10 

4.20 

6.30 

8.40 

10.49 

12.59 

14.69 

16.79 

18.89 

.8 

70 

2.16 

4-32 

6.48 

8.64 

10.80 

12.96 

15.12 

17.28 

19-44 

70 

.2 

2.22 

4-44 

6.67 

'8.89 

ii.  ii 

1333 

15.56 

17.78 

20.00 

.2 

•4 

2.28 

4-57 

6.85 

9-14 

11.42 

13.7° 

15.99 

18.27 

20.56 

•4 

.6 

2.35 

4-69 

7.04 

9-38 

11-73 

14.07 

16.42 

18.77 

21.  II 

.6 

.8 

2.41 

4.81 

7.22 

9-63 

12.04 

14.44 

16.85 

19.26 

21.67 

.8 

8.0 

2.47 

4-94 

7-41 

9-88 

12.35 

14.81 

17.28 

19-75 

22.22 

8.0 

.2 

3-53 

5.o6 

7-59 

10.12 

12.65 

15.19 

17.72 

20.25 

22.78 

.2 

•4 

2.59 

5-19 

7-78 

10.37 

12.96 

15.56 

18.15 

20.74 

23-33 

-4 

.6 

2.65 

5-31 

7.96 

10.62 

13-27 

15-93 

18.58 

21.23 

23-89 

.6 

.8 

2.72 

5-43 

8.15 

10.86 

13-58 

16.30 

19.01 

21.73 

24.44 

.8 

9.0 

2.78 

5.56 

8.33 

ii.  ii 

13-89 

16.67 

19.44 

22.22 

25-00 

9.0 

.2 

2.84 

5.68 

8.52 

11.36 

14.20 

17.04 

19.88 

22.72 

25.56 

.2 

•  4 

2.90 

5-8o 

8.70 

ii.  60 

14-51 

17.41 

20.31 

23.21 

26.11 

.4 

.6 

2.96 

5-93 

8.89 

11.85 

14.81 

17.78 

20.74 

23.70 

26.67 

.6 

.8 

3.02 

6.05 

9.07 

12.10 

15.12 

18.15 

2T.I7 

24.20 

27.22 

.8 

10.0 

3-09 

6.17 

9.26 

12.35 

15-43 

18.52 

21.  60 

24.69 

27.78 

10  0 

(276) 


TABLE  XLI.  —  (Continued} 


\D-Di 

D—Di/ 

I 

2 

3 

4 

5 

6 

7 

8 

9 

^/ 

c-c^\ 

/c-c, 

10.2 

3-15 

6.30 

9-44 

12.59 

15-74 

18.89 

22.04 

25.19 

28.33 

IO.2 

.4 

3-21 

6.42 

9-63 

12.84 

16.05 

19.26 

22.47 

25.68 

28.89 

•4 

.6 

3-27 

6-54 

9-81 

13-09 

16.36 

19-63 

22.90 

26.17 

29.44 

.6 

.8 

3-33 

6.67 

IO.OO 

13  33 

16.67 

20.00 

23-33 

26.67 

30.00 

.8 

II.  O 

3.40 

6.79 

10.19 

13.58 

16.98 

20.37 

23-77 

27.16 

30.56 

II.  O 

.2 

3.46 

6.91 

10.37 

13-83 

17.28 

20.74 

24.20 

27-65 

31.11 

.2 

•  4 

3.52 

7.04 

10.56 

14.07 

17-59 

21.  II 

24-63 

28.15 

31-67 

•4 

.6 

3-58 

7.16 

10.74 

14-32 

17.90 

21.48 

25.06 

28.64 

32.22 

.6 

.8 

3.64 

7.28 

10.93 

14-57 

18.21 

21.85 

25-49 

29.14 

32.78 

.8 

12.0 

3.70 

7.41 

ii.  ii 

14.81 

18.52 

22.22 

25-93 

29-63 

33-33 

12.0 

.2 

3-77 

7-53 

11.30 

15.06 

18.83 

22.59 

26.36 

30.12 

33.89 

.2 

•  4 

3.83 

7-65 

11.48 

15.31 

19.14 

22.96 

26:79 

30.62 

34-44 

•  4 

.6 

3-89 

7-78 

11.67 

15.56 

19.44 

23-33 

27.22 

31.11 

35.00 

.6 

.8 

3-95 

7-9° 

11.85 

15.80 

19.75 

23.70 

27.65 

31.60 

35.56 

.8 

13  o 

4.01 

8.02 

12.04 

16.05 

20.06 

24.07 

28.09 

32.10 

36.11 

13  o 

.2 

4.07 

8.15 

12.22 

16.30 

20.37 

24.44 

28.52 

32.59 

36.67 

.2 

•  4 

4.14 

8.27 

12.41 

16.54 

20.68 

24.8l 

28.95 

33-09 

37-22 

•4 

.6 

4.20 

8.40 

12.59 

16.79 

20.99 

25.19 

29.38 

33-58 

37.78 

.6 

.8 

4.26 

8.52 

12.78 

17.04 

21.30 

25.56 

29.81 

34-07 

38.33 

.8 

14.0 

4-32 

8.64 

12.96 

17.28 

21.60 

25-93 

30.25 

34-57 

38.89 

14.0 

.2 

•  38 

8.77 

13.15 

17-53 

21.91 

26.30 

30.68 

35.o6 

39-44 

.2 

•  4 

•44 

8.89 

13.33 

17-78 

22.22 

26.67 

31-  II 

35.56 

40.00 

•  4 

.6 

•  51 

9.01 

13.52 

18.02 

22.53 

27.04 

31-54 

36.05 

40.56 

.6 

.8 

.57 

9-14 

13.70 

18.27 

22.84 

27.41 

31.98 

36.54 

41.  II 

.8 

IS  o 

.63 

9.26 

13.89 

18.52 

23.15 

27.78 

32.41 

37-04 

41-67 

15  o 

.2 

•69 

9-38 

14.07 

18.77 

23.46 

28.15 

32.84 

37-53 

42.22 

.2 

.4 

4-75 

9-51 

14.26 

19.01 

23-77 

28.52 

33-27 

38.02 

42.78 

•  4 

.6 

4.81 

9.63 

14.44 

19.26 

24.07 

28.89 

33-70 

38.52 

43-33 

.6 

.8 

4.88 

9-75 

14.63 

19.51 

24.38 

29.26 

34.14 

39-01 

43-89 

•      .8 

16.0 

4-94 

9.88 

14-81 

19-75 

24.69 

29.63 

34-57 

39-51 

44-44 

16.0 

.2 

S.oo 

10.00 

15.00 

20.00 

25.OO 

30.00 

35-00 

40.00 

45.00 

.2 

-4 

S.o6 

10.12 

15-19 

20.25 

25.31 

30.37 

35-43 

40.49 

45.56 

•  4 

.6 

5.12 

10.25 

15-37 

20.49 

25.62 

30-74 

35-86 

40.99 

46.11 

.6 

.8 

S-I9 

10.37 

15  56 

20.74 

25  93 

31.11 

36.30 

41.48 

46.67 

.8 

17.0 

5-25 

10.49 

15-74 

20.99 

26.23 

31.48 

36.73 

41.98 

47.22 

17.0 

.2 

5-31 

10.62 

15-93 

21.23 

26.54 

31.85 

37-l6 

42.47 

47-78 

.2 

•  4 

5-37 

10.74 

16.11 

21.48 

26.85 

32.22 

37-59 

42.96 

48.33 

•4 

.6 

5-43 

10.86 

16.30 

21-73 

27.16 

32.59 

38.02 

43-46 

48.89 

.6 

.8 

5-49 

10.99 

16.48 

21.98 

27.47 

32.96 

38.46 

43-95 

49-44 

.8 

18.0 

5-56 

ii.  ii 

16.67 

22.22 

27-78 

33-33 

38.89 

44-44 

50.00 

18.0 

.2 

5-62 

11.23 

16.85 

22.47 

28.09 

33-70 

39-32 

44-94 

50.56 

.2 

•  4 

5-68 

11.36 

17.04 

22.72 

28.40 

34-07 

39-75 

45-43 

51.  ii 

•  4 

.6 

5-74 

11.48 

17.22 

22.96 

28.70 

34-44 

40.19 

45-93 

5I.67 

.6 

.8 

5.8o 

ii.  60 

17.41 

23.21 

29.01 

34.81 

40.62 

46.42 

52.22 

.8 

19.0 

5-86 

11-73 

17-59 

23.46 

29.32 

35-19 

41-05 

46.91 

52.78 

19.0 

.2 

5-93 

11.85 

17.78 

23.70 

29.63 

35.56 

41.48 

47-41 

53-33 

.2 

•4 

5-99 

11.98 

17.96 

23-95 

29.94 

35-93 

4I-9I 

47-90 

53-89 

•4 

.6 

6.05 

12.  IO 

18.15 

24.20 

30.25 

36.30 

42.35 

48.40 

54-44 

.6 

.8 

6.  ii 

12.22 

18.33 

24-44 

30.56 

36.67 

42.78 

48.89 

55-00 

.8 

20.0 

6.17 

12.35 

18.52 

24.69 

30.86 

37-04 

43-21 

49.38 

55.56 

20.0 

(277) 


TABLE  XLII.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.     Roadbed  14  feet.     Slope  i|  :  i. 


Center 
height 

0.0 

O.I 

0.2 

03 

0.4 

0.5 

0.6 

0.7 

0.8 

0.9 

Center 
height 

0 

5 

II 

16 

22 

27 

33 

39 

45 

51 

0 

i 

"57 

64 

70 

77 

83 

90 

97 

104 

III 

119 

i 

2 

126 

133 

141 

149 

156 

164 

172 

181 

189 

197 

2 

3 

206 

214 

223 

232 

241 

250 

259 

268 

277 

287 

3 

4 

296 

306 

316 

326 

336 

346 

356 

366 

377 

387 

4 

5 

398 

409 

420 

431 

442 

453 

465 

476 

488 

499 

5 

6 

523 

535 

547 

559 

572 

584 

597 

609 

622 

6 

7 

635 

648 

661 

675 

688 

701 

715 

729 

742 

756 

7 

8 

770 

785 

799 

813 

828 

842 

857 

872 

887 

902 

8 

9 

917 

932 

947 

963 

978 

994 

IOIO 

1026 

1042 

1058 

9 

10 

1074 

1090 

1107 

1123 

1140 

H57 

1174 

1191 

1208 

1225 

10 

ii 

1243 

1260 

1278 

1295 

1313 

I33i 

1349 

1367 

1385 

1404 

ii 

12 

1422 

1441 

1459 

1478 

1497 

1516 

1535 

1555 

1574 

1593 

12 

13 

1613 

1633 

1652 

1672 

1692 

1713 

1733 

1753 

1774 

1794 

13 

14 

1815 

1836 

1857 

1878 

1899 

1920 

1941 

1963 

1984 

2006 

14 

2028 

2050 

2072 

2094 

2116 

2138 

2161 

2183 

2206 

2229 

IS 

SO 

2252 

2275 

2298 

2321 

2345 

2368 

2392 

2415 

2439 

2463 

16 

3 

2487 
2733 

2511 
2759 

2535 
2784 

2560 
2809 

2584 
2835 

2861 

2633 
2886 

2658 
2912 

2683 
2938 

2708 
2965 

a 

19 

2991 

3017 

3044 

3070 

3097 

3124 

3151 

3178 

3205 

3232 

19 

Center 

o  n 

9  A 

Center 

height 

O.O 

I  .O 

o.o 

•  O 

height 

20 

3259 

3539 

3830 

4131 

4444 

4769 

5104 

5450 

5807 

6176 

20 

30 

6556 

6946 

7348 

776l 

8185 

8620 

9067 

9524 

9993 

10472 

30 

40 

10963 

11465 

11978 

12502 

13037 

13583 

14141 

14709 

15289 

25880 

40 

TABLE  XLIII.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.     Roadbed  16  feet.     Slope  i£  :  i. 


Center 
height 

o.o 

O.I 

O.2 

0.3 

0-4 

o.S 

0.6 

0.7 

0.8 

09 

Center 
height 

o 

~ 

12 

is" 

25 

31" 

38 

44 

Si 

58 

O 

i 

"65 

72 

79 

86 

94 

101 

109 

117 

125 

133 

I 

2 

141 

149 

157 

166 

174 

183 

192 

2OI 

209 

219 

2 

3 

228 

237 

247 

256 

266 

275 

285 

295 

305 

3i6 

3 

4 

326 

336 

347 

358 

368 

379 

390 

401 

412 

424 

4 

I 

435 
556 

447 
568 

458 
58l 

470 
594 

482 
607 

494 
620 

506 
633 

518 
646 

531 
660 

673 

I 

I 

68? 
830 

701 
845 

715 
859 

729 
875 

743 
890 

757 
90S 

771 
921 

786 
936 

800 
952 

815 
967 

I 

9 

983 

999 

1015 

1032 

1048 

1064 

1081 

1098 

1114 

1131 

9 

10 

1148 

1165 

1182 

I2OO 

1217 

1235 

1252 

1270 

1288 

1306 

10 

ii 

1324 

1342 

1361 

1379 

1398 

1416 

1435 

1454 

1473 

1492 

ii 

12 

I5II 

1530 

1550 

1569 

1589 

1609 

1629 

1649 

1669 

1689 

12 

13 

1709 

1730 

1750 

1771 

1792 

1813 

1833 

1855 

1876 

1897 

13 

14 

1919 

1940 

1962 

1983 

2005 

2027 

2049 

2072 

2094 

2116 

14 

2139 

2162 

2184 

2207 

2230 

2253 

2276 

2300 

2323 

2347 

IS 

16 

2370 

2394 

2418 

2442 

2466 

2490 

2515 

2539 

2564 

2588 

16 

3 

2613 
2867 

2638 
2893 

2663 
2919 

2688 
2945 

2713 
2971 

2738 
2998 

2764 
3024 

2789 
3051 

2815 
3078 

2841 
3105 

3 

i9 

3131 

3159 

3186 

3213 

3241 

3268 

3296 

3323 

3351 

3379 

19 

Center 
height 

O.O 

I.O 

2.0 

30 

4.0 

So 

6.0 

7.0 

8.0 

90 

Center 
height 

20 

3407 

3694 

3993 

4302 

4622 

4954 

5296 

5650 

6015 

6391 

20 

30 

6778 

7176 

7585 

8006 

8437 

8880 

9333 

9798 

10274 

10761 

30 

40 

H259 

11769 

12289 

12820 

13363 

I39I7 

14481 

15057 

15644 

16243 

40 

(278) 


TABLE  XLIV.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.     Roadbed  20  feet.     Slope  ij  :  i. 


Center 
height 

0.0 

O.I 

O.2 

03 

0.4 

o.S 

0.6 

07 

0.8 

09 

Center 
height 

o 

7 

15 

23 

31 

38 

46 

55 

63 

7i 

o 

i 

'So' 

88 

97 

106 

US 

124 

133 

142 

161 

i 

2 
3 

170 
272 

180 
283 

190 
294 

200 

305 

210 
316 

220 
327 

230 
339 

240 
350 

I 

262 
373 

2 
3 

4 

385 

397 

409 

421 

446 

458 

471 

484 

496 

4 

I 

IS 

522 
659 

535 
673 

549 
687 

702 

575 
716 

589 
731 

603 
746 

617 
761 

630 
776 

I 

7 

791 

806 

821 

837 

852 

868 

884 

900 

916 

932 

7 

8 

948 

964 

981 

998 

IOI4 

1031 

1048 

1065 

1082 

8 

9 

1117 

1  134 

1152 

1169 

IIS? 

1205 

1223 

1241 

1259 

1278 

9 

10 

1296 

1315 

1334 

1352 

1371 

1390 

1409 

1429 

1448 

1461 

10 

ii 

1487 

1507 

1527 

1546 

1566 

1587 

1607 

1627 

1648 

1668 

ii 

12 

1689 

1710 

1731 

1752 

1773 

1794 

1815 

1837 

1858 

1880 

12 

13 

1902 

1924 

1946 

1968 

1990 

2012 

2035 

2058 

2080 

2103 

13 

14 

2126 

2149 

2172 

2195 

2219 

2242 

2266 

2289 

2313 

2337 

14 

2361 
2607 

2385 
2633 

2409 
2658 

2458 
2709 

2483 

2735 

2508 
2761 

2532 
2786 

2557 
2812 

2582 

2839 

11 

z 

2865 
3133 

2891 
3161 

2918 
3188 

2944 
3216 

2971 
3244 

2998 
3272 

3025 
3300 

3052 
3328 

3356 

3106 

3384 

17 
18 

19 

3413 

3442 

3470 

3499 

3528 

3557 

3586 

3615 

3645 

3674 

19 

Center 
height 

0.0 

I.O 

2.0 

30 

4.0 

So 

6.0 

7.0 

8.0 

9-0 

Center 
height 

20 

3704 

4006 

4319 

4643 

4979 

5324 

568i 

6050 

6430 

6820 

20 

30 

7222 

7635 

8059 

8494 

8941 

9398 

9867 

10346 

10837 

"339 

30 

40 

II852 

12376 

I29II 

13457 

14015 

14583 

15163 

15754 

16356 

16969 

40 

TABLE  XLV.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.    Roadbed  20  feet.     Slope  i  :  i. 


Center 

OH 

o  6 

n  T 

OQ 

ft  A 

Center 

height 

3 

0.4 

•5 

U.U 

O-7 

.O 

o.y 

height 

0 

7 

15 

23 

30 

38 

46 

54 

62 

70 

0 

i 

78 

86 

94 

103 

in 

114 

128 

137 

145 

154 

i 

2 

163 

172 

181 

190 

199 

208 

218 

227 

236 

246 

2 

3 

256 

265 

275 

285 

295 

305 

315 

325 

335 

345 

3 

4 

356 

366 

376 

387 

398 

408 

419 

430 

441 

452 

4 

I 

463 
578 

474 
590 

485 
602 

497 
614 

508 
626 

638 

531 

lal 

554 
675 

566 
687 

I 

7 

700 

713 

725 

738 

751 

764 

777 

790 

803 

816 

7 

8 
9 

830 
967 

843 
981 

856 
995 

870 
1009 

884 
1024 

897 
1038 

9" 

1052 

925 
1067 

939 
1082 

1096 

8 
9 

10 

IIII 

1126 

1141 

1156 

1171 

1186 

1  201 

1217 

1232 

1247 

IO 

ii 

1263 

1279 

1294 

1310 

1326 

1342 

1358 

1374 

1390 

1406 

ii 

12 

1422 

1439 

1455 

1471 

1488 

1505 

1521 

1538 

1555 

1572 

12 

13 

1589 

1606 

1623 

1640 

1658 

1675 

1692 

1710 

1728 

1745 

13 

14 

1763 

1781 

1799 

1817 

1835 

1853 

1871 

1889 

1908 

1926 

14 

15 

1944 

1963 

1982 

2OOO 

2019 

2038 

2057 

2076 

2095 

2114 

IS 

IO 

2133 

2153 

2172 

2191 

2211 

2231 

2250 

2270 

2290 

2310 

16 

11 

2330 
2533 

2350 
2554 

2370 
2575 

2390 
2596 

24IO 
2617 

2431 
2638 

2451 
2659 

2471 
2680 

2492 

2702 

2513 
2723 

17 
18 

19 

2744 

2766 

2788 

2809 

2831 

2853 

2875 

2897 

2919 

2941 

19 

Center 
height 

0.0 

I.O 

2.0 

30 

4.0 

So 

6.0 

7.0 

8.0 

9-0 

Center 
height 

20 

2963 

3189 

3422 

3663 

3991 

4167 

4430 

4700 

4978 

5263 

20 

30 

5556 

5856 

6163 

6478 

68OO 

7130 

7467 

7811 

8163 

8522 

3O 

40 

8889 

9263 

9644 

10033 

10430 

10833 

11244 

11663 

12089 

12522 

40 

(279) 


TABLE  XLVI.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.     Roadbed  24  feet.     Slope  i|  :  i. 


Center 
height 

0.0 

O.I 

0.2 

0-3 

0.4 

o.S 

0.6 

0.7 

0.8 

0.9 

Center 
height 

o 

9 

18 

27 

36 

46 

55 

65 

75 

85 

0 

z 

94 

105 

US 

125 

135 

146 

156 

167 

178 

189 

I 

2 

200 

211 

222 

234 

245 

257 

269 

280 

292 

304 

2 

3 

317 

329 

341 

354 

366 

379 

392 

405 

418 

431 

3 

4 

444 

458 

471 

485 

499 

512 

526 

540 

555 

569 

4 

5 

583 

598 

612 

627 

642 

657 

672 

687 

702 

7i8 

6 

733 

749 

765 

780 

812 

829 

845 

861 

878 

7 

894 

fcn 

928 

945 

962 

979 

996 

1014 

1031 

1049 

7 

8 

1067 

1085 

1  102 

II2I 

"39 

1157 

1175 

1194 

1212 

1231 

8 

9 

1250 

1269 

1288 

1307 

1326 

1346 

1365 

1385 

1405 

9 

10 

1444 

1465 

1485 

1505 

1525 

1546 

1566 

1587 

1608 

1629 

10 

ii 

1650 

1671 

1692 

1714 

1735 

1757 

1779 

1800 

1822 

1845 

ii 

12 

1867 

1889 

I9II 

1934 

1956 

1979 

2OO2 

2025 

2048 

2071 

12 

13 

2094 

2118 

2141 

2165 

2189 

2213 

2236 

2261 

2285 

2309 

13 

14 

2333 

2358 

2382 

2407 

2432 

2457 

2482 

2507 

2532 

2558 

14 

IS 

2609 

2635 

2661 

2686 

2713 

2739 

2765 

2791 

2818 

15 

16 

2844 

2871 

2898 

2925 

2952 

2979 

3006 

3034 

3061 

3089 

16 

11 

3H7 

3400 

3145 
3429 

3172 

3458 

3201 

3487 

3229 
35i6 

3257 
3546 

3285 
3575 

3314 
3605 

3342 
3635 

3371 
3665 

3 

19 

3694 

3725 

3755 

3785 

38i5 

3846 

3876 

3907 

3938 

3969 

19 

Center 
height 

o.o 

I.O 

2.0 

3-0 

40 

S.o 

6.0 

7.0 

8.0 

90 

Center 
height 

20 

4000 

4317 

4644 

4983 

5333 

5694 

6067 

6450 

6844 

7250 

20 

30 

7667 

8004 

8533 

8983 

9444 

9917 

10400 

10894 

11400 

11917 

30 

40 

12444 

12983 

13533 

14094 

14667 

15250 

15844 

16450 

17067 

17694 

40 

TABLE  XLVII.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.     Roadbed  24  feet.     Slope  i  :  i. 


Center 
height 

0.0 

O.I 

0.2 

0-3 

o-4 

o.S 

0.6 

0.7 

0.8 

o.9 

Center 
height 

0 

9 

18 

27 

36 

45 

55 

64 

74 

83 

0 

i 

93 

102 

112 

122 

132 

142 

152 

162 

172 

182 

i 

2 

193 

203 

214 

224 

235 

245 

267 

278 

289 

2 

3 

300 

3" 

322 

334 

345 

356 

368 

380 

391 

403 

3 

4 

415 

427 

439 

451 

463 

475 

487 

500 

5io 

524 

4 

5 

537 

550 

562 

575 

588 

601 

614 

627 

640 

653 

6 

667 

680 

694 

707 

721 

734 

748 

762 

756 

790 

7 

804 

818 

832 

846 

861 

875 

890 

904 

919 

933 

7 

8 

948 

963 

978 

993 

1008 

1023 

1038 

1054 

1069 

1084 

8 

9 

IIOO 

1116 

1131 

1147 

1163 

H79 

1195 

I2II 

1226 

1243 

9 

xo 

1259 

1276 

1292 

1308 

1325 

1342 

1358 

1375 

1392 

1409 

10 

ii 

12 

1426 
1600 

1443 
1618 

1460 
1636 

1477 
1654 

1495 
1672 

1512 
1690 

1530 
1708 

1547 
1726 

1745 

1582 
1763 

ii 

12 

13 

1782 

1800 

1819 

1837 

1856 

1875 

1894 

1913 

1932 

1951 

13 

14 

1970 

1990 

2009 

2028 

2048 

2068 

2087 

2107 

2127 

2147 

14 

11 

2167 
2370 

2187 
2391 

2207 
2412 

2227 
2433 

2247 
2454 

2268 
2475 

2288 
2496 

2308 
2517 

2329 
2539 

2560" 

11 

17 

2582 

2603 

2625 

2646 

2668 

2690 

2712 

2734 

2756 

2778 

17 

18 

2800 

2822 

2845 

2867 

2889 

2912 

2935 

2957 

2980 

3003 

18 

19 

3026 

3049 

3072 

3095 

3"8 

3142 

3165 

3188 

3212 

3236 

19 

Center 
height 

o.o 

I.O 

2.0 

3-0 

4.0 

So 

6.0 

7.0 

8.0 

9.0 

Center 
height 

20 

3259 

3500 

3748 

4004 

4267 

4537 

4815 

5100 

5393 

5692 

20 

30 

6000 

6315 

6637 

6967 

7304 

7648 

8000 

8359 

8726 

9100 

30 

40 

9481 

9870 

10267 

10670 

11081 

11500 

11926 

12359 

12800 

13248 

40 

(280) 


TABLE  XLVIII.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.     Roadbed  26  feet.     Slope  ij  :  i. 


Center 
height 

0.0 

O.I 

0.2 

0.3 

04 

o.S 

0.6 

0.7 

0.8 

0.9 

Center 
height 

0 

10 

19 

29 

39 

50 

6o~ 

70 

81" 

9I 

0 

i 

102 

113 

124 

135 

146 

157 

168 

180 

191 

203 

i 

2 

215 

227 

239 

251 

263 

275 

288 

301 

313 

326 

2 

3 

339 

352 

365 

378 

392 

405 

419 

432 

446 

460 

3 

4 

474 

488 

517 

531 

546 

56i 

575 

590 

605 

4 

620 

636 

651 

666 

682 

698 

713 

729 

745 

762 

5 

778 

794 

811 

827 

844 

861 

878 

895 

912 

929 

6 

7 

946 

964 

981 

999 

1017 

1035 

1053 

1071 

1089 

7 

8 

1126 

1144 

1163 

1182 

1  201 

1220 

1258 

1278 

1297 

8 

9 

1317 

1333 

1356 

1376 

1396 

I4l6 

1436 

1457 

1477 

1498 

9 

10 

1519 

1539 

1560 

1581 

I6O2 

1624 

1645 

1666 

1688 

1710 

10 

ii 

1731 

1753 

1775 

1798 

1820 

1842 

1865 

1887 

1910 

1933 

ii 

12 

1956 

1979 

2002 

2025 

2048 

2072 

2095 

2119 

2143 

2167 

12 

13 

2191 

2215 

2239 

2263 

2288 

2312 

2337 

2362 

2387 

2412 

13 

14 

2437 

2462 

2488 

2513 

2539 

2564 

2590 

2616 

2642 

2668 

14 

13 

2694 
2963 

2721 
2990 

2747 
3018 

2774 
3046 

2800 
3073 

2827 
3101 

2854 
3129 

2881 
3158 

2908 
3186 

2936 
3214 

3 

X 

3243 
3533 

3300 

3593 

3329 
3623 

3358 
3653 

3387 
3683 

3713 

3445 
3743 

3474 
3774 

3504 
3804 

a 

i9 

3835 

3866 

3897 

3928 

3959 

3990 

4022 

4053 

4085 

4116 

19 

Center 
height 

0.0 

I.O 

2.O 

30 

4.0 

So 

6.0 

7-0 

8.0 

90 

Center 
height 

20 

4148 

4472 

4807 

5154 

5511 

5880 

6259 

6650 

7052 

7465 

20 

30 

7889 

8324 

8770 

9228 

9696 

10176 

10667 

11168 

11681 

12205 

30 

40 

12741 

13287 

13844 

I44I3 

14992 

15583 

16185 

16798 

17422 

18057 

40 

TABLE  XLIX.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.     Roadbed  26  feet.     Slope  i  :  i. 


Center 
height 

0.0 

O.I 

0.2 

0-3 

0.4 

o.S 

0.6 

0.7 

0.8 

0-9 

Center 
height 

o 

IO 

19 

29 

39 

49 

59 

69 

79 

90 

0 

i 

100 

no 

121 

131 

142 

153 

164 

174 

185 

196 

i 

2 

207 

219 

230 

241 

252 

264 

275 

287 

299 

3io 

2 

3 

322 

334 

346 

358 

370 

382 

395 

407 

419 

432 

3 

4 

444 

457 

470 

483 

495 

508 

521 

534 

548 

56i 

4 

5 

574 

587 

601 

614 

628 

642 

655 

669 

683 

697 

5 

6 

711 

725- 

739 

754 

768 

782 

797 

811 

826 

841 

6 

7 

856 

870 

885 

900 

915 

931 

946 

961 

976 

992 

7 

8 

1007 

1023 

1039 

1054 

1070 

1086 

1  102 

1118 

"34 

1150 

8 

9 

1167 

1183 

1199 

1216 

1232 

1249 

1266 

1283 

1299 

1316 

9 

10 

1333 

1350 

1368 

1385 

1402 

1419 

1437 

1454 

1472 

1490 

10 

ii 

1507 

1525 

1543 

1561 

1579 

1597 

1615 

1634 

1652 

1670 

ii 

12 

1689 

1707 

1726 

1745 

1764 

1782 

1801 

1820 

1839 

1859 

12 

13 

1878 

1897 

1916 

1936 

1955 

1975 

1995 

2014 

2034 

2054 

13 

14 

2074 

2094 

2114 

2134 

2155 

2175 

2195 

2216 

2236 

2257 

14 

IS 

2278 

2299 

2319 

2340 

2361 

2382 

2404 

2425 

2467 

IS 

16 

2489 

2510 

2532 

2554 

2575 

2597 

2619 

2641 

2663 

2685 

16 

11 

2707 
2933 

2730 
2956 

2752 
2979 

2774 
3003 

2797 
3026 

2819 

2842 
3072 

2865 
3096 

3H9 

2910 
3143 

3 

19 

3l67 

3190 

3214 

3238 

3262 

3286 

33io 

3334 

3359 

3383 

19 

Center 
height 

o.o 

I.O 

2.0 

30 

4.0 

S.o 

6.0 

7.0 

8.0 

9.0 

Center 
height 

20 

3407 

3656 

3911 

4174 

4444 

4722 

5007 

53oo 

5600. 

5907 

20 

30 

6222 

6544 

6874 

7211 

7556 

7907 

8267 

8633 

9007 

9389 

30 

40 

9778 

10174 

10578 

10989 

11407 

11833 

12267 

12707 

13156 

13611 

40 

(281) 


TABLE  L.  —  LEVEL  SECTION  VOLUMES 
100  feet  long.     Roadbed  28  feet.     Slope  i£  : 


Center 
height 

0.0 

O.I 

O.2 

03 

0.4 

o.S 

0.6 

0-7 

0.8 

0.9 

Center 
height 

0 

.... 

10 

21 

32 

42 

53~ 

64 

75 

sT 

98 

0 

i 

'109 

121 

132 

144 

156 

168 

180 

192 

205 

217 

i 

a 

230 

242 

255 

268 

281 

294 

307 

320 

334 

348 

2 

3 

361 

375 

389 

403 

417 

431 

445 

460 

474 

489 

3 

4 

504 

519 

534 

549 

564 

595 

610 

626 

fie 

4 

I 

656 
822 

673 
839 

690 
856 

706 
874 

722 

891 

909 

755 
926 

772 
944 

788 
962 

805 
980 

I 

7 

998 

1016 

1035 

1053 

1072 

1090 

1109 

1128 

1147 

1166 

7 

8 

1185 

1204 

1224 

1243 

1263 

1283 

1303 

1322 

1343 

1363 

8 

9 

1383 

1403 

1424 

1445 

1465 

1486 

ISO? 

1528 

1549 

1571 

9 

10 

1592 

1614 

1635 

1657 

1679 

1701 

1723 

1745 

1767 

1790 

10 

ii 

1812 

1835 

1858 

1881 

1904 

1927 

1950 

1973 

1997 

2020 

ii 

12 

2044 

2068 

2092 

2116 

2140 

2164 

2189 

2213 

2238 

2262 

12 

13 

2287 

2312 

2337 

2362 

2387 

2413 

2438 

2464 

2489 

2515 

13 

14 

2541 

2567 

2619 

2645 

2672 

2698 

2725 

2752 

2779 

14 

11 
11 

2806 
3081 
3368 
3667 

2833 
3109 
3397 
3697 

3138 
3427 
3728 

2887 
3166 
3456 
3758 

2915 
3195 
3486 
3789 

2942 
3223 
35i6 
3820 

2970 
3252 
3546 
3851 

2997 
3281 
3576 
3882 

3025 

33 

39i3 

3053 

3339 
3636 
3944 

3 

11 

19 

3976 

4007 

4039 

4070 

4102 

4134 

4166 

4198 

4231 

4263 

i9 

Center 
height 

0.0 

I.O 

2.0 

30 

4.0 

So 

6.0 

7.0 

8.0 

90 

Center 
height 

20 

4296 

4627 

4970 

5324 

5689 

6065 

6451 

6850 

7259 

7680 

20 

30 
40 

8111 
13037 

8554 
I3S9I 

9007 
14156 

9472 
I473I 

9948 
I53I8 

10435 
I59I7 

10933 
16526 

1  1443 
17146 

11963 
17778 

12494 
18420 

30 
40 

TABLE  LI.  —  LEVEL  SECTION  VOLUMES 
loo  feet  long.     Roadbed  28  feet.     Slope  i  :  i 


Center 
height 

0.0 

O.I 

0.2 

0-3 

0.4 

0-5 

0.6 

0-7 

0.8 

o.9 

Center 
height 

o 

IO 

21 

31 

42 

53 

64 

74 

85 

96 

0 

i 

107 

119 

130 

141 

152 

164 

175 

167 

199 

210 

i 

2 

222 

234 

246 

258 

270 

282 

295 

307 

319 

332 

2 

3 

344 

357 

370 

383 

395 

408 

421 

434 

448 

461 

3 

4 

474 

487 

501 

514 

528 

542 

555 

569 

583 

597 

4 

5 

6ll 

625 

639 

654 

668 

682 

697 

711 

726 

74i 

5 

6 

656 

770 

785 

800 

816 

831 

846 

861 

876 

892 

6 

7 

908 

923 

939 

954 

970 

986 

1002 

1018 

1034 

1050 

7 

8 

1067 

1083 

1099 

1116 

1132 

1149 

1166 

1182 

"99 

1216 

8 

9 

1233 

1250 

1267 

1285 

1302 

1319 

1337 

1354 

1372 

1390 

9 

10 

1407 

1425 

1443 

1461 

1479 

1497 

1515 

1534 

1552 

1570 

10 

iz 

12 

1589 
1778 

1607 
1797 

1626 
1816 

1645 
1836 

1664 
1855 

1682 
1875 

1701 
1895 

1720 
1914 

1739 
1934 

1759 
1954 

ii 

12 

13 

1974 

1994 

2014 

2034 

2055 

2075 

2095 

2116 

2136 

2157 

13 

14 

2178 

2199 

2219 

2240 

2261 

2282 

2304 

2325 

2346 

2367 

14 

3 

2389 
2607 

2410 
2630 

2432 
2652 

2454 
2674 

2475 
2697 

2497 
2719 

2519 
2742 

2541 
2765 

2563 
2788 

2585 
2810 

51 

3 

2833 
3067 

2856 
3090 

2879 
3H4 

2903 
3138 

2926 
3162 

2949 
3186 

2972 
3210 

2996 
3234 

3019 
3259 

3043 
3283 

3 

19 

3307 

3332 

3356 

3381 

3406 

3431 

3455 

348o 

3505 

3530 

i9 

Center 
height 

0.0 

I.O 

2.O 

30 

4.0 

S.o 

6.0 

7-0 

8.0 

90 

Center 
height 

20 

3556 

3811 

4074 

4344 

4622 

4907 

5200 

5500 

5807 

6122 

20 

30 

6444 

6774 

7111 

7456 

7807 

8167 

8533 

8907 

9289 

9678 

30 

40 

10074 

10478 

10889 

11307 

II733 

12167 

12607 

13056 

I35H 

13974 

40 

(282) 


TABLE  LII.  —  LEVEL  SECTION  VOLUMES 
ioo  feet  long.     Roadbed  30  feet.     Slope  i$  :  i. 


Center 

O  O 

4 

o.S 

0.6 

O-7 

0.8 

O  Q 

Center 

height 

**•  y 

height 

o 

II 

22 

34 

45 

57 

69 

80 

92 

104 

0 

i 

ii? 

129 

141 

154 

166 

179 

192 

205 

218 

231 

i 

2 

244 

258 

271 

285 

299 

312 

326 

340 

355 

369 

2 

3 

4 

383 
533 

398 
549 

412 

565 

42? 
580 

442 
596 

457 
612 

472 

487 

645 

502 

661 

678 

3 

4 

5 

694 

711 

728 

745 

762 

779 

796 

814 

831 

849 

5 

6 

7 

867 
1050 

884 
1069 

902 
1088 

920 
1107 

939 
1126 

957 
1146 

975 
1165 

994 
1185 

1012 

1205 

1031 
1224 

6 

7 

8 
9 

1244 
1450 

1264 
1471 

1285 
1492 

1305 
1514 

1325 
1535 

1346 
1557 

1366 
1579 

1387 
1600 

1408 
1622 

1644 

8 
9 

10 

1667 

1689 

1711 

1756 

1779 

1802 

1825 

1848 

1871 

10 

ii 

1894 

1918 

1941 

1965 

1981 

2012 

2036 

2060 

2085 

2109 

ii 

12 

2133 

2158 

2182 

2207 

2232 

2257 

2282 

2307 

2332 

2358 

12 

13 

2383 

2409 

2435 

2460 

2486 

2512 

2539 

2565 

2591 

2618 

13 

14 

2644 

2671 

2698 

2725 

2752 

2779 

2806 

2834 

286l 

2889 

14 

15 

16 

2917 
3200 

2944 
3229 

2972 
3258 

3000 
3287 

3029 
33i6 

3057 
3346 

3085 
3375 

3405 

3142 

3435 

3464 

3 

3 

3494 
3800 

3525 
3831 

3555 
3862 

3615 
3925 

3646 
3957 

3676 
3989 

3707 
4020 

3738 

4052 

3769 
4084 

3 

19 

4117 

4149 

4181 

4214 

4246 

4279 

4312 

4345 

4378 

4411 

19 

Center 
height 

0.0 

I.O 

2.0 

30 

4.0 

So 

6.0 

7.0 

8.0 

9-0 

Center 
height 

20 

4444 

4783 

5133 

5494 

5867 

6250 

6644 

7050 

7467 

7894 

20 

30 

8333 

8783 

9244 

9717 

10200 

10694 

1  1200 

11717 

12244 

12783 

30 

40 

13333 

13894 

14467 

15050 

15644 

16250 

16867 

17494 

18133 

18783 

40 

TABLE  LI  1 1.  —  LEVEL  SECTION  VOLUMES 
ioo  feet  long.     Roadbed  30  feet.     Slope  i  :  i. 


Center 

Om 

0.6 

Okl 

o  8 

f\  a 

Center 

height 

O.3 

0.4 

-5 

•7 

u.o 

o.y 

height 

O 

II 

22 

34 

45 

56 

68 

80 

91 

103 

0 

I 

115 

127 

139 

151 

163 

175 

187 

200 

212 

224 

i 

2 

237 

250 

262 

275 

288 

301 

314 

327 

340 

353 

2 

3 

4 

367 

504 

380 
518 

393 
532 

407 
546 

421 

56l 

434 
575 

448 
589 

462 
604 

476 
619 

490 
633 

3 

4 

1 

648 
800 

663 

816 

678 
831 

693 

847 

708 
863 

723 
879 

738 
895 

754 
911 

769 
927 

784 
943 

I 

7 

959 

976 

992 

1008 

1025 

1042 

1058 

1075 

1092 

1109 

7 

8 

1126 

H43 

1160 

1177 

1195 

1212 

1229 

1247 

1265 

1282 

8 

9 

1300 

1318 

1336 

1354 

1372 

1390 

1408 

1426 

1445 

1463 

9 

10 

1481 

1500 

1519 

1537 

1556 

1575 

1594 

1613 

1632 

1651 

10 

ii 

1670 

1690 

1709 

1728 

1748 

1768 

1787 

1807 

1827 

1847 

ii 

12 

1867 

1887 

1907 

1927 

1947 

1968 

1988 

2008 

2029 

2050 

12 

13 

2070 

2091 

2112 

2133 

2154 

2175 

2196 

2217 

2239 

2260 

13 

14 

2281 

2303 

2325 

2346 

2368 

2390 

2412 

2434 

2456 

2478 

14 

15 

2500 

2522 

2545 

2567 

2589 

2612 

2635 

2657 

2680 

2703 

16 

2726 

2749 

2772 

2795 

2818 

2842 

2865 

2888 

2912 

2936 

16 

3 

2959 
3200 

2983 
3224 

3007 
3249 

3031 
3274 

3298 

3079 
3323 

3103 

3127 
3373 

3151 
3399 

3176 
3423 

3 

19 

3448 

3473 

3499 

3524 

3549 

3575 

3601 

3626 

3652 

3678 

19 

Center 
height 

0.0 

I.O 

2.0 

30 

4.0 

So 

6.0 

70 

8.0 

9.0 

Center 
height 

20 

3704 

3967 

4237 

4515 

4800 

5093 

5393 

5700 

6015 

6337 

20 

30 

6667 

7004 

7348 

7700 

8059 

8426 

8800 

9181 

9570 

9967 

30 

40 

10370 

10781 

II2OO 

11626 

12059 

12500 

12948 

13404 

13867 

14337 

40 

(283) 


TABLE  LIV.  —  LEVEL  SECTION  VOLUMES 
ioo  feet  long.     Roadbed  32  feet.     Slope  i|  :  i. 


Center 

height 

0.0 

O.I 

0.2 

0-3 

0.4 

o.S 

0.6 

0.7 

0.8 

0.9 

Center 
height 

o 

12 

24 

36~ 

48 

eT 

73 

sT 

98 

in 

0 

i 

124 

137 

ISO 

163 

177 

190 

204 

218 

231 

245 

i 

2 

259 

273 

288 

302 

316 

331 

346 

360 

375 

390 

2 

3 

406 

421 

436 

452 

467 

483 

499 

515 

547 

3 

4 

563 

579 

596 

612 

629 

646 

680 

697 

714 

4 

5 

731 

749 

767 

784 

802 

820 

838 

856 

874 

6 

911 

930 

948 

967 

986 

1005 

1024 

1043 

1063 

1082 

6 

7 

IIO2 

1122 

1141 

1161 

1181 

1201 

1222 

1242 

1262 

1283 

7 

8 

1304 

1324 

1345 

1366 

1388 

1409 

1430 

1452 

1473 

1495 

8 

9 

1517 

1539 

1561 

1583 

1605 

1627 

1650 

1672 

1695 

1718 

9 

10 

1741 

1764 

1787 

1810 

1833 

1857 

1881 

1904 

1928 

1952 

10 

ii 

1976 

2000 

2024 

2049 

2073 

2099 

2122 

2147 

2172 

2197 

ii 

12 

2222 

2247 

2273 

2298 

2324 

2350 

2375 

2401 

2427 

2453 

12 

13 

2480 

2506 

2532 

2559 

2586 

26l2 

2639 

2666 

2694 

2721 

13 

14 

2748 

2776 

2803 

2831 

2859 

2887 

2915 

2943 

2971 

2999 

14 

3 

3028 
3319 

3056 
3348 

3085 

3378 

3H4 
3408 

3143 
3438 

3172 
3468 

3201 

3498 

3230 

3259 
3559 

3289 
3590 

3 

;87 

362O 

3933 

3651 
3965 

3682 

3997 

3713 

4029 

3744 
4062 

3775 

4094 

3807 

4126 

4159 

3870 
4192 

3902 
4224 

11 

19 

4257 

4290 

4324 

4357 

4390 

4424 

4457 

4491 

4525 

4559 

19 

Center 

height 

o.o 

I.O 

2.O 

30 

4-0 

5-0 

6.0 

7.o 

8.0 

9-0 

Center 
height 

20 

4593 

4939 

5296 

5665 

6044 

6435 

6837 

7250 

7674 

8109 

20 

30 

8556 

9013 

9482 

9962 

10452 

10954 

11467 

11991 

12526 

13072 

30 

40 

13630 

14198 

14778 

15369 

15970 

16583 

17207 

17843 

18489 

19146 

40 

TABLE  LV.  —  LEVEL  SECTION  VOLUMES 
ioo  feet  long.     Roadbed  32  feet.     Slope  i  :  i. 


Center 
height 

O.O 

O.I 

O.2 

03 

0.4 

0-5 

0.6 

0.7 

0.8 

0.9 

Center 
height 

0 

12 

24 

36 

48 

60 

72 

85 

97 

no 

o 

i 

122 

135 

148 

160 

173 

186 

199 

212 

225 

239 

i 

2 

252 

265 

279 

292 

306 

319 

333 

347 

36i 

375 

2 

3 

389 

403 

417 

431 

446 

460 

475 

489 

504 

519 

3 

4 

31 

548 
701 

563 
716 

578 
732 

593 
748 

608 
764 

624 
780 

654 
812 

670 
828 

4 

5 

6 

844 

861 

877 

894 

910 

927 

944 

960 

977 

994 

6 

7 

ion 

1028 

1045 

1063 

1080 

1097 

HIS 

1132 

1150 

1167 

7 

8 

1185 

1203 

1221 

1239 

1257 

1275 

1293 

13" 

1330 

1348 

8 

9 

1367 

1385 

1404 

1423 

1441 

1460 

1479 

1498 

1517 

1536 

9 

10 

1556 

1575 

1594 

1614 

1633 

1653 

1672 

1692 

1712 

1732 

10 

ii 

1752 

1772 

1792 

1812 

1832 

1853 

1873 

1894 

1914 

1935 

ii 

12 

1956 

1976 

1997 

2018 

2039 

2060 

2081 

2103 

2124 

2145 

12 

13 

2167 

2188 

22IO 

2231 

2253 

2275 

2297 

2319 

2341 

2363 

13 

14 

2385 

2407 

2430 

2452 

2475 

2497 

2520 

2543 

2565 

2588 

14 

15 

2611 

2634 

2657 

2680 

2704 

2727 

2750 

2774 

2797 

2831 

15 

16 

2844 

2868 

2892 

2916 

2940 

2964 

2988 

3012 

3036 

3061 

16 

17 

3085 

3110 

3134 

3159 

3184 

3208 

3233 

3258 

3283 

3308 

17 

18 

3333 

3359 

3384 

3409 

3435 

346o 

3486 

35ii 

3537 

3563 

18 

i9 

3589 

3615 

3641 

3667 

3693 

3719 

3746 

3772 

3799 

3825 

19 

Center 
height 

0.0 

I.O 

2.0 

30 

4.0 

So 

6.0 

7.0 

8.0 

9-0 

Center 
height 

20 

"3852" 

4122 

4400 

4685 

4978 

5278 

5585 

5900 

6222 

6552 

20 

30 

6889 

7233 

7585 

7944 

8311 

8685 

9067 

9456 

9852 

10256 

30 

40 

10667 

11085 

II5II 

11944 

12385 

12833 

13289 

13752 

14222 

14700 

40 

(284) 


TABLE  LVI.  —  LEVEL  SECTION  VOLUMES 
TOO  feet  long.     Roadbed  20  feet.     Slope  |  :  i 


Center 
height 

0.0 

O.I 

O.2 

0-3 

0.4 

o.S 

0.6 

0-7 

0.8 

0.9 

Center 
height 

0 

7 

IS 

22 

30 

37 

45 

52 

60 

67 

0 

i 

75 

83 

90 

98 

106 

121 

129 

136 

144 

i 

2 

152 

160 

167 

175 

183 

191 

199 

207 

214 

223 

2 

3 

231 

238 

246 

254 

263 

271 

279 

287 

295 

303 

3 

4 

319 

327 

.  336 

344 

352 

360 

369 

377 

385 

4 

5 

394 

402 

410 

419 

427 

435 

444 

452 

461 

469 

5 

6 

478 

486 

495 

503 

512 

521 

529 

538 

546 

555 

6 

7 

564 

573 

581 

590 

599 

608 

616 

625 

634 

643 

7 

8 

652 

661 

670 

679 

688 

696 

706 

714 

724 

733 

8 

9 

742 

75i 

760 

769 

778 

787 

796 

806 

8i5 

824 

9 

10 

ii 

833 
927 

936 

852 
946 

861 
955 

870 
965 

880 
974 

889 
984 

899 
993 

908 
1003 

917 
1013 

10 
ii 

12 

1022 

1032 

1042 

1051 

1061 

1071 

1080 

1090 

IIOO 

IIIO 

12 

13 

III9 

1129 

H39 

1149 

1  159 

1169 

1179 

1189 

1199 

1209 

13 

14 

1219 

1229 

1239 

1249 

1269 

1279 

1289 

1299 

1309 

14 

11 

1319 
1422 

1330 
1433 

1340 
1443 

1350 
1453 

1464 

I37i 

1474 

1381 
1485 

1495 

1402 
1506 

1412 
1516 

;i 

17 

1527 

1537 

1548 

1559 

1569 

1580 

1591 

1601 

1612 

1623 

17 

18 

1633 

1644 

1655 

1666 

1676 

1687 

1698 

1709 

1720 

I73i 

18 

19 

1742 

1753 

1764 

1774 

1785 

1796 

1808 

1819 

1830 

1841 

19 

Center 
height 

0.0 

1.0 

2.0 

30 

4.0 

5-0 

6.0 

7.0 

8.0 

9-0 

Center 
height 

20 

1852 

1964 

2078 

2194 

2311 

2431 

2552 

2675 

2800 

2927 

20 

30 

3056 

3186 

3319 

3453 

3589 

3727 

3867 

4008 

4152 

4297 

30 

40 

4444 

4593 

4744 

4897 

5052 

5208 

5367 

5527 

5689 

5853 

40 

TABLE  LVII.  —  LEVEL  SECTION  VOLUMES 
ioo  feet  long.     Roadbed  24  feet.     Slope  £  :  i. 


Center 

OA 

Og 

0.6 

Om 

0.8 

o  O 

Center 

height 

3 

•4 

•5 

•  7 

u.y 

height 

o 

9 

18 

27 

36 

45 

54 

63 

72 

sT 

0 

i 

90 

99 

108 

117 

126 

145 

154 

172 

i 

2 

181 

191 

200 

209 

219 

228 

237 

247 

256 

266 

2 

3 

275 

284 

294 

303 

313 

322 

332 

342 

351 

361 

3 

4 

370 

380 

39° 

399 

409 

419 

428 

438 

448 

458 

4 

5 

468 

477 

487 

497 

507 

517 

527 

537 

547 

557 

5 

6 

567 

577 

587 

597 

607 

617 

627 

637 

647 

657 

6 

7 

668 

678 

688 

698 

708 

719 

729 

739 

750 

760 

7 

8 

770 

78i 

791 

802 

812 

822 

833 

843 

854 

864 

8 

9 

875 

886 

896 

907 

917 

928 

939 

949 

960 

971 

9 

10 

981 

992 

1003 

1014 

1025 

1035 

1046 

1057 

1068 

1079 

10 

ii 

1000 

IIOI 

III2 

1123 

1  134 

H45 

1156 

1167 

1178 

1189 

ii 

12 

I2OO 

I2II 

1222 

1233 

1245 

1256 

1267 

1278 

1289 

1301 

12 

13 

1312 

1323 

1335 

1346 

1357 

1369 

1380 

1392 

1403 

1414 

13 

14 

1426 

1437 

1449 

1460 

1472 

1484 

1495 

1507 

1518 

1530 

14 

3 

1542 
1659 

1553 
1671 

1565 
1683 

1577 
1695 

1588 
1707 

1600 
1719 

1612 
1731 

1624 
1743 

1636 
1755 

1647 
1767 

3 

17 

1779 

1791 

1803 

1815 

1827 

1839 

1851 

1863 

1876 

1888 

17 

18 

1900 

1912 

1924 

1937 

1949 

1961 

1974 

1986 

1998 

201  1 

18 

i9 

2023 

2036 

2048 

2060 

2073 

2085 

2098 

2110 

2123 

2I36 

19 

Center 
height 

0.0 

1.0 

2.0 

30 

4-0 

5-0 

6.0 

7.0 

8.0 

9-0 

Center 
height 

20 

2148 

2275 

2404 

2534 

2667 

2801 

2937 

3O75 

3215 

3356 

20 

30 

35oo 

3645 

3793 

3942 

4093 

4245 

4400 

455§ 

4715 

4875 

30 

40 

5037 

5201 

5367 

5534 

5704 

5875 

6048 

6223 

6400 

6579 

40 

(285) 


286 


RAILROAD    FIELD   MANUAL 


TABLE  LVIIL  —  MIDDLE  ORDINATES  FOR  CURVING  RAILS 
Ordinate  given  in  inches 

From  Roberts'  "  Track  Formulae  and  Tables." 


Degree 

of 
curve 

o;S° 
i.5° 

2° 
2.5° 

3° 
3;5° 

4-5° 

5° 

5-5° 

6° 

6.5° 

7° 

7-5° 

8° 

8.5° 

9° 

9-5° 
10° 
10.5° 
11° 
ii.5° 

12° 

12.5° 

13° 

13-5° 

14° 

U-Se 

15° 

15-5° 
16° 


Length  of  rails  in  feet 


H 


H 


14 


16         18 


H 


H 


i 
iH 


xH 


M 


24 


ifi 


2*4 

2% 


26  28 


2H 

214 

2% 


2% 


Hi 


3% 


2% 
2% 
2% 

3 


3M 


30 


2 

2% 

2% 

2% 
2% 
2% 

3 
3 


3W 
3*4 


33 

~ 


2% 
23/4 

3 

3*6 
3H 

3H 
3% 
3*4 
3% 
4 

4H 
4*6 


TABLE  LVIIIa.  —  GAGE  ON  CURVES 


Degree  of  curve 

Gage 

Degree  of  curve 

Gage 

8°  and  under 

4'  8H" 

i5°-i6° 

4'  9" 

9°-io° 

4'  8H" 

i7°-i8° 

4'  9*6" 

II°-I2° 

4'  8%" 

I9°-20° 

4'  9H" 

I3°-I4° 

4'  8%" 

ESTIMATING  AND  CONSTRUCTION  TABLES          287 


CANTING  THE  TRACK 

Using  the  gage  for  the  base,  if  R  =  radius,  5  =  speed  in  miles  per 
hour  and  e  is  the  difference  in  level  of  the  two  rails  in  feet, 

4-708 

+  223.5  -^ 

Using  gage  plus  one  rail  head  which  the  author  recommends  for  use 
with  the  common  track  level, 


The   corresponding   approximate   formulas   are   e  =  —  and 


e  =  .     In  inches  E  =  0.00066  &D  and  E  =  0.000686  S*D. 

K 

The  formula  of  the  American  Railway  Engineering  Association  for 
difference  of  level  measured  at  the  gage  lines  is 
E  =  0.00066  S*D, 

but  the  author  recommends  E  =  0.000686  S2D.     Both  formulas  are 
tabulated  in  Tables  LIX  and  LIXa. 


TABLE  LIX 

Difference  of  level  in  inches  of  the  two  rails  of  a  standard  gage 
track  on  curves  of  various  degrees  for  various  speeds. 
Formula:  £  =  0.00066  S2D 
(Nearest  |  inch) 


Degree 

nf 

Speed  in  miles  per  hour 

Degree 

nf 

curve 

10 

IS 

2O 

as 

30 

35 

40 

45 

So 

55 

60 

65 

70 

curve 

i 

_ 

H 

H 

% 

H 

% 

Itt 

i% 

i5/i 

2 

2% 

2% 

3H 

i 

2 

H 

% 

Vn. 

^i 

iH 

I  $£ 

2^ 

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3H 

4 

43/4 

5H 

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M- 

y> 

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iH 

i?4 

2% 

3H 

4 

4% 

6 

8% 

9% 

3 

4 

H 

H 

i 

1% 

2% 

3/4 

4/4 

5% 

6% 

8 

9^ 

4 

5 

% 

% 

i/4 

2 

3 

4 

sH 

65/^ 

8H 

5 

6 

% 

i 

iH 

2^ 

3/i 

47/^ 

6H 

8 

6 

7 

y* 

iH 

i% 

27^ 

4H 

554 

73/6 

7 

8 

v/ 

yi/ 

^ 

^T/ 

4% 

6^-4 

Q3Z 

8 

9 

5£ 

iH 

->*<<* 

3% 

7H 

9 

10 

% 

iV£ 

5% 

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ii 

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T3/j 

27A 

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8% 

ii 

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13 

7Z 

2 

3?4 

5% 

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13 

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?5>* 

5% 

83-8 

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15 

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2H 

3% 

8% 

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2K* 

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6H 

16 

17 

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1W 

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20 

TABLE   LIXa 

From  Formula  E   =  0.000686  S2D 
(Nearest  T\  inch) 


Degree 
of 
curve 

Speed  in  miles  per  hour 

Degree 
of 
curve 

10 

IS 

20 

25 

30 

35 

40 

45 

So 

55 

60 

65 

70 

o.S 

i 

2 
3 
4 
5 
6 
7 
8 
9 
10 
ii 

12 

14 

16 

18 

20 

He 
He 
M 

Me 
H 

M 

He 
H 
Me 
H 
'He 
% 
i*i« 
'Me 
iHe 
iH 
ift 

He 

M 

Me 
Me 
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% 
'Me 
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i?i« 
i'He 
i% 
2Me 

2H 
2% 

3He 

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2% 

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3'  Me 
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5'Me 
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5 
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8 
9 
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12 
14 

16 
18 

20 

... 

(288) 


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(289) 


TABLE  LXI 
Conversion  of  linear  feet  of  100  ft.  wide  right-of-way  into  acres 

From  Roberts'  "  Track  Formulae  and  Tables." 


Acres 

Lin.  ft. 
R.  of  W. 

Acres 

Lin.  ft. 
R.  of  W.       Acres 

Lin.  ft. 
R.-of  W. 

Acres 

Lin.  ft. 
R.  of  W. 

I.O 

435-6 

II.  0 

4791.6               21.  O 

9147.6 

31.0 

13503.6 

2.O 

871.2 

12.0 

5227  .2               22  .  0 

9583-2 

32.0 

13939-2 

3-o 

1306.8 

13.0 

5662.8               23.0 

10018.8 

33-0 

»  14374  -8 

4.0 

1742.4 

14.0 

6098.4               24.0 

10454-4 

34-0 

14810.4 

S.o 

2178.0 

15.0 

6534.0               25.0 

10890.0 

35-0 

15246.0 

6.0 

2613.6 

16.0 

6969.6               26.0 

11325.6 

36.0 

15681.6 

7.0 

3049.2 

17.0 

7405.2               27.0 

11761.2 

37-0 

16117.2 

8.0 

3484.8 

18.0 

7840.8               28.0 

12196.8 

38.0 

16552.8 

9.0 

3920.4 

19.0 

8276.4               29.0 

12632.4 

39-0 

16988.4 

10.  0 

4356.0 

20.0 

87I2.O               30.0 

13068.0 

40.0 

17424.0 

Acres 

Lin.  ft. 

Acres 

Lin.  ft. 

Acres 

Lin.  ft. 

Acres 

Lin. 

ft. 

Acres 

Lin.  ft. 

2.2 

89-3 

176.4 

263.5 

350.7 

O.OI 

0.21 

0.41 

0.61 

0.81 

6.5 

93- 

7 

180.8 

267.9 

355-0 

O.O2 

O.22 

0.42 

0.62 

0.82 

10.9 

98.0 

185.1 

272.3 

359-4 

0.03 

0.23 

0-43 

0.63 

0.83 

15.2 

102. 

4 

189.5 

276.6 

363-7 

0.04 

0.24 

0.44 

0.64 

O.I 

54 

19.6 

IO6.7 

193-8 

281 

.0 

368.1 

0.05 

0.25 

0.45 

0.65 

0.85 

24.0 

III. 

I 

198.2 

285-3 

372-4 

0.06 

0.26 

0.46 

0.66 

o.l 

56 

28.3 

IIS- 

4 

202.6 

289.7 

376.8 

0.07 

0.27 

0.47 

0.67 

0.87 

32.7 

119- 

8 

206.9 

294 

.0 

381.2 

0.08 

0.2 

8 

0.48 

0.68 

o.i 

58 

37-0 

124. 

I 

211.  3 

298 

•  4 

385.5 

0.09 

O.29 

0-49 

0.69 

0.89 

41.4 

128.5 

215.6 

302.7 

389.9 

O.IO 

0.30 

0.50 

•  0.70 

0.90 

45-7 

132.9 

220.0 

307 

.1 

394-2 

O.II 

0.31 

0.51 

0.71 

0.91 

50.1 

137- 

2 

224-3 

311 

•  5 

398-6 

0.12 

0.32 

0.52 

0.72 

0.92 

54-5 

MX. 

6 

228.7 

315 

.8 

402.9 

0.13 

0.33 

0.53 

0.73 

0-93 

58.8 

145.9 

233-0 

320 

.2 

407.3 

0.14 

0.34 

0.54 

0.74 

0-94 

63.2 

150.3 

237-4 

324 

•  5 

411.6 

0.15 

0-35 

0.55 

0.75 

0.95 

67-5 

154. 

6 

241.8 

328.9 

416.0 

0.16 

0.36 

0.56 

0.76 

0.96 

71-9 

159. 

0 

246.1 

333-2 

420.4 

0.17 

0.37 

0.57 

0.77 

0.9? 

76.2 

163. 

4 

250.5 

337 

.6 

424-7 

0.18 

0.38 

0.58 

0.78 

0.98 

80.6 

167.7 

254-8 

341 

-9 

429-1 

0.19 

0.39 

0.59 

0.79 

0.99 

84.9 

172. 

I 

259-2 

346 

-3 

433  4 

0.20 

0.40 

0.60 

0.80 

1.  00 

89-3 

176. 

4 

263.5 

350.7 

437  8 

(290) 


ESTIMATING  AND   CONSTRUCTION  TABLES 


291 


TABLE  LXII.  —  DRAINAGE  AREAS 

Sq.  ft.  opening  =  C  $  (drainage  area,  in  acres)3 
From  Roberts'  "  Track  Formulae  and  Tables." 


Acres 
drained 

Steep  slopes 
C  =  i 

Moderately 
steep  slopes 
C  =  % 

Rolling  land 

C*M 

Flat  farm 
lands 
C  =  H 

Sq.  ft.  opening  required 

10 

5-6 

2.7 

1.9 

i.i 

20 

9-5 

6.3 

32 

1-9 

30 

12.8 

8.5 

4-3 

2.6 

40 

iS-9 

10.6 

5-3 

3-2 

50 

18.8 

12.5 

6.3 

3-8 

60 

21.5 

14-3 

7-2 

4-3 

70 

24.2 

16.1 

8.1 

4-8 

80 

26.7 

17.8 

8.9 

5-3 

90 

29.2 

19-5 

9-7 

5-8 

100 

31-6 

21.  1 

10.5 

6-3 

ISO 

42-9 

28.6 

14-3 

8.6 

160 

44-9 

29.9 

15-0 

9-0 

200 

53-2 

35.5 

17.7 

10.6 

240 

60.9 

40.6 

20.3 

12.2 

300 

72.1 

48.1 

24.0 

14.4 

320 

75-9 

50.6 

25-3 

15.  a 

400 

89-4 

59-6 

29.8 

17-9 

480 

102.  S 

68.3 

34-2 

20.5 

500 

105-7 

70-S 

35.2 

21.  1 

560 

II5-I 

76-7 

38.4 

23.0 

600 

121.  2 

80.8 

40.4 

24.2 

640 

127.2 

84.8 

42.4 

25-4 

800 

150.4 

100.3 

50.1 

30.1 

1000 

177.8 

118.5 

59-3 

35.6 

2000 

299.0 

199-3 

99-7 

59-8 

2500 

353-5 

235-7 

117.8 

70.7 

3600 

464.8 

309.9 

154-9 

93-0 

5000 

594-6 

396.4 

198.2 

118.9 

6000 

681.7 

454-5 

227.2 

136.3 

7000 

765.3 

510.2 

255-1 

I53-I 

8000 

845.9 

563.9 

282.0 

169.2 

9000 

924.4 

616.3 

308.1 

184.9 

10  OOO 

IOOO.O 

666.7 

333-3 

200.0 

I.  C.  R.R.  Co.,  1906. 


Extended,  1909,  by  S.  S.  R. 


292 


RAILROAD   FIELD  MANUAL 


'   30 

O 

3 

|  20 

r 

§10 


TABLE  LXllI 
From  Roberts'  "  Track  Formulae  and  Tables." 

CURVES  OF  CONTENTS   OF  ABUTMENTS 


APPROXIMATE  CONTENTS 

OF"T"  ABUTMENTS 

SINGLE  TRACK 


50        100        150         200       250        300       350       400       450        500 
Contents  of  Two  Abutments  in  Cu.Yds. 

Illinois  Central  R-R.Cc. 


Distance  from  Base  of  Rail  to  Ground 
o  «.  S  S  £  g 

,  *~ 

^-*~ 

,^— 

^ 

-^ 

.X 

x*^ 

X 

X^^ 

x 

x 

/ 

X 

/ 

/ 

APPROXIMATE  CONTENTS 
STRAIGHT  ABUTMENTS 
SINGLE  TRACK, 

/ 

100  200          300  400  500  600          700 

Contents  of  Two  Abutments  in  Cu.Yds. 


800 


ESTIMATING  AND   CONSTRUCTION  TABLES 


293 


TABLE  LXIV.  —  COST  CURVES  TIMBER  TRESTLES 

From  Roberts'  "  Track  Formulae  and  Tables." 
Unit  Prices. 

Material  in  Place. 
Creosoted  Material: 

Caps $55-oo  per  M.  Ft.  B.M. 

Stringers 55.00  per  M.  Ft.  B.M. 

Other  material 43.00  per  M.  Ft.  B.M. 

Piles 0.37  per  linear  foot. 

Untreated  Material: 

Caps $42.00  per  M.  Ft.  B.M. 

Stringers 42.00  per  M.  Ft.  B.M. 

Other  Material 30.00  per  M.  Ft.  B.M. 

Piles 0.24  per  M.  Ft.  B.M. 

Iron 0.05  per  pound. 

To  the  cost  of  the  trestle  obtained  from  the  following  curves  by 
multiplying  the  cost  per  foot  by  the  length,  add  for  single  track: 
$25.00  for  two  bulkheads  in  all  cases. 

0.70  per  linear  foot  for  ties  and  ballast  for  ballast  floors  only. 
For  double  track  add: 

$50.00  for  two  bulkheads  in  all  cases. 

1.40  per  linear  foot  for  ties  and  ballast  for  ballast  floors  only. 
Creosoted  open  deck  trestles  have  piles,  caps  and  braces  creosoted. 
Ballast  floor  trestles  have  all  material  creosoted. 
The  cost  per  linear  foot  given  by  the  following  curves  does  not  include 
longitudinal  bracing.     This  should  be  figured  separately  for  each  trestle 
as  the  conditions  at  the  opening  may  require. 


— 

28 

825 
£24 
£23 
022 
£21 
§2d 
^19 

11? 
P 

fa 

S1S 

•K 

s 

s 

/ 

s 

/' 

s 

pfr 

s 

_<5 

w 

ag 

^ 

<s 

»/ 

/ 

/ 

/*^ 

S 

/ 

SINGLE  TRACK 
OPEN  DECK  FRAME 
TRESTLE   - 

— 

f 

/ 

— 

S* 

,^-^* 

—  -— 

.10    -15      20      25      30     35      40      45      50     55 

Height  •  Base  of  Bail  to  Ground  Line 


65     70     75     80 

Illinois  Central  R.B.CO. 


294  RAILROAD  FIELD  MANUAL 

COST  CURVES  TIMBER  TRESTLES — (Continued) 


f  10.UU 

•313 
I12 

!*i 

a  10 

11 

^^> 

*^ 

^,- 

\e 



,  • 

_£, 

% 

£ 

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^ 

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SINGLE  TRACK, 
UNTREATED,  OPEN  DECK 
TRESTLE. 

.--" 

^ 

**^~ 

!  1 

1 

12  4M6    18  20  22    24  26   28   30    32  34    36   38  40  42   44    46  48 
Height-Base  of  Rail  to  Ground  Line 

IlUnoii  Central  R.B.C*. 


f  18.00 

1  16 
«gl5 

I14 
fill 

§12 
pll 

i: 

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SINGLE  TRACK, 
CREOSOTED,  OPEN  DECK 
TRESTLE.  ' 

^""ii* 

1      1      1      1      1      1      1 

10 


15 


20  25  30  35  40 

Height-Base  of.  Rail  to  Ground  Line 


45          5( 

IlUoola  Central  R.R.CO. 


10  12    14  16  18   20  22   24  26  28  30    32  34  36  38  40  42   44  46    48  50 
Height- Base  of  Bail  to  Ground  Line  niiaoii  c«otna  B.R.O*. 


ESTIMATING  AND   CONSTRUCTION  TABLES 
COST  CURVES  TIMBER  TRESTLES  —  (Continued) 


295 


f  23.00 

2  21 
•320 
g  19 
5  18 
1  17 

a  16 

|14 
13 

a 

^ 

^ 

..^ 

cA 

^- 

•^ 

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x^ 

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- 

--- 

x 

YO^ 

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/ 

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X 

SINGLE  TRACK, 
BALLAST  FLOOR  TRESTLES. 
"CREOSOTED." 

—  • 

•*" 

0 

15            20            25            30            35            40            45           Wl 

Height -Base  of  Bail  to  Ground.Line 

UliuoU  CentnlJLR.Co. 


42 

*»      41 
o      40 

h      39 
S  »  f~ 

. 

S^ 

.. 

***^ 

^* 

•oW5 

^^ 

f\\ 

*^Je*Z. 

Cost  per  Linei 
ofTrest 

e8852.8gS2SS§?J 

^v.^ 

^^ 

^\ 

'V^ 

^^, 

[  —  •—  ' 

DOUBLE  TRACK. 
BALLAST  FLOOR  TRESTLE 
"CREOSOTED" 

— 

^s 

^^x 

x" 

^^x* 

*-*^" 

\ 

0    12    14  .16    18    20   22    24   26    28    30    32    34   36    38    40   42    44    44 
Height-  Base  of  Bail  to  Ground  Line             «^ 

TABLE  LXV.  —  PRELIMINARY  CULVERT  ESTIMATES  AND  BRIDGE 

WEIGHTS 


Iron  pipe 

Concrete  arch 

eter, 
inches 

Area, 
sq.  ft. 

Weight, 
Ibs.  per 
lin.  ft. 

Cu.  yds. 

masonry, 
two  ends 

Dimen- 
sions, 
feet 

Area, 
sq.  ft. 

Cu.  yds. 
per  ft. 
length 

Cu.  yds., 
two  ends 

12 

0.79 

72.5 

4.0 

2X   2 

3-5 

0.57 

8.0* 

16 

1.40 

107.8 

S.o 

3X  4 

10.9 

1.  06 

26.1* 

18 

1.77 

127.7 

5-7 

4X  6 

22.  0 

1.63 

60.9* 

20 

2.18 

165.7 

6.5 

6X  6 

30.4 

3.10 

42.  5t 

24 

3-14 

200.  6 

7.8 

SX  8 

54-4 

3-99 

76.  at 

30 

4-91 

290.2 

10.8 

10X10 

85-4 

5-57 

109.  ot 

36 

7.07 

391-6 

13.2 

12X12 

123-3 

6.89 

i68.4t 

42 

9.62 

512.2 

17.8 

15X15 

193-2 

8.81 

278.  5t 

48 

12.57 

665.2 

22.3 

20X18 

306.2 

12.08 

499-ot 

Square  end  walls. 


t  Thirty-degree  wing  walls. 


296 


RAILROAD   FIELD   MANUAL 


BRIDGE  WEIGHTS* 

W  =  weight  of  steel  in  pounds.     /  =  span  in  feet  for  truss  bridges 

and  length  overall  for  girder  bridges. 

Plate  Girders: 

Deck  plate  girder W  =  12  P  +  150  / 

Through  plate  girder,  iron  floor  system . .  W  =  12  P  +  500  / 
Through  plate  girder,  large  ties  on  shelf 

or  flange  angles W  =  9^  I2  +  150  / 

Through  plate  girder,  solid  iron  floor W  =  12  P-  +  800  / 

Riveted  Lattice  Bridges: 

Deck  bridge,  cross-ties  on  top  chord W  =    7  P  +  200  / 

Through  bridge,  iron  floor  system W  =    7 12  +  300  / 

Pin  Connected  Bridges: 

Deck  span,  cross-ties  on  top  chord W  =    5  /2  +  250  / 

Deck  span,  iron  floor  system .  .  , JF  =    5 12  +  475  / 

Through  span,  iron  floor  system W  =    7  P  +  650  / 

TABLE  LXVI.  —  PRELIMINARY  BALLAST  ESTIMATES 

Ties  6"  X  8"  X  8'. 

18  ties  to  a  33-ft.  rail. 

Tabular  quantities  are  in  cubic  yards  per  mile. 


Depth 

Gravel  3"  above  tie  at 
center  slope  2-1 

Broken  stone  level  with 
top  of  ties  I  ft.  outside 
slopes  iH-i 

j     j.' 

in  inches 

Single 

Double  track 

Single 

Double  track 

track 

14'  C.  to  C. 

track 

14'  C.  to  C. 

6 

1400 

4iS9 

1965 

4418 

8 

1737 

4952 

2396 

5306 

10 

2095 

5767 

2845 

6210 

12 

2476 

6603 

3309 

7i3i 

From  "Modern  Framed  Structures"  by  Johnson,  Bryan  and  Turneaure. 


CHAPTER  VI 

TURNOUTS  AND  CROSSOVERS 

Let  F  =  frog  angle. 
S  —  switch  angle. 

/  =  toe  length  of  frog  from  theoretic  point. 
T  =  heel  spread  of  switch. 
/  =  point  thickness  of  switch  rail. 
/'  =  point  thickness  of  actual  frog  point. 
N  =  number  of  frog. 

Frog  Distance  I 


FIG.  26. 

/  =  length  of  switch  rail. 
R  =  radius  of  turnout  curve. 
G  =  gage  of  track. 

T  —  t 

N  =  3  cot  5  F ,     sin  S  = • 

i 

Frog  distance  =  I  +  [G  -  (T  +/sin  F)]  cot  |  (F  +  S)  +  /cos  F  +  ?N 
p  .   i^_          G-(r+/sin/Q 


297 


2Q8 


RAILROAD  FIELD  MANUAL 


Values  for  F,  R,  frog  distance,  S,  and  other  quantities  for  varying 
values  of  N  and  /  are  given  in  Tables  XLVII  and  XLVIII,  and  for 
spring  rail  frogs  in  Table  XLIX. 


^^"""^   A  .                                        ' 

JG 

W 

cH&W  ^^>^-— 

P     D^^                   > 

'          1G 

FIG.  27. 

BD  =  (W  -G)cotF-  - 

ED  =  y^£-GcotF. 
sm  F 


Total  length  =  BD  +  2  X  frog  distance  to  theoretic  point. 


FIG.  28. 
0  =  r-CR-f-|G)versS, 


R 


TURNOUTS  AND   CROSSOVERS 

e  =  (F  +  e)  -  F, 

p  =  /  -  (R  +  i  G)  sin  5, 

L  =  length  of  crossover  —  2  \R  sin  (Jf7  +  6) 


299 


Distance  between  frogs  =  L  —  2  X  frog  distance. 

rt 

Length  of  connecting  rail  =  2R  — —  • 

57*3 


FIG.  29. 


W-G-fsin/? 
versF 


Curve  length  is  R 


57-3 


300 


RAILROAD  FIELD  MANUAL 


FIG.  30 

K  and  the  elements  for  both  turnouts  with  equal  frog  angles  F  are 
known.     To  find  F"  and  the  crotch  frog  distance. 

O  =  T-(R  +  %G)  vers 5, 
AC  =  2(12 


AC 


'cos/3,  1?" 

0  =  /8  —  a. 
Crotch  frog  distance  from  first  point  is 


07' =  -4-      or      -*£., 
sin  a.  cos  a 

F"  =  2fi, 


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TURNOUTS   AND   CROSSOVERS 


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CHAPTER  VII 
AZIMUTH,  LATITUDE,  AND  TIME 

Meridian  Determinations,  i.  By  an  Observation  on  Polaris  at  Elon- 
gation. —  Find  the  time  of  elongation  from  Table  LXXI.  Just  before 
the  time  of  elongation  set  the  transit  over  a  point  and  with  the  alidade 
clamped  turn  the  telescope  on  the  star,  clamp  the  limb  and  follow  the 
star  with  the  slow  motion  till  it  seems  to  stop  traveling  east  or  west 
as  the  case  may  be.  Plunge  the  telescope  and  range  out  a  stake  in 
line.  If  the  observer  is  quick  he  may  transit  the  telescope  and  take  a 
second  observation  with  the  telescope  reversed  before  the  star  moves 
in  azimuth  appreciably.  Compute  the  azimuth  of  the  star  at  elongation 

from  the  formula 

0.     „      sin  pole  distance 

Sm  Z  =  £— : — : — j 

cos  latitude 

The  pole  distance  is  found  in  Table  LXX.  The  latitude  may  be  taken 
to  the  nearest  minute  from  a  good  map  or  determined  as  in  the  next 
article.  Next  morning  set  again  over  the  transit  point  and  from  the 
established  line  set  off  Z  and  range  out  the  meridian. 

2.  By  an  Observation  on  Polaris  at  Any  Time.  — This  is  not  so  good 
as  the  preceding  method  but  is  often  more  convenient  and  sufficiently 
precise  for  practically  all  field  purposes. 

Set  the  transit  over  a  point  and  at  any  instant  set  the  intersection  of 
the  wires  on  the  star  by  clamps  and  slow  motions.  Range  out  a  line 
in  the  azimuth  plane  of  the  star.  Compute  the  azimuth  of  this  line 
from  the  equation 

in  which  s  =  |  (d  +  a  +  /),  d  being  the  pole  distance,  a  the  co-altitude, 
and  /  the  co-latitude. 

Since  there  are  two  equal  azimuth  angles  —  one  east,  the  other  west 
—  for  any  given  altitude,  and  four  positions  of  the  star  that  will  give 
the  same  Z  angle  —  two  east  and  two  west  of  the  meridian  —  the  ob- 
server must  know  from  the  observed  motion  of  the  star  in  which  quad- 
rant of  its  apparent  revolution  the  star  is,  or  he  may  know  from  the 

305 


306  RAILROAD  FIELD  MANUAL 

times  of  observation  and  culmination,  the  latter  taken  from  Table 
LXXI. 

3.  By  Equal  Altitudes  of  a  Star.  —  In  the  southern  hemisphere  or 
elsewhere  when  not  convenient  to  use  Polaris,  use  equal  altitudes  of 
any  star  that  may  be  observed  on  both  sides  of  the  meridian  at  reason- 
able altitudes  of  between  20°  and  40°. 

Select  a  star;  set  up  the  instrument  over  a  fixed  point;  clamp  one 
horizontal  motion,  and  with  the  other  and  the  vertical  motion  of  the 
telescope  bring  the  intersection  of  the  wires  approximately  on  the  star; 
clamp  both  motions;  set  the  vertical  circle  to  read  a  whole  minute  or 
0.01°  such  that  the  star  is  approaching  the  horizontal  wire;  follow  with 
the  azimuth  motion  so  that  when  the  star  is  on  the  horizontal  wire  it 
shall  be  also  on  the  vertical  wire,  i.e.,  at  the  intersection  of  the  wires. 
Plunge  the  telescope  and  range  out  a  stake  some  distance  ahead.  Re- 
peat once  or  twice  at  intervals  of  from  ten  to  twenty  minutes  and  range 
out  other  points,  numbering  the  points  I,  2,  3,  etc.  Set  the  vertical 
circle  to  read  the  last  measured  altitude  and  wait  till  the  star  again 
reaches  it  when  an  exact  setting  is  made  and  a  stake  ranged  out;  set 
at  the  next  altitude  and  repeat  the  operation  until  as  many  stakes  are 
set  on  one  side  of  the  meridian  as  on  the  other,  numbering  them  3,  2,  i. 
The  extra  stakes  are  for  checks  on  the  work.  In  the  morning  bisect 
the  angles  I -instrument- 1,  2-instrument-2,  etc.,  and  set  points  which 
should  coincide  but  may  not.  If  they  do  not  coincide  set  a  point  to 
average  them  unless  there  is  enough  variation  to  indicate  an  error. 
To  average  them  select  the  most  east  or  west  of  the  middle  points  as  an 
origin  and  measure  the  distance  to  each  of  the  other  middle  points, 
add  and  divide  by  the  number  of  middle  points.  The  result  is  the  dis- 
tance of  the  average  point  from  the  origin.  Use  this  and  the  instru- 
ment point  to  define  the  meridian.  The  times  should  be  at  least  from 
one  and  one-half  to  two  hours  either  side  of  the  meridian.  A  star 
reaching  culmination  early  in  the  night  should  be  chosen.  Approxi- 
mate north  and  south  will  be  known  by  the  needle  or  the  daytime 
position  of  the  sun. 

4.  By  a  Transit  Observation  on  the  Sun.  —  Measure  the  altitude  of 
the  sun  and  its  azimuth  from  any  fixed  line  at  the  same  instant;   sub- 
stitute the  altitude,  the  latitude  of  the  place  determined  from  a  good 
map  to  the  nearest  minute  or  by  one  of  the  methods  of  the  next  article, 
and  the  declination  of  the  sun  (explained  later)  in  the  formula, 


=  ±  ./sin  (,'-*)  sin  (/-ft) 

T  COS  0  COS  h 


AZIMUTH,   LATITUDE,   AND   TIME  307 

in  which  Z  is  the  azimuth  of  the  sun  measured  from  the  meridian,  <f>  is  the 
latitude,  h  is  the  altitude,  and  s'  =  %  (90  —  5  +  <j>  +  h),  5  being  the  declin- 
ation taken  with  its  proper  sign,  +  when  north  and  —  when  south. 
The  difference  between  Z  and  the  observed  azimuth  from  the  fixed  line 
gives  the  azimuth  of  that  line  from  which  the  meridian  may  be  run  out. 

To  make  the  observation,  set  the  transit  over  a  point  at  least  one  and 
one-half  hours  before  or  after  noon  and  as  long  after  sunrise  or  before 
sunset,  and  use  any  fixed  distant  point  for  zero  azimuth.  Use  a  piece 
of  colored  or  smoked  glass  in  the  eyepiece  cap  or  before  the  object 
glass,  and  bring  the  cross  wires  tangent  to  the  sun 's  disc,  approximately 
by  hand  motion  of  the  alidade  and  telescope  and  clamps  and  precisely 
by  both  slow  motions  together;  read  the  vertical  circle  and  the  azimuth. 
Subtract  the  refraction  correction  of  Table  LXX  for  the  measured  alti- 
tude from  the  vertical  circle  reading. 

If  the  horizontal  wire  has  been  made  tangent  to  the  lower  limb  (edge) 
of  the  sun,  add  the  sun's  semi-diameter,  i6m  or  0.26667°,  to  the  corrected 
vertical  circle  reading;  if  the  upper  limb  has  been  observed  subtract 
the  semi-diameter.  The  result  is  the  correct  altitude  of  the  sun  at  the 
instant  of  observation.  The  sun's  semi-diameter  is  not  exactly  i6m 
but  varies  during  the  year  and  may  be  had  from  the  Nautical  Almanac 
mentioned  later  if  greater  precision  is  desired. 

The  measured  azimuth  from  the  reference  line  is  increased  or  dimin- 
ished according  as  the  edge  nearest  or  farthest  from  the  reference  line 
is  observed,  by  16'  X  sec  h  or  0.27°  sec  h.  If  the  observer  is  satisfied 
to'quarter  the  sun's  image  with  the  cross  wires  no  semi-diameter  correc- 
tion is  required  either  for  altitude  or  azimuth. 

Explanation  of  Astronomical  Terms.  —  Celestial  bodies  are  located 
on  the  celestial  sphere  by  coordinates  corresponding  to  latitude  and 
longitude  of  the  terrestrial  sphere.  The  celestial  equator  is  a  circle 
cut  from  the  celestial  sphere  by  the  terrestrial  equatorial  plane  ex- 
tended, and  angular  distances  north  or  south  of  the  celestial  equator 
are  called  declinations,  corresponding  to  terrestrial  latitude.  An  arbi- 
trary meridian  of  the  celestial  sphere  is  chosen  as  the  reference  for  what 
is  called  right  ascension,  corresponding  to  longitude.  Right  ascension 
is  not  used  in  the  methods  of  this  chapter. 

The  declination  of  the  sun  changes  constantly.  The  Nautical 
Almanac  or  American  Ephemeris,  published  by  the  Government  annu- 
ally, gives  the  hourly  change.  Several  instrument  makers  distribute 
gratis  in  pocket  form  reprints  of  that  part  of  the  Nautical  Almanac 
relating  to  the  sun  and  useful  to  surveyors.  Every  surveyor  should 
have  one  of  these  reprints. 


308  RAILROAD  FIELD  MANUAL 

To  determine  the  declination  at  a  given  place  and  hour  on  a  given 
day  the  approximate  Greenwich  time  of  the  observation  must  be  known. 
In  North  America  if  standard  time  is  carried'  by  the  observer,  he  will 
know  what  meridian  time  he  carries  and  hence  how  many  hours  slow 
he  is  of  Greenwich  time;  Eastern  time  is  5  hours,  Central  time  6  hours, 
Mountain  time  7  hours,  and  Pacific  time  8  hours  slow  of  Greenwich 
time.  The  Almanac  gives  the  coordinates  of  the  sun  for  Greenwich 
apparent  and  mean  noon,  and  some  reprints  give  the  coordinates  for 
one  and  some  for  the  other. 

Noon.  —  The  sun  does  not  appear  to  move  at  a  uniform  rate  around 
the  earth.  Apparent  noon  is  the  instant  the  sun  appears  to  cross  the 
meridian.  Mean  noon  is  the  instant  that  an  imaginary  sun,  moving  at 
a  uniform  rate  and  making  the  same  number  of  revolutions  in  a  year  as 
the  real  sun,  appears  to  cross  the  meridian.  Mean  time  is  time  accord- 
ing to  the  mean  sun  and  is  what  is  carried  by  clocks  and  watches.  The 
difference  between  apparent  and  mean  time  is  called  the  equation  of 
time  and  is  found  in  the  Nautical  Almanac  and  reprints.  It  is  some- 
times to  be  added  and  sometimes  subtracted  to  convert  one  time  into 
the  other.  The  sign  to  be  used  is  given  with  the  equation. 

Assuming  standard  time  at  any  place  where  central  time  is  used, 
9  o'clock  in  the  morning,  being  3  hours  before  noon,  would  be  (6  —  3) 
hours  =  3  hours  after  noon  at  Greenwich,  and  the  declination  of  the 
table  for  a  given  day  must  be  corrected  for  3  hours  change.  In  the 
table  —  means  south  and  +  north.  If  the  change  is  marked  —  the  sun 
is  going  south,  and  north  or  +  declination  is  decreasing,  while  south 
or  —  declination  is  increasing. 

If  local  mean  time  is  carried  by  the  observer  he  must  know  his  approx- 
imate longitude  and  must  convert  this  into  time,  15°  to  the  hour,  to 
find  the  difference  between  Greenwich  and  local  time.  In  either  case 
if  his  reprint  gives  the  position  of  the  sun  for  apparent  noon,  he  must 
apply  the  equation  of  time  to  his  mean  time  to  find  the  local  or  stand- 
ard apparent  time. 

The  positions  of  heavenly  bodies  are  figured  from  the  center  of  the 
earth.  With  a  body  as  near  as  the  sun  this  gives  rise  to  a  correction 
to  altitudes  measured  at  the  surface  known  as  the  correction  for  paral- 
lax. It  is  but  a  few  seconds  and  is  neglected  in  this  discussion.  The 
methods  of  this  chapter  are  such  as  are  suited  to  field  instruments  read- 
ing to  minutes  or  o.oi  of  a  degree  and  many  refinements  necessary  in 
astronomical  work  are  omitted. 

Latitude.  I.  By  Polaris.  —  The  altitude  of  the  north  pole  equals  the 
latitude  of  the  place  of  observation.  Measure  the  altitude  of  Polaris 


AZIMUTH,  LATITUDE,   AND   TIME 


309 


at  upper  or  lower  culmination,  subtract  the  refraction  correction  found 
in  Table  LXX.  Add  or  subtract  the  pole  distance  of  the  star  as  found 
in  Table  LXX,  according  as  lower  or  upper  culmination  is  observed. 
The  result  is  the  latitude. 


TABLE  LXX.  —  POLAR  DISTANCE  OF  POLARIS 
For  January  i  of  years  named 


1915 

1918 

1921 

1924 

1927 

1930 

1933 

1936 

1939 

1942 

i.i49° 

1.133° 

1.118° 

1.102° 

1.087° 

1.071° 

1.056° 

1.041° 

1.026° 

1.011° 

0.       ..  sin  polar  distance 

Sm  of  azimuth  at  elongation  =   — -. : — : — -= 

cosine  latitude 

Latitude  =  altitude  of  Polaris  at  culmination  ±  polar  distance 
refraction  correction  given  below. 


Latitude  or 
altitude 

Correction 

Latitude  or 
altitude 

Correction 

20° 

30° 
40° 

0.043° 
0.027° 

50° 
60° 

0.013° 
0.009° 

To  observe,  set  up  a  little  before  the  time  of  culmination  found  in 
Table  LXX  I;  set  the  horizontal  wire  on  the  star  and  follow  with  the 
slow  motions  till  the  star's  motion  seems  to  be  wholly  in  azimuth  and 
not  at  all  in  altitude.  Read  the  vertical  angle. 

2.  By  a  Noon  Observation  of  the  Sun. —  Measure  the  altitude  of  the 
sun  when  at  its  highest  point;  subtract  the  refraction  correction  of 
Table  LXX  for  the  altitude  found;  subtract  the  sun's  declination  if 
north  or  add  if  south;  the  result  is  the  co-latitude. 

To  observe  set  up  the  transit  a  little  before  noon;  set  the  horizontal 
wire  on  the  upper  or  lower  limb  (edge)  of  the  sun's  disc  and  keep  it 
there  as  the  sun  rises  and  until  it  has  ceased  to  rise  and  its  motion  seems 
to  be  wholly  in  azimuth;  read  the  vertical  circle  very  carefully  and 
subtract  or  add  the  sun's  semi-diameter  according  as  the  upper  or  lower 
limb  was  observed.  Colored  or  smoked  glass  must  be  used,  prefer- 
ably in  the  eyepiece  cap  rather  than  before  the  object  glass,  but  either 
may  answer.  The  sun's  semi-diameter  is  an  average  of  16  minutes  or 


3io 


RAILROAD   FIELD  MANUAL 


0.26667°.  It  varies  during  the  year  and  may  be  had  from  the  Nautical 
Almanac  or  makers'  reprint  (see  previous  article)  if  desired  to  greater 
precision. 


TABLE  LXXI* 

Approximate  local  mean  times  (counting  from  noon  24  hours)  of 
the  elongations  and  culminations  of  polaris  in  the  year  1915  for  lati- 
tude 40°  N.;  longitude  6H  W.  from  Greenwich. 


Date 

East 
elongation 

West 
elongation 

Upper 
culmination 

Lower 
culmination 

Jan.      i 

h.          m. 
o       52  i 

h.          m. 

12          42   I 

h.          m. 

h.          m. 

IS 

23       53  o 

II        46  8 

Feb.     i 

22        45  9 

10        39  7 

16        42  8 

*5 

21        50  6 

944  2 

Mar.     i  
15    

20       55.4 

20          CO  2 

8        49-2 
7        54  ° 

2       54.2 

I          V)  0 

14        52-3 

Apr.     i  

is  

May     i 

18        53-3 
17        58.1 
16        55  3 

6       47.1 
5       51-9 
4        49  I 

o       52.1 
23       43-i 

12        50.2 
ii        55-0 

IS 

16        oo  4 

•7                 CA     2 

June     i  . 

14        S3  8 

2        47  6 

8        So  7 

15 

13       58  9 

I        52  7 

7        55  8 

July     i  
15  

12        S6.3 

12          OI  5 

o        50.1 
23        51-5 

18        51.3 

6        53-2 
5        58  4 

Aug.     i  

10       55  .  o 

22        45  .  o 

16       50  o 

4        51-9 

IS  
Sept.    i  

10          OO.I 

8        53.5 

21          50.1 
2O          43-5 

IS        55.1 
14        48  <> 

3        57-0 
2          50.4 

je 

7        58  6 

19       48  6 

I        55  5 

Oct.     i 

6        55  8 

18        45  8 

12        50  8 

o       52.7 

IS 

6       oo  8 

i?        So  8 

II        55  8 

23       53  9 

Nov.    i  

4        54.o 

16       44-O 

10        49.0 

22         47.1 

15.  .. 

3       58  9 

15        48  .  9 

9       53-9 

21          52.O 

Dec.     i  
IS  

2        55.  8 

2          00.6 

14       45-8 
13       50.6 

8       50.8 
7       55-6 

20          48.9 

19       53-7 

*  From  data  furnished  by  the  U.  S.  Coast  and  Geodetic  Survey. 

Approximate  Determination  of  Time.  i.  To  Find  the  Error  of  a 
Watch.  —  The  observation  for  azimuth  on  the  sun  may  be  utilized. 
The  instant  of  the  observation  should  be  noted  on  the  watch.  Then 


sin/ 


sin  Z  cos  h 
cos  6 


AZIMUTH,  LATITUDE,  AND  TIME  311 

in  which  /  is  the  hour  angle  in  degrees  before  or  after  apparent  local 
noon.  Reduce  t  to  hours  by  dividing  by  15  and  find  the  apparent 
local  time;  apply  the  equation  of  time  for  the  day  from  the  Nautical 
Almanac,  and  the  result  is  mean  local  time.  The  longitude  of  the  place 
must  in  general  be  had  from  a  map,  if  possible  to  the  nearest  minute. 
The  difference  between  local  longitude  and  the  standard  meridian 
whose  time  is  carried  reduced  to  time  is  applied  to  the  determined  mean 
local  time  to  get  the  mean  standard  time.  The  difference  between  this 
and  the  observed  time  of  the  observation  is  the  error  of  the  watch. 
If  the  watch  carries  local  time,  longitude  is  needed  only  to  compute 
change  in  declination  and  need  not  be  so  precisely  determined. 

To  refer  to  any  calendar  day  other  than  the  first  and  fifteenth  of 
each  month,  subtract  3.94™  for  every  day  between  it  and  the  preced- 
ing tabular  day,  or  add  3.94"*  for  every  day  between  it  and  the  succeed- 
ing tabular  day. 

To  find  the  times  for  the  tabular  dates  after  1915,  to  the  tabular  value 
add  1.36™  for  each  year  after  1915  less  3.9™  for  each  leap  year.  In 
any  leap  year  deduction  for  that  year  is  not  made  until  March  i. 

To  find  the  time  of  western  elongation  for  Jan.  18,  1919: 

For  January  15,  1915,  western  elongation,  tabular  time  is  IIA  46.8"*. 
1919  —  1915  =4;  4  X  1.36  =  5.4.  One  leap  year  has  intervened, 
and,  therefore,  5.4  —  3.9  =  1.5™  to  be  added.  IIA  46.8™  +  1.5™  = 
11*48.3™  for  January  15,  1919.  For  January  18  subtract  38  —  15  = 
3  X  3  X  3-94m  =  n-8m  getting  nh  36.5™. 

To  refer  to  any  other  than  the  tabular  latitude  between  the  limits  of 
25°  and  50°  north  add  to  the  time  of  west  elongation  0.13*"  for  every 
degree  south  of  latitude  40°,  and  subtract  from  the  time  of  west  elonga- 
tion o.i8m  for  every  degree  north  of  40°.  Reverse  these  signs  for  cor- 
rections to  the  times  of  east  elongation.  For  latitudes  as  high  as  60° 
diminish  the  times  of  west  elongation  and  increase  the  times  of  east 
elongation  by  0.23™  for  every  degree  north  of  latitude  40°. 

To  refer  to  other  longitudes,  add  o.i6TO  for  each  hour  east  of  6  hours 
and  subtract  o.i6m  for  each  hour  west  of  6  hours. 


312 


RAILROAD   FIELD  MANUAL 


TABLE  LXXII 

Length  of  0.01°  of  latitude  and  0.01°  of  longitude  to  the  nearest 
whole  foot 


Latitude 

Length 
0.01° 
latitude 

Length 
0.01° 
longitude 

Latitude 

Length 
0.01° 
latitude 

Length 

0.01° 

longitude 

0 

I 

3628 

3652 

31 

3637 

3133 

2 

3628 

3650 

32 

3638 

3100 

3 

3628 

3647 

33 

3638 

3066 

4 

3628 

3643 

34 

3639 

3031 

5 

3628 

3638 

35 

3640 

2995 

6 

3628 

3632 

36 

3641 

2958 

7 

3628 

3625 

37 

3641 

2920 

8 

3628 

36i7 

38 

3641 

2882 

9 

3628 

3608 

39 

3642 

2842 

10 

3629 

3597 

40 

3643 

2802 

ii 

3629 

3586 

4i 

3643 

.2761 

12 

3629 

3573 

42 

3644 

2719 

13 

3629 

3559 

43 

3645 

2675 

14 

3630 

3545 

44 

3646 

2632 

IS 

3630 

3529 

45 

3646 

2587 

16 

3631 

3512 

46 

3647 

2542 

17 

3631 

3494 

47 

3647 

2495 

18 

3631 

3475 

48 

3648 

2449 

19 

3631 

3455 

49 

3649 

2401 

20 

3632 

3433 

50 

3649 

2353 

21 

3632 

3411 

51 

3650 

2303 

22 

3633 

3388 

52 

3650 

2254 

23 

3633 

3364 

53 

3651 

2203 

24 

3634 

3338 

54 

3652 

2152 

25 

3634 

3312 

55 

3652 

2099 

26 

3635 

3285 

56 

3653 

2047 

27 

3635 

3256 

57 

3653 

1994 

28 

363S 

3227 

58 

3654 

1940 

29 

3636 

3197 

59 

3655 

1886 

30 

3637 

3166 

60 

3655 

1831 

AZIMUTH,  LATITUDE,  AND  TIME 


TABLE  LXXIII.  —  CONVERGENCE  OF  MERIDIANS 


,  Latitude 

Angular 
convergence 
per  mile, 
degrees 

Distance  for 
convergence 
of  0.01°, 
feet 

Latitude 

Angular 
convergence 
per  mile, 
degrees 

Distance  for 
convergence 
of  0.01°, 
feet 

i 

o.ooo 

209,240 

31 

0.009 

6084 

2 

.001 

104,588 

32 

.009 

5851 

3 

.001 

69,690 

33 

.009 

5629 

4 

.001 

52,231 

34 

.010 

5420 

5 

.001 

4L747 

35 

.010 

5222 

6 

.002 

34,750 

36 

.010 

5032 

7 

.OO2 

29,747 

37 

.Oil 

4852 

8 

.002 

26,002 

38 

•          .Oil 

4681 

9 

.002 

23,062 

39 

.012 

45i6 

10 

.003 

20,715 

40 

.012 

4359 

ii 

.003 

18,792 

41 

.013 

4208 

12 

.003 

17,185 

42 

.013 

4062 

13 

.003 

15,823 

43 

.013 

3922 

14 

.004 

14,651 

44 

.014 

3788 

IS 

.004 

13,634 

45 

.014 

3658 

16 

.004 

12,740 

46 

.015 

3533 

i? 

.004 

ii,9So 

47 

.015 

3412 

18 

.005 

11,244 

48 

.016 

3295 

19 

.005 

10,611 

49 

.017 

3181 

20 

.005      • 

10,039 

50 

.017 

3071 

21 

.006 

9,5i8 

Si 

.018 

2964 

22 

.006 

9,044 

52 

.018 

2860 

23 

.006 

8,609 

53 

.019 

2758 

24 

.006 

8,208 

54 

.020 

2660 

25 

.007 

7,837 

55 

.021 

2563 

26 

.007 

7,493 

56 

.021 

2469 

27 

.007 

7,173 

57 

.022 

2377 

28 

.008 

6.874 

58 

.023 

2288 

29 

.008 

6,594 

59 

.024 

22OO 

30 

.008 

6,331 

60 

.025 

2114 

CHAPTER  VIII 
TABLES  FOR  METRIC  CURVES 

METRIC  curves  are  used  in  Latin-American  countries.  The  "degree" 
is  the  angle  subtended  by  a  chord  of  20  meters.  Practically  all  usually 
tabulated  curve  functions  may  be  converted  from  feet  values  in  tables 
for  curves  used  in  the  United  States  to  meter  values  for  metric  curves 
by  dividing  by  five. 

The  more  commonly  used  functions  have  been  tabulated  in  the  three 
following  tables.  The  tabular  values  are  in  meters. 


314 


TABLE  LXXIV.  —  RADII,  TANGENT  OFFSETS  AND  MIDDLE 

ORDINATES  FOR  METRIC  CURVES 
Degree  =  angle  subtended  by  chord  of  20  meters 


Deg., 
D 

Radius, 
R 

Logarithm, 
log/? 

Tan. 
off.,  t 

Mid. 
ord.,  m 

Deg., 
D 

Radius, 
R 

Logarithm, 
log/? 

Tan. 
off.,< 

Mid. 
ord.,  m 

0.0 

00 

00 

.000 

.000 

10.0 

114.74 

2.05970 

1-743 

•  437 

.2 

5729.57 

3.75812 

•  035 

.009 

.2 

112.49 

2.05113 

1.778 

•  445 

4 

2864.80 

3.45709 

.070 

.017 

•  4 

110.34 

2.04272 

1.813 

•  454 

.6 

1909.87 

3.28100 

.105 

.026 

.6 

108.26 

2.03447 

1.847 

.463 

.8 

1432  '.41 

3-15607 

.140 

.035 

.8 

106.26 

2.02637 

1.882 

•  472 

I.O 

1145-93 

3.059J6 

.175 

.044 

II.  0 

104-33 

2  .  01843 

I.9I7 

.480 

.2 

954-95 

2.97998 

.209 

.052 

.2 

102.48 

2  .  01063 

1-952 

.489 

-4 

8i8.53 

2.91304 

.244 

.061 

•4 

100.68 

2.00296 

1.986 

•  498 

.6 

716.22 

2.85505 

.279 

.070 

.6 

98.95 

1-99544 

2.021 

•  507 

.8 

636.65 

2.80390 

.314 

.079 

.8 

97.28 

I  .  98804 

2.056 

•  SIS 

20 

572.99 

2.75814 

•  349 

.087 

12.0 

95.67 

1.98077 

2.O9I 

•  524 

.2 

520.90 

2.71676 

.384 

.096 

.2 

94-11 

I.9736I 

2.125 

•  533 

-4 

477-50 

2.67897 

.419 

.105 

•  4 

92.59 

1.96658 

2.160 

•  542 

.6 

440-77 

2.64422 

•  454 

.113 

.6 

91.13 

1.95966 

2.195 

•  550 

.8 

409.30 

2.61204 

.489 

.122 

.8 

89.71 

I.9528S 

2.229 

•  559 

30 

382.02 

2.58208 

.524 

.131 

13  o 

88.34 

I.946I4 

2.264 

.568 

.2 

358-15 

2.55406 

.558 

.140 

.2 

87.00 

1-93954 

2.299 

•  577 

•4 

337-08 

2.52774 

.593 

.I48 

•4 

8S-7I 

1-93304 

2.333 

.585 

.6 

318-36 

2.50292 

.628 

.157 

.6 

84.46 

1.92663 

2.368 

•  594 

.8 

301.61 

2.47945 

.663 

.166 

.8 

83.24 

1.92032 

2.403 

.603 

4.0 

286.54 

2.45718 

.698 

.175 

14.0 

82.06 

1.91411 

2.437 

.612 

.2 

272.90 

2.43600 

•  733 

.183 

.2 

80.91 

1.90798 

2.472 

.620 

4 

260  .  50 

2.41581 

.768 

.192 

•  4 

79-79 

1.90193 

2.507 

.629 

.6 

249-18 

2.39651 

.803 

.201 

.6 

78.70 

1.89598 

2.541 

.638 

.8 

238.80 

2.37804 

.838 

.209 

.  8 

77.64 

1.89010 

2.576 

.647 

So 

229.26 

2.36032 

.872 

.218 

15.0 

76.61 

1.88430 

2.611 

.655 

.2 

220.44 

2.34330 

.907 

.22? 

.2 

75-61 

1.87858 

2.645 

.664 

•4 

212.29 

2.32692 

•  942 

.236 

•  4 

74.63 

1.87294 

2.680 

.673 

.6 

204.71 

2.31114 

•  977 

.244 

.6 

73.68 

1.86737 

2.714 

.682 

.8 

197-66 

2.29591 

I.OI2 

•  253 

.8 

72.76 

1.86187 

2.749 

.690 

6.0 

191.07 

2.28120 

1.047 

.262 

16.0 

71.85 

1.85644 

2.783 

.699 

.2 

184.92 

2.26697 

.082 

.271 

.2 

70-97 

1.85109 

2.818 

.708 

•  4 

179.14 

2.25320 

.116 

.279 

•  4 

70.11 

1.84579 

2.853 

.717 

.6 

173.72 

2.23985 

.151 

.288 

.6 

69.27 

1.84056 

2.887 

.726 

.8 

168.62 

2.22690 

.186 

.297 

.8 

68.45 

1.83540 

2.922 

-734 

7.0 

163.80 

2.21432 

.221 

.306 

17.0 

67.65 

I  .  83030 

2.956 

•  743 

.2 

159-26 

2.2O2II 

.256 

.314 

.2 

66.87 

1.82526 

2.991 

•  752 

•  4 

154.96 

2.19022 

.291 

.323 

•  4 

66.11 

1.82027 

3-025 

.761 

.6 

150.89 

2.17866 

.325 

•  332 

.6 

65.37 

I.8I535 

3-o6o 

.769 

.8 

147.03 

2.16739 

.360 

•  340 

.8 

64.64 

1.81048 

3.094 

-778 

8.0 

143.36 

2.15642 

•  395 

•  349 

18.0 

63.92 

1.80567 

3.129 

.787 

.2 

139.87 

2.I457I 

.430 

.358 

.2 

63  23 

1.80091 

3-163 

-796 

•  4 

136.54 

2.13526 

.465 

.367 

•  4 

62.55 

1.79620 

3.198 

.805 

.6 

133-37 

2.I25O6 

.500 

•  375 

.6 

61.88 

I.79I55 

3-232 

.813 

.8 

130.35 

2.II5IO 

•  534 

.384 

.8 

61.23 

1.78694 

3.267 

.822 

9.o 

127-45 

2.10536 

.569 

-393 

19.0 

60.59 

1.78239 

3-301 

.831 

.2 

124.69 

2.09583 

.604 

.402 

.2 

59.96 

1.77789 

3-335 

.840 

•  4 

122.04 

2.08651 

.639 

.410 

4 

59-35 

1.77343 

3-370 

.849 

.6 

II9-5I 

2.07739 

.674 

.419 

.6 

58.75 

1.76902 

3.404 

.857 

.8 

117.07 

2.06846 

.708 

.428 

.8 

58.16 

1.76465 

3-439 

.866 

10  0 

"4.74 

2.05970 

1-743 

•  437 

20.0 

57-59 

1.76033 

3-473 

.875 

(315) 


TABLE  LXXV.  —  METRIC  CURVES 


Degree 

Actual  arc, 

Long  chords 

Degree 

of 
curve 

one 
station 

2Sta. 

3Sta. 

4Sta. 

.5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

of 
curve 

02 

ao.ooom. 

40.00 

60.00 

80.00 

IOO.OO 

120.00 

139-99 

159-99 

02 

•  4 

.000 

o.oo 

o.oo 

o.oo 

o.oo 

H9-99 

9-98 

9-98 

•  4 

.6 

.000 

o.oo 

o.oo 

79.99 

99-99 

9-98 

9-97 

9-95 

.6 

.8 

.000 

o.oo 

o.oo 

9-99 

9-98 

9-97 

9-95 

9.92 

.8 

I.O 

20.000 

40.00 

59-99 

79-99 

99-97 

119-95 

139.92 

159-87 

I.O 

.2 

.000 

o.oo 

9-99 

9.98 

9.96 

9-92 

9.88 

9.82 

.2 

•  4 

.000 

o.oo 

9-99 

9-97 

9-94 

9-90 

9-83 

9-75 

•4 

.6 

.001 

o.oo 

9.98 

9.96 

9.92 

9.86 

9.78 

9.67 

.6 

.8 

.001 

o.oo 

9-98 

9-95 

9-90 

9-83 

9.72 

9-59 

.8 

2.0 

2O.OOI 

39.99 

59-97 

79-94 

99-88 

119.78 

139.66 

159-49 

2.0 

.2 

.001 

9-99 

9-97 

9-93 

9-85 

9-74 

9-59 

9-38 

.2 

•4 

.001 

9-99 

9.96 

9-91 

9.82 

9.69 

9-51 

9.26 

•  4 

.6 

.002 

9-99 

9.96 

9.90 

9.80 

9-64 

9.42 

9-14 

.6 

.8 

.OO2 

9-99 

9-95 

9.88 

9.76 

9-58 

9-33 

9.00 

.8 

30 

20.002 

39-99 

59-94 

79.86 

99-73 

II9.52 

I39.23 

158.85 

30 

.2 

.003 

9.98 

9-94 

9-84 

9.69 

9-45 

9-13 

8.69 

.2 

•  4 

.003 

9-98 

9-93 

9.82 

9-65 

9-39 

9.02 

8.53 

•  4 

.6 

.003 

9-98 

9.92 

9.80 

9.60 

9-31 

8.90 

8.35 

.6 

.8 

.004 

9.98 

9.91 

9-78 

9  56 

9-23 

8-77 

8.16 

.8 

4.0 

20.004 

39-98 

59-90 

79-76 

99-51 

"9-15 

138.64 

157-96 

4.0 

.2 

.004 

9-97 

9.89 

9-73 

9-46 

9.06 

8.50 

7-75 

.2 

-4 

.005 

9-97 

9.88 

9-71 

9-41 

8.97 

8.36 

7-54 

•  4 

.6 

.005 

9-9? 

9-87 

9.68 

9.36 

8.87 

8.20 

7-30 

.6 

.8 

.006 

9-97 

9.86 

9-65 

9-30 

8.78 

8.04 

7-07 

.8 

S.o 

20.006 

39.96 

59-85 

79-62 

99-24 

118.67 

137-88 

156.82 

S.o 

.2 

.007 

9.96 

9-84 

9-59 

9.18 

8.56 

7.71 

6.56 

.2 

•4 

.007 

9.96 

9.82 

9-56 

9.12 

8.45 

7-52 

6.29 

•  4 

.6 

.008 

9-95 

9.81 

9-52 

9-05 

8-34 

7-34 

6.02 

.6 

.8 

.009 

9-95 

9.80 

9-49 

8.98 

8.21 

7-iS 

5-73 

.8 

6.0 

20.009 

39-94 

59-78 

79-45 

98.91 

118.09 

136.95 

155-43 

6.0 

.2 

.010 

9-94 

9-77 

9-41 

8.83 

7-96 

6.74 

5-12 

.2 

•  4 

.010 

9-94 

9-75 

9-38 

8.76 

7-83 

6.53 

4.81 

•  4 

.6 

.Oil 

9-93 

9-74 

9-34 

8.68 

7-69 

6.31 

4.48 

.6 

.8 

.012 

9-93 

9-72 

9-30 

8.60 

7-55 

6.09 

4-15 

.8 

7.0 

20.012 

39-92 

59-70 

79.26 

98.51 

117.40 

135.86 

I53.8o 

7.0 

.2 

.013 

9.92 

9.69 

9-21 

8-43 

7-25 

5-62 

3-45 

.2 

-4 

.014 

9.92 

9-67 

9.17 

8-34 

7.10 

5-37 

3-o8 

•  4 

.6 

•  CIS 

9-91 

9-65 

9.12 

8.25 

6-94 

5.12 

2.71 

.6 

.8 

.015 

9.91 

9-63 

9.08 

8.16 

6.78 

4.87 

2.32 

.8 

8.0 

20.016 

39-90 

59-6i 

79-03 

98.06 

116.62 

134-60 

151-94 

8.0 

.2 

.017 

9-90 

9-59 

8.98 

7-96 

6-45 

4-33 

I.  S3 

.2 

•  4 

.018 

9.89 

9-57 

8.93 

7.86 

6.27 

4.06 

1.  12 

•  4 

.6 

.019 

9-89 

9-55 

8.88 

7.76 

6.09 

3-77 

0.70 

.6 

.8 

.020 

9.88 

9-53 

8.83 

7.66 

5-91 

3-49 

0.27 

.8 

9-0 

20.O2I 

39-88 

59-51 

78.77 

97-55 

H5-73 

I33-I9 

149.83 

9-o 

.2 

.022 

9-87 

9-49 

8.72 

7-44 

5-54 

2.89 

9.38 

.2 

•  4 

.022 

9.87 

9.46 

8.66 

7-33 

5-34 

2.58 

8.93 

•  4 

6 

.023 

9.86 

9-44 

8.60 

7.21 

5-15 

2.27 

8.46 

.6 

.8 

.024 

9-85 

9-42 

8.55 

7.10 

4-94 

1-95 

7-99 

.8 

10  0 

2O  .  O25 

39.85 

59-39 

78.48 

96.98 

114-74 

131.62 

147-50 

10.0 

Degree 

Actual  arc 

2Sta. 

3Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 

(316) 


TABLE   LXXV.  —  (Continued) 


Degree 
of 

Actual  arc, 
one 

Long  chords 

Degree 
of 

curve 

station 

2Sta. 

3Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

curve 

10.0 

20.025m. 

39-85 

59-39 

78.48 

96.98 

H4-74 

131.62 

147-50 

10.0 

.2 

.026 

9-84 

9-37 

8.42 

6.86 

4-53 

1.29 

7.01 

.2 

.4 

.027 

9-84 

9-34 

8.36 

6.74 

4-31 

0.95 

6.51 

-4 

.6 

.029 

9-83 

9-32 

8.30 

6.61 

4.10 

0.61 

6.00 

.6 

.8 

.030 

9-82 

9-29 

8.23 

6.48 

3-87 

0.25 

5-48 

.8 

II.  0 

20.031 

39-82 

59-27 

78.17 

96.35 

113-65 

129.90 

144-95 

II.  0 

.2 

.032 

9.81 

9-24 

8.10 

6.22 

3-42 

9-54 

4.42 

.2 

•  4 

•  033 

9.80 

9.21 

8.03 

6.08 

3-19 

9-17 

3-87 

•  4 

.6 

•  034 

9.80 

9.18 

7-97 

5-95 

2.95 

8.80 

3-32 

.6 

.8 

.035 

9-79 

9-15 

7-90 

5-8i 

2.71 

8.42 

2.76 

.8 

12.0 

20.037 

39-78 

59-13 

77-82 

95-6? 

112.47 

128.03 

142.19 

12.0 

.2 

.038 

9-77 

9.10 

7-75 

5-52 

2.21 

7.64 

1.61 

.2 

•  4 

•039 

9-77 

9-07 

7-68 

5.38 

1.96 

7.24 

1.03 

•  4 

.6 

.040 

9-76 

9-04 

7.60 

5-23 

I.7I 

6.84 

0-43 

.6 

.8 

.042 

9-75 

9.01 

7-53 

5-o8 

1-45 

6.43 

139-83 

.8 

13  o 

20.043 

39-74 

58.98 

77-45 

94-93 

111.18 

126.01 

139-22 

13  o 

.2 

•  044 

9-73 

8.94 

7-37 

4-77 

0.92 

5-59 

8.60 

.2 

•  4 

.046 

9-73 

8.91 

7.29 

4-61 

0.65 

5-17 

7-98 

•  4 

.6 

.047 

9-72 

8.88 

7.21 

4-45 

0.37 

4-73 

7-34 

.6 

.8 

.048 

9-71 

8.85 

7-13 

4-29 

0.09 

4-30 

6.70 

.8 

14.0 

20.050 

39-70 

58.81 

77-05 

94-13 

109.81 

123.86 

136.05 

14.0 

.2 

.051 

9-69 

8.78 

6.96 

3-96 

9-53 

3-41 

5-40 

.2 

-4 

•  053 

9.68 

8.74 

6.88 

3.8o 

9-23 

2-95 

4-73 

•  4 

.6 

.054 

9-68 

8.71 

6-79 

3-63 

8.95 

2.50 

4.06 

.6 

.8 

.056 

9-67 

8.67 

6.70 

3  45 

8.65 

2.03 

3-38 

.8 

IS  o 

20.057 

39-66 

58.64 

76.61 

93-28 

108.35 

121.56 

132.70 

15  o 

.2 

•  059 

9-65 

8.60 

6.52 

3-10 

8.04 

1.09 

2.0O 

.2 

•  4 

.060 

9.64 

8.56 

6.43 

2.92 

7-74 

0.61 

1.30 

•4 

.6 

.062 

9-63 

8.53 

6.34 

2.74 

7-43 

0.12 

O.6O 

.6 

.8 

.064 

9.62 

8.49 

6.25 

2.56 

7.  II 

119.63 

129-88 

.8 

16.0 

20.065 

39  -61 

58.45 

76.15 

92-37 

106.79 

119.14 

I29.I6 

16.0 

.2 

.067 

9.60 

8.41 

6.06 

2.18 

6.48 

8.64 

8.44 

.2 

•  4 

.068 

9-59 

8.37 

5-96 

1.99 

6.15 

8.13 

7-70 

•  4 

.6 

.070 

9-58 

8.33 

5-86 

1.  80 

5-82 

7.62 

6.96 

.6 

.8 

.072 

9-57 

8.29 

5.76 

1.61 

5-49 

7.11 

6.21 

.8 

17.0 

20.074 

39-56 

58.25 

75-66 

91.41 

105.16 

116.59 

125.46 

17.0 

.2 

.075 

9-55 

8.21 

5-56 

1.22 

4.82 

6.06 

4-70 

.2 

•  4 

•  077 

9-54 

8.17 

5-46 

1.  01 

4-47 

5-53 

3-93 

•4 

.6 

•  079 

9-53 

8.13 

5-36 

0.8l 

4-13 

S.oo 

3-16 

.6 

.8 

.081 

9  52 

8.08 

5-25 

0.61 

3-78 

4-46 

2.38 

.8 

18.0 

20.082 

39-51 

58.04 

75-15 

90.40 

103-43 

H3-9I 

121.59 

18.0 

.2 

.084 

9-50 

8.00 

5-04 

0.19 

3-o8 

3-36 

0.80 

.2 

•  4 

.086 

9-48 

7-95 

4-93 

89-98 

2.72 

2.81 

o.oo 

•4 

.6 

.088 

9-47 

7-91 

4-83 

9-77 

2.36 

2.26 

119.20 

.6 

.8 

.090 

9-46 

7-87 

4-71 

9-56 

i-99 

1.69 

8.39 

.8 

19.0 

20.092 

39-45 

57-82 

74-6o 

89-34 

101  .  63 

111.13 

117-58 

19.0 

.2 

.094 

9-44 

7-78 

4-49 

9-12 

1.26 

0.56 

6.76 

.2 

•  4 

.096 

9-43 

7-73 

4-38 

8.90 

0.88 

109.98 

5-93 

•  4 

.6 

.098 

9-42 

7-68 

4-27 

8.68 

0.51 

9.40 

5.10 

.6 

.8 

.100 

9-40 

7.64 

4-15 

8.46 

0.13 

8.82 

4.27 

.8 

20.0 

20.102 

39-39 

57-59 

74.03 

88.23 

99-74 

108.23 

113-43 

20.0 

Degree 

Actual  arc 

2Sta. 

3Sta. 

4  Sta. 

5  Sta. 

6  Sta.^ 

7  Sta. 

8  Sta. 

Degree 

(317) 


TABLE  LXXVI.  —  METRIC  CURVES 


Degree 

Middle  ordinates 

Degree 

of 
curve 

i  Sta. 

2  Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

of 
curve 

0.2 

.009 

-035 

.079 

.140 

.218 

'•314 

.428 

•  558 

0.2 

•  4 

.017 

.070 

.157 

.279 

•  436 

.628 

.855 

1.  117 

-4 

.6 

.026 

.105 

.236 

•  419 

.654 

•  942 

1.283 

1.675 

.6 

.8 

.035 

.140 

•  314 

•  558 

.873 

.256 

1.710 

2.233 

.8 

I.O 

.044 

•  175 

•  393 

.698 

.091 

•  570 

2.137 

2.791 

I.O 

.2 

.052 

.209 

•  471 

.838 

.309 

.884 

2.565 

3-349 

.2 

•  4 

.061 

.244 

•  550 

•  977 

.527 

.198 

2.992 

3.907 

4 

.6 

.070 

.279 

.624 

1.117 

•  745 

•  512 

3.418 

4.464 

.6 

.8 

.079 

•  314 

.707 

1.256 

.963 

.825 

3-845 

5.020 

.8 

2.0 

.087 

•  349 

.785 

1-396 

2.180 

3-139 

4-271 

5.576 

2.0 

.2 

.096 

.384 

.864 

1-535 

2.398 

3  452 

4.697 

6.132 

.2 

•  4 

.105 

.419 

•  942 

1.675 

2.616 

3.765 

5-122 

6.687 

-4 

.6 

.113 

•  454 

1.  021 

1.814 

2.833 

4-078 

5.548 

7-241 

.6 

.8 

.122 

.489 

.099 

1-953 

3-051 

4-391 

5-973 

7-795 

.8 

30 

.131 

.524 

.178 

2.093 

3-268 

4.703 

6-397 

8-348 

30 

.2 

.140 

•  558 

.256 

2.232 

3.485 

5-015 

6.821 

8.900 

.2 

•  4 

.148 

•  593 

•  335 

2.371 

3.703 

5-327 

7.244 

9-451 

-4 

.6 

.157 

.628 

•  413 

2.510 

3-920 

5.639 

7.667 

10.  OO2 

.6 

.8 

.166 

.663 

•  491 

2.650 

4-136 

5-950 

8.090 

10.551 

.8 

4.0 

.175 

.698 

•  570 

2.789 

4-353 

6.262 

8.511 

II.IOO 

4.0 

.2 

.183 

•  733 

.648 

2.928 

4-570 

6.572 

8.933 

11.647 

.2 

•  4 

.192 

.768 

.726 

3.067 

4-786 

6.883 

9-353 

12.194 

•4 

.6 

.201 

.803 

.805 

3-205 

5.002 

7-193 

9-773 

12.739 

.6 

.8 

.209 

.838 

.883 

3-344 

5.218 

7-502 

10.192 

13.283 

.8 

50 

.218 

.872 

.961 

3.483 

5-434 

7.812 

10.611 

13.826 

50 

.2 

.227 

.907 

2.040 

3-622 

5-650 

8.  121 

11.028 

14.367 

.2 

4 

.236 

•  942 

2.118 

3.76o 

5-865 

8.429 

11-445 

14.907 

-4 

.6 

.244 

•  977 

2.196 

3-899 

6.081 

8.737 

11.862 

15.446 

.6 

.8 

.253 

I.OI2 

2.274 

4-037 

6.296 

9-045 

12.277 

15.983 

.8 

6.0 

.262 

1.047 

2.352 

4.175 

6.511 

9-352 

12.691 

16.519 

6.0 

.2 

.271 

.082 

.431 

4-314 

6.725 

9.658 

13-104 

17.053 

.2 

-4 

.279 

.116 

.509 

4-452 

6.940 

9.965 

13.517 

17.586 

•  4 

.6 

.288 

.151 

.587 

4-590 

7-154 

10.270 

13.929 

18.117 

.6 

.8 

.297 

.186 

.665 

4.728 

7.368 

10-575 

14-339 

18.646 

.8 

70 

.306 

.221 

•  743 

4.866 

7.581 

10.880 

14-749 

19.174 

7.0 

.2 

.314 

.256 

.821 

5-003 

7-795 

11.184 

I5-I57 

19.700 

.2 

•  4 

•  323 

.291 

2.899 

5.I4I 

8.008 

11.487 

15.565 

20.223 

•  4 

.6 

•  332 

.325 

2.977 

5-279 

8.221 

11.790 

15.971 

20.745 

.6 

.8 

•  340 

.360 

3.055 

5.4i6 

8.433 

12.092 

16.376 

21.265 

.8 

8.0 

•  349 

•  395 

3  133 

5-553 

8.645 

12.394 

16.780 

21.783 

8.0 

.2 

•  358 

•  430 

3-2II 

5-691 

8.857 

12.695 

17.183 

22.299 

.2 

•  4 

.367 

.465 

3-288 

5-828 

9.069 

12.995 

17.584 

22.813 

.4 

.6 

•  375 

.500 

3.366 

5-965 

9.280 

13-294 

17.985 

23.325 

.6 

.8 

.384 

•  534 

3-444 

6.101 

9.491 

13-594 

18.384 

23-834 

.8 

9.0 

•  393 

.569 

3-522 

6.238 

9.702 

13.892 

18  .  782 

24.342 

90 

.2 

.402 

.604 

3-599 

6.375 

9.912 

14.189 

19.178 

24.847 

.2 

4 

.410 

-639 

3.677 

6.511 

IO.I22 

14.486 

19-573 

25.350 

•  4 

6 

.419 

.674 

3-754 

6.647 

10.332 

14.782 

19.967 

25.850 

.6 

.8 

.428 

.708 

3-832 

6.784 

10-541 

15.078 

20.359 

26.348 

.8 

10.0 

•  437 

1-743 

3.9io 

6.919 

10.750 

15-372 

20.750 

26.843 

10  0 

Degree 

I  Sta. 

2  Sta. 

3  Sta. 

4  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 

(318) 


TABLE  LXXVI.  —  (Continued) 


Degree 

Middle  ordinates 

Degree 

of  curve 

I  Sta. 

2  Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

of  curve 

10.0 

•  437 

1-743 

3-910 

6.919 

10.750 

15-372 

20.750 

26.843 

10.0 

.2 

•  445 

1.778 

3.987 

7-055 

10.958 

15-666 

21.139 

27.336 

.2 

•  4 

•  454 

1-813 

4.065 

7.191 

11.167 

15-959 

21.527 

27.827 

•4 

.6 

.463 

1.847 

4.142 

7-327 

H-374 

16.251 

21.913 

28.315 

.6 

.8 

.472 

1.882 

4.219 

7-462 

11.582 

16.542 

22  .  298 

28.800 

.8 

XI.  O 

.480 

1.917 

4-297. 

7-597 

11.789 

16.832 

22.681 

29.282 

II.  0 

.2 

.489 

1-952 

4-374 

7-732 

H-995 

17.122 

23.063 

29.762 

.2 

•  4 

.498 

1.986 

4-451 

7.867 

12.201 

17.410 

23-443 

30.239 

•  4 

.6 

•  SO? 

2.O2I 

4-539 

8.  002 

12.407 

17.698 

23.821 

30.714 

.6 

.8 

•  SIS 

2.O56 

4-605 

8.137 

I2.6I2 

17-985 

24.198 

31  185 

.8 

12.0 

.524 

2.O9I 

4.682 

8.271 

12.817 

18.271 

24-573 

31  654 

12.0 

.2 

.533 

2.125 

4-759 

8.405 

13-021 

18.556 

24.946 

32.119 

.2 

•  4 

•  542 

2.160 

4-836 

8.539 

13.225 

18.840 

25.317 

32-582 

•  4 

.6 

•  550 

2.195 

4.913 

8.673 

13.429 

19-123 

25-687 

33-041 

.6 

.8 

•  559 

2.229 

4.990 

8.807 

13.632 

19-405 

26.055 

33.498 

.8 

13.0 

.568 

2.264 

5.067 

8.940 

13-834 

19.686 

26.421 

33.951 

13  o 

.2 

•  577 

2.299 

5-144 

9.074 

14.036 

19.966 

26.785 

34-402 

.2 

•  4 

.585 

2.333 

5-220 

9.207 

14.238 

20  .  245 

27-147 

34-849 

•  4 

.6 

•  594 

2.368 

5-297 

9-339 

14.439 

20.523 

27.507 

35.292 

.6 

.8 

.603 

2.403 

5-374 

9-472 

14.639 

20.800 

27.866 

35-733 

.8 

14.0 

.612 

2.437 

5-450 

9-6os 

14.839 

21.076 

28.222 

36.171 

14.0 

.2 

.620 

2.472 

5.527 

9-737 

15.039 

21-351 

28.576 

36.604 

.2 

•  4 

.629 

2.507 

5.603 

9.870 

15.238 

21.625 

28.929 

37-035 

•  4 

.6 

.638 

2.541 

5.679 

IO.OOI 

15.437 

21.897 

29.279 

37.462 

.6 

.8 

.647 

2.576 

5.756 

10.133 

15.634 

22.169 

29.628 

37-886 

.8 

15.0 

.655 

2.611 

5.832 

10.264 

15.832 

22.439 

29.974 

38.306 

15  o 

.2 

.664 

2.645 

5.908 

10.395 

16.028 

22.709 

30.318 

38.723 

.2 

•  4 

.673 

2.680 

5.984 

10.526 

16.225 

22.977 

30.660 

39-137 

•  4 

.6 

.682 

2.704 

6.060 

10.657 

16.421 

23.244 

31.000 

39-546 

.6 

.8 

.690 

2.749 

6.136 

10.788 

16.616 

23-509 

31.338 

39-952 

.8 

16.0 

•699 

2.783 

6.212 

10.918 

16.810 

23.774 

31.673 

40.355 

16.0 

.2 

.708 

2.818 

6.288 

11.048 

17.005 

24-037 

32.007 

40-753 

.2 

•  4 

.717 

2.853 

6.364 

11.178 

17.198 

24.299 

32.338 

41.148 

•  4 

.6 

.726 

2.887 

6.439 

11.308 

17-390 

24-560 

32.667 

41-540 

.6 

.8 

•  734 

2.922 

6.515 

H-437 

17-583 

24.820 

32-993 

41.927 

.8 

17.0 

•  743 

2-956 

6.591 

11.566 

17-774 

25.078 

33-317 

42.311 

17.0 

.2 

•  752 

2.991 

6.666 

11.696 

17.966 

25-335 

33.639 

42.691 

.2 

•  4 

.761 

3-025 

6.741 

11.824 

18.156 

25-591 

33-959 

43-067 

•  4 

.6 

.769 

3.060 

6.817 

11-953 

18.346 

25.846 

34.276 

43-439 

.6 

.8 

.778 

3-094 

6.892 

12.081 

18-534 

26.099 

34-591 

43-807 

.8 

18.0 

.787 

3.129 

6.967 

12.208 

18.723 

26.351 

34.903 

44.171 

18.0 

.2 

•  796 

3-163 

7-043 

12.336 

18.911 

26  .  601 

35-213 

44-531 

.2 

•  4 

.805 

3.198 

7.117 

12.464 

19.098 

26.850 

35-521 

44.887 

•  4 

.6 

.813 

3.232 

7-193 

12.593 

19-285 

27.098 

35.826 

45-239 

.6 

.8 

.822 

3.266 

7.267 

12.717 

19.470 

27-345 

36.129 

45.587 

.8 

19.0 

.831 

3-301 

7-342 

12.844 

19.656 

27.590 

36.429 

45.931 

19.0 

.2 

.840 

3  335 

7.417 

12.971 

19.840 

27-833 

36.727 

46.271 

.2 

•  4 

.849 

3-370 

7-492 

13.097 

20.024 

28.076 

37-022 

46.606 

•  4 

.6 

.857 

3.404 

7.566 

13.222 

20  .  207 

28.316 

37.314 

46.938 

.6 

.8 

.866 

3-439 

7-641 

13.348 

20.389 

28.556 

37.604 

47-265 

.8 

20  0 

.875 

3-473 

7.715 

13  473 

20.571 

28.794 

37.892 

47-588 

20.0 

Degree 

i  Sta. 

2  Sta. 

3  Sta. 

4  Sta. 

5  Sta. 

6  Sta. 

7  Sta. 

8  Sta. 

Degree 

(319) 


CHAPTER  IX 


MISCELLANEOUS  TABLES 

TABLE  LXXVII.  —  TRIGONOMETRIC  FORMULAS,  CIRCULAR 
MEASURE,  ETC. 

Trigonometric  Functions  and  Formulas.     Solution  of  Triangles 

By  definition,  if  R  =  I , 
ED  =  sine  a. 
OD  =  cosine  a. 
DA  —  versed  sine  a. 
HF  =  coversed  sine  a. 
BA  =  tangent  a. 
FC  =  cotangent  a. 
OB  =  secant  a. 
OC  =  cosecant  a. 
If  R  is  other  than  I,  it  follows 
from  the  above  definitions  and  the 
proportionality  of  similar  figures, 
that 

1.  ED  =  Rsina.  5.  BA  =R  tan  a. 

2.  OD  =  R  cos  a.  6.  FC  =  R  cot  a. 

3.  DA  '=  R  versin  a.  7.  OB  =  R  sec  a. 

4.  HF  =  R  coversin  a.  8.  OC  =  R  cosec  a. 

from  which  also  in  any  right  triangle  of  angles  a  and  ft,  if  o  be  the  side 
opposite  the  angle  a,  o  the  side  adjacent  thereto,  and  h  the  hypotenuse, 


sin  a 


IO.    cos  a 


cos  ft. 


13- 


14. 


sec  a  =  -  =  cosec  ft. 


1 1 .   tan  a  =  -  =  cot  ft. 
a 


12.    cot  a  =  -  = 


cosec  a 


versa 


-  =  sec  0. 


1 6.     covers  a  = 


fr-a 

h 
h-o 


covers  /3. 


vers  0. 


Hence, 


17- 


o  =  h  sin  a  =  h  cos  0. 


cos/3 


18. 


320 


h  cos  a  =  h  sin  /3. 

a  a 

cos  a       sin  /3 


MISCELLANEOUS  TABLES 
o  =  a  tan  a  =  a  cot  0. 


321 


I9. 


21. 


tan  a       cot  /3 
a  =  o  cot  a  =  o  tan  /3. 


22. 


24. 


h  =  o  cosec  a  =  o  sec  0. 
o  = 


cosec  a       sec  /3 


a)  (h—a). 


=  acosec/3.        25-    *= 


322 


RAILROAD   FIELD   MANUAL 


Oblique  triangles  may  be  solved  by  some  one  of  the  following  formulas: 


GIVEN 

SOUGHT 

FORMULAS 

27.   A,B,  a, 

28.   A,a,b, 

29.    C,  a,  b, 
30.    C,  a,  b, 

31.    C,  a,  b, 
32.    C,  a,  b, 

33-    C,  o,  b, 
34.   a,  6,  c, 

35-   a,b,ct 
36.  4,B,  C,  a, 

B,  C,  c, 

%  (A  +  5), 
4(4-  5), 

4,5, 
c, 

Area, 

Area, 
Area, 

c-^tai'-jg^ 

~:nR_sln4T    ^  _     qno       /  4    I    R\ 

sin  .4  01 
4  (-4  +  5)  =  90°  -  4  C. 

7 

tan  l  (  A           Tt\               ~         tan  *•  (  A    -H-  R\ 

|  5  =  |  (A  +  B}  -  |  (A  -  B)'. 

Area  —  \ab  sin  C. 

If  ^  =  i  (a  +  b  +  c), 

4  /(5  _  &)  (s  —  c) 

sin  2  A  —  V/              ,               » 

1A-  V  /  5  ^  ~  °^ 

^             7(5  _  ft)  (5  -  c) 

uu  2  4  -  y     5  (5  _  a) 

j    _  2  V(^  —  a)  (5  —  6^  (5  ~~  C) 

2(5-6)(f-c) 

V^lo^                          ^ 

Area    =  Vs(s  —  a)  (s  —  6)  (5  —  c). 
A               a2  sin  5  sin  C 

2  sin  A 

MISCELLANEOUS  TABLES  323 

From  the  definitions  of  the  trigonometric  functions,  the  geometrical 
properties  of  right  triangles  and  in  some  cases  algebraic  transformations, 
it  may  be  shown  that  if  A  is  any  angle  and  B  any  other  angle, 

37.   sin2  A  +  cos2  A  =  I . 

-58.   sin    A  =  7  =  VI  —  cos2  A  =  tan  A  cos  A 

cosec  A 

=  2  sin  £  A  cos  £  A  =  vers  A  cot  5 .4 


39-  cos 
40.  tan 

41.  cot 

V£  (i  —  cos  2  A). 

A                                 A/T 

sin2  A  =  cot  A  sin  A 
>  cos2  \A  —  i  =  i  —  2  sin2  j  /I 

sec  A 
—  i  —  vers  A  =  : 

—  cos2  \  A  —  sin2  • 
sin  A           i 

j  /I   =  V£  +  %  COS  2  .4  . 

=  Vsec2  A  -  i 

cos  A      cot  A 

-\/      '          -!- 

Vi  —  cos2  A            sin  2  A 

'  VcosM 

I    —  COS  2  A 

cos  A             i  +  cos  2  A 
vers  2  A 

sin  2  A 
cos  A           i 

sin2A 

sin  A      tan  A 
sin  2  A 

sin  2  A        I  +  cos  2  A        tan  |  /I 

I  —  COS  2  A 

vers  2  -4          sin  2  /I           sec  /4  —  i 

42.  vers  A  =  i  —  cos  A  =  sin  A  tan  \A  =  2  sin2  %  A  =  cosA  (sec  A  —  i). 

43.  sin  (/I  ±  5)  =  sin  -4  cos  B  ±  sin  5  cos  -4. 

44.  cos  04  ±  B)  =  cos  /4  cos  B  =F  sin  -4  sin  B. 

.    ,   .       4  /i  —  cos  ^4       4  /vers  -4 

45.  sm^==y — —   =V-T-' 

46.   sin  2/1  =  2  sin  .4  cos  A . 

'i 


47.  cos* ,4 

48.  cos  2 ^4  =  2  cos2  A  —  i  =  cos2 -4  —  sin2  A  =  i  —  2  sin2  A. 

tan  A  I  — cos  ^4      4/1—  cos  A 

49.  tan  $  .4  =  — : -;  =  cosec  A  —  cot  A  =  — ; — -. —  =  V  — ; T 

i  +sec  A  sin  A          T  i  +  cos  A 

2  tan  A 


si  s{nA     I+cosA 


vers  /4          sin  ^4          cosec  A  —  cot  -4  * 


S2.  MiA-0**-.1 

2  COt  A 


324 


RAILROAD   FIELD   MANUAL 


5  vers  A 


53.  vers^4= 

I  +  V  i  —  5  vers  .4 

54.  vers  2 A  =  2  sin2  -4 . 

55.  sin  A  +  sin  B  =  2  sin 

56.  sin  -4  —  sin  B  =  2  cos 

57.  cos  A  -f  cos  5  =  2  cos 

58.  cos  5  —  cos  A  =  2  sin 


—  cos  A 


2  +  V2  (i  +  cos  A) 

(A  +  B)  cos%(A  -  B). 
(A  +  B}  sin  \(A  -  B}. 
(&'¥&)  cosi  (4  -  5).. 
(A  +  B)  sin  J(4  -  B). 


B  =  cos2  5  -  cos2  ,4  =  sin  (A  +  B}  sin  (A  -  B). 


59.  sin2  4  -  sin 

60.  cos2  A  -  sin2  B  =  cos  (-4  +  B)  cos  C4  - 

'       sin  (A  +  5) 

61.  tanA+tanB  =  -  .          ' 

cos.  -4  cos  5 


62.   tan  4  —  tan  B 


sin  (A  —  ff) 
cos  A  cos B 


LENGTH  OF  CIRCULAR  ARCS  TO  RADIUS  i 


Deg. 

Length 

Deg. 

Length 

Deg. 

Length 

Deg. 

Length 

Deg. 

Length 

10 

0.1745329 

50 

0.8726646 

90 

1.5707963 

130 

2.2689280 

170 

2.967059? 

20 

0.3490659 

60 

1.0471976 

IOO 

i  -  7453293 

140 

;  2.  4434610 

180 

3.1415927 

30 

0.5235988 

70 

i  .  2217305 

no 

1.9198622 

150 

2.6179939 

190 

3.3161256 

40 

0.6981317 

80 

1.3962634 

1  20 

2.0943951 

160 

2.7925268 

200 

3.4906585 

IT   =  3.I4I59 

Degrees  in  arc  of  length  equal  to  radius, 
Degrees  in  arc  of  length  equal  to  TT, 
Circumference  =  2  irr  = 
Area  =  irr2. 


If  /  =  length  of  circular  arc 
d  =  number  of  degrees  in  same 
r  =  radius  of  same 
c  =  chord  of  same 
m  —  middle  ordinate 


J7T    =  0.497150 

5,                      57.295780. 

180. 

360°. 

I 

T 

1  80° 

7T 

-^57- 

3°  approx. 

I 

d 

1  80° 

*S» 

•3 

0  approx. 

d         '  -d 

I  =  — r-  irr  =         o  r  approx. 
1 80          57.3° 

Area  of  sector  —  \  Ir. 

:.f  d 

Area  of  sector  =  —^-  irr2. 
Approx.  area  of  segment  =  \cm. 


-  =  0.31831. 

Volume  of  sphere  =  f  irr3. 
Square  feet  in  i  acre  =  43,560. 
Cubic  feet  in  i  cubic  meter  =  35.3145. 


MISCELLANEOUS  TABLES 


325 


TABLE  LXXVIII.  —  STADIA  FUNCTIONS 
Differences  of  elevation  for  100  feet  rod  reading 


Deg. 

o 

I 

2 

3 

4 

5 

6' 

7 

8 

9 

Deg. 

.00 

o.oo 

1-74 

3-49 

5-23 

6.96 

8.68 

10.40 

12.10 

13-78 

15-45 

.00 

05 

0.09 

1.83 

3-57 

5-31 

7-05 

8.77 

10.48 

12.18 

13-87 

15.53 

•05 

.1 

0.17 

1.92 

3.66 

5-40 

7-13 

8.85 

10.57 

12.26 

13-95 

15.62 

.1 

•  IS 

0.26 

2.01 

3-75 

5-49 

7.22 

8-94 

10.65 

12.35 

14-03 

15-70 

.15 

.2 

0.35 

2.09 

3-84 

5-57 

7-3° 

9-03 

10.74 

12.43 

14.12 

15.78 

.2 

.25 

0.42 

2.18 

3-92 

S-66 

7-39 

9  .11 

10.82 

12.52 

14.20 

15-87 

•25 

•  3 

0.52 

2.27 

4.01 

5-75 

7.48 

9.20 

10.91 

12.60 

14.28 

15.95 

3 

•  35 

0.61 

2.36 

4.10 

5.83 

7.56 

9.28 

10.99 

12.69 

14-37 

16.03 

•  35 

•4 

0.70 

2.44 

4.18 

5-92 

7.65 

9-37 

11.08 

12.77 

14-45 

16.11 

•4 

•45 

0.79 

2.  S3 

4.27 

6.01 

7-73 

9.46 

ii.  16 

12.86 

14-54 

16.20 

45 

.5 

0.87 

2.62 

4-36 

6.09 

7.82 

9-54 

11.25 

12.94 

14.62 

16.28 

•  5 

•  55 

0.96 

2.70 

4-44 

6.18 

7.91 

9-63 

H-33 

13-03 

14.70 

16.36 

•  55 

.6 

i.  05 

2.79 

•  53 

6.27 

7-99 

9-71 

11.42 

13.11 

14-79 

16.44 

.6 

-65 

1.  13 

2.88 

.62 

6.35 

8.08 

9.80 

11.50 

13-19 

14.87 

16.52 

65 

•  7 

1.22 

2.97 

•  71 

6-44 

8.17 

9-88 

11-59 

13.28 

14-95 

16.61 

.7 

•  75 

I.3I 

3-OS 

•  79 

6.53 

8.25 

9-97 

11.67 

13.36 

15.04 

16.69 

•  75 

.8 

1.40 

3-14 

.88 

6.61 

8.34 

10.05 

11.76 

13.45 

15.12 

16.77 

8 

.85 

1.48 

3-23 

4-97 

6.70 

8.42 

10.14 

11.84 

13  53 

15.20 

16.86 

.85 

•  9 

1.57 

3-31 

5-05 

6.79 

8.51 

IO.22 

H-93 

13.61 

15  28 

16.94 

•9 

•95 

1.66 

3-40 

5-14 

6.87 

8.60 

10.31 

12.  OI 

13.70 

15-37 

17.02 

95 

I.OO 

1-74 

3-49 

5-23 

6.96 

8.68 

10.40 

12.10 

13.78 

15-45 

17.10 

I.OO 

Corrections  to  rod  readings  for  horizontal  distance 


Rod 

o° 

1° 

2° 

3° 

4° 

5° 

6° 

7° 

8° 

9° 

Rod 

100 

0.0 

0.0 

O.I 

0.3 

o.S 

0.8 

i.i 

1-5 

i-9 

2.5 

100 

200 

0.0 

O.I 

O.2 

o.S 

I.O 

1-5 

2.2 

3-0 

3-9 

4-9 

2OO 

300 

o.o 

O.I 

0.4 

0.8 

1-5 

2.3 

3-3 

4-5 

5-8 

7-4 

300 

400 

0.0 

O.I 

o.S 

i.i 

2.O 

3-0 

4-4 

6.0 

7-8 

9-8 

400 

500 

o.o 

0.2 

0.6 

1-4 

2.5 

3-8 

5-5 

7-5 

9-7 

12.3 

500 

600 

0.0 

0.2 

0-7 

1.6 

2-9 

4.6 

6-5 

8-9 

ii.  6 

14-7 

600 

700 

0.0 

0.2 

0.8 

ii-9 

3-4 

5-3 

7-6 

10.4 

13.6 

17.2 

700 

800 

o.o 

O.2 

I.O 

2.2 

3-9 

6.1 

8-7 

11.  9 

I5-S 

19.6 

800 

900 

o.o 

0-3 

I.I 

2.4 

4-4 

6.8 

9-8 

13-4 

17-5 

22.1 

900 

IOOO 

o.o 

0.3 

1.2 

2.7 

4-9 

7-6 

10.9 

14-9 

19.4 

24:5 

IOOO 

326 


RAILROAD   FIELD   MANUAL 


TABLE   LXXVIII.  —  (Continued) 


Deg. 

10 

ii 

12 

13 

14 

15 

16 

17 

18 

19 

Deg. 

.00 

17.10 

18.73 

20.34 

21.92 

23.47 

25.00 

26.50 

27.96 

29-39 

30.78 

.00 

.05 

17.18 

18.81 

20.42 

22.00 

23.55 

25.08 

26.57 

28.03 

29-46 

30.85 

.05 

.z 

17.26 

18.89 

20.50 

22.08 

23.63 

25.15 

26.64 

28.10 

29.53 

30.92 

.1 

.15 

17.35 

18.97 

20.58 

22.15 

23.70 

25  23 

26.72 

28.18 

29.60 

30.99 

•  15 

.2 

17.43 

19-05 

20.66 

22.23 

23.78 

25.30 

26.79 

28.25 

29.67 

31.06 

.2 

•25 

17.51 

19.13 

20.73 

22.31 

23.86 

25.38 

26.87 

28.32 

29-74 

3I-I3 

•  25 

3 

17.59 

19.21 

20.81 

22.39 

23.93 

25.45 

26.94 

28.39 

29.81 

3I.I9 

3 

•35 

17.67 

19.30 

20.89 

22.47 

24.01 

25.53 

27.01 

28.46 

29.88 

31.26 

•  35 

•  4 

17.76 

I9.38 

20.97 

22.54 

24.09 

25.60 

27.09 

28.54 

29.95 

31-33 

•  4 

•45 

17.84 

19.46 

21.05 

22.62 

24.16 

25.68 

27.16 

28.61 

30.02 

31.40 

•  45 

•  5 

17.92 

19-54 

21.13 

22.70 

24.24 

25-75 

27.23 

28.68 

30.09 

31-47 

•  5 

.55 

18.00 

19.62 

21.21 

22.78 

24.32 

25-83 

27-31 

28.75 

30.16 

31-53 

.55 

.6 

18.08 

19.70 

21.29 

22.85 

24.39 

25.90 

27-38 

28.82 

30.23 

31.60 

.6 

.65 

18.16 

19.78 

21.37 

22.93 

24.47 

25-98 

27-45 

28.89 

30.30 

31  67 

.65 

.7 

18.24 

19.86 

21.45 

23.01 

24.55 

26.05 

27.52 

28.96 

30-37 

31-74 

.7 

•  75 

18.33 

19-94 

21.53 

23.09 

24.62 

26.13 

27.60 

29.04 

30.44 

31-80 

•  75 

.8 

18.41 

20.02 

21.  60 

23.16 

24.70 

26.20 

27.67 

29.11 

30.51 

31-87 

.8 

.85 

18.49 

20.  10 

21.68 

23.24 

24.77 

26.27 

27-74 

29.18 

30.58 

31-94 

.85 

9 

18.57 

20.18 

21.76 

23.32 

24-85 

26.35 

27.81 

29.25 

30.65 

32.01 

•  9 

•95 

18.65 

20.26 

21.84 

23.40 

24.92 

26.42 

27-89 

29.32 

30.71 

32.07 

95 

x.oo 

18.73 

20.34 

21.92 

23.47 

25.00 

26.50 

27.96 

29-39 

30.78 

32.14 

1.  00 

Corrections  to  rod  readings  for  horizontal  distance 


Rod 

10° 

11° 

12° 

13° 

14° 

15° 

16° 

17° 

18° 

19° 

Rod 

_____ 

100 

3-0 

3-6 

4-3 

S.I 

5-9 

6.7 

7-6 

8.5 

9-5 

10.6 

100 

200 

6.0 

7-3 

8.6 

IO.I 

II.  7 

13-4 

15.2 

17.1 

19.1 

21.2 

2OO 

300 

9-1 

10.9 

13-0 

15-2 

17.6 

20.1 

22.8 

25.6 

28.6 

31-8 

300 

400 

12.  1 

14.6 

17-3 

20.  2 

23-4 

26.8 

30.4 

34-2 

38.2 

42-4 

400 

500 

I5-I 

18.2 

21.6 

25-3 

29-3 

33-5 

38.0 

42.7 

47-7 

53-0 

500 

600 

18.1 

21.8 

25-9 

30-4 

35-1 

40.2 

45-6 

51-3 

57-3 

63.6 

600 

700 

21.  1 

25-5 

30.2 

35-4 

41.0 

46.9 

53-2 

59-8 

66.8 

74.2 

700 

800 

24.2 

29.1 

34-6 

40.5 

46.8 

53-6 

60.8 

68.4 

76.4 

84.8 

800 

900 

27.2 

32.8 

38.9 

45.5 

52.7 

60.3 

68.4 

76-9 

85-9 

95-4 

900 

•1000 

30.2 

36.4 

43-2 

50.6 

** 

67.0 

76.0 

85-5 

95-5 

106.0 

IOOO 

MISCELLANEOUS  TABLES 


327 


TABLE   LXXVIII.  —  (Continued) 


Deg. 

20 

21 

22 

23 

24 

25 

26 

2? 

28 

29 

Deg. 

.00 

32.14 

33.46 

34  73 

35-97 

37-i6 

38-30 

39-40 

40.45 

41-45 

42.40 

.00 

.05 

32.21 

33.52 

34-80 

36.03 

37-22 

38.36 

39-45 

40.50 

41-50 

42-45 

.05 

.1 

32.27 

33-59 

34-86 

36.09 

37-27 

38-41 

39-51 

40.55 

41-55 

42-49 

.x 

•  IS 

32.34 

33.65 

34.92 

36.15 

37-33 

38-47 

39.56 

40.60 

41.60 

42.54 

-IS 

.2 

32.41 

33-72 

34-98 

36.21 

37-39 

38.53 

39-6i 

40.66 

41-65 

42.59 

.2 

•25 

32.47 

33.78 

35-05 

36-27 

37-45 

38-58 

39-67 

40.71 

41.69 

42.63 

.25 

3 

32-54 

33.84 

35-11 

36.33 

37-51 

38.64 

39-72 

40.76 

41-74 

42.68 

•  3 

•  35 

32.61 

33-91 

35-17 

36.39 

37-56 

38.69 

39-77 

40.81 

41-79 

42.72 

.35 

•4 

32.67 

33-97 

35-23 

36.45 

37.62 

38.75 

39-83 

40.86 

41.84 

42.77 

•  4 

•  45 

32.74 

34-04 

35-29 

36.51 

37-68 

38.80 

39-88 

40.91 

41.89 

42.81 

•  45 

•  5 

32.80 

34-10 

35-36 

36.57 

37-74 

38.86 

39-93 

40.96 

41-93 

42.86 

•  5 

•55 

32.87 

34-i6 

35-42 

36.63 

37-79 

38-91 

39-98 

41.01 

41-98 

42.90 

•  55 

.6 

32.93 

34-23 

35-48 

36.69 

37-85 

38.97 

40.04 

41.06 

42.03 

42.95 

.6 

.65 

33-00 

34.29 

35-54 

36.75 

37-91 

39-02 

40.09 

41.11 

42.08 

42.99 

.65 

•  7 

33-07 

34-35 

35-6o 

36.80 

37.96 

39-08 

40.14 

41.16 

42.12 

43-04 

•  7 

.75 

33  13 

34-42 

35-66 

36.86 

38.02 

39-13 

40.19 

41.21 

42.17 

43-08 

•  75 

.8 

33  20 

34.48 

35-72 

36.92 

38.08 

39-18 

40.24 

41.26 

42.22 

43-13 

.8 

.85 

33.26 

34-54 

35-78 

36.98 

38.13 

39-24 

40.30 

41-31 

42.26 

43-17 

.85 

•  9 

33-33 

34-6i 

35-85 

37-04 

38.19 

39-29 

40-35 

41-35 

42.31 

43-21 

.9 

•  95 

33-39 

34.67    35-91 

37-10 

38.25 

39  35 

40.40 

41.40 

42.36 

43-26 

•95 

1.  00 

33.46 

34-73    35-97 

37-16 

38.30 

39-40 

40.45 

41-45 

42.40 

43-30 

1.  00 

Corrections  to  rod  readings  for  horizontal  distance 


Rod 

20° 

21° 

22° 

23° 

24° 

25° 

26° 

27° 

28° 

29° 

Rod 

100 

II.  7 

12.8 

14-0 

15-3 

16.5 

17.9 

19.2 

20.6 

22.0 

23.5 

100 

200 

23.4 

25.7 

28.1 

30.5 

33-1 

35-7 

38-4 

41.2 

44-1 

47.0 

200 

300 

35-  i 

38.5 

42.1 

45-8 

49-6 

53-6 

57-7 

61.8 

66.1 

70.5 

300 

400 

46.8 

51.4 

56.1 

61.1 

66.2 

7i-4 

76.9 

82.4 

88.2 

94-0 

400 

500 

58.5 

64.2 

70.2 

76.4 

82.7 

89-3 

96.1 

103.1 

IIO.  2 

II7-5 

500 

600 

70.2 

77-0 

84.2 

91.6 

99-2 

107.2 

II5-3 

123.7 

132.2 

141.0 

600 

700 

81.9 

89.9 

98.2 

106.9 

115.8 

125.0 

134-5 

144.3 

154-3 

164-5 

700 

800 

93-6 

102.7 

112.  2 

122.2 

132-3 

142.9 

153-8 

164.9 

176.3 

188.0 

800 

900 

105-3 

115.6 

126.3 

137-4 

148.9 

160.7 

173-0 

185.5 

198.4 

211.5 

900 

1000 

117.0 

128.4 

140-3 

152.7 

165.4 

178.6 

192.2 

206.1 

22O.4 

235.0 

1000 

328 


RAILROAD   FIELD  MANUAL 


TABLE  LXXIX.  —  BAROMETRIC  ELEVATIONS 

Giving  altitudes  above  arbitrary  sea  level  (barometer  reading 
30  inches)  for  various  barometer  readings  B. 

To  determine  difference  of  elevation  of  two  points  having  barometer 
readings  B  and  Bi,  take  from  the  table  the  altitudes  corresponding 
to  B  and  BI,  and  correct  their  difference  by  Table  LXXX.  The 
corrected  difference  is  the  quantity  required. 


B 

A 

Diff. 
for  o  .  01 

B 

A 

Diff. 
for  c  .  01 

B 

A 

Diff. 
for  o  .  01 

Inches 

Feet 

Feet 

Inches 

Feet 

Feet 

Inches 

Feet 

Feet 

II.  0 

ii.  i 

27,336 

27,090 

-24.6 

14.0 
14.1 

20,765 
20,570 

-19-5 

17.0 
17.1 

15,476 
I5,3i6  ' 

—  16.0 

II.  2 

ii.  3 
11.  4 
ii.  5 

26,846 
26,604 
26,364 
26,126 

24.4 
24.2 
24.0 
23.8 
23.6 

14.2 

14-3 
14.4 
14-5 

20,377 
20,186 
19,997 
19,809 

19-3 

19.1 

18.9 
18.8 
18.6 

•  17.2 

17-3 
17-4 
17-5 

15,157 

14,999 
14,842 
14,686 

15-9 
15.8 

15-7 
15.6 
15.5 

II.  6 
ii.  7 

25,890 
25,656 

23.4 

14.6 
14-7 

19,623 

19.437 

18.6  ' 

I7.6 
17-7 

14,531 
14,377 

15.4 

II.  8 

25,424 

23.2 

14.8 

19,252 

18.5 

17.8 

14,223 

15-4 

23.0 

18.4 

15-3 

11.9 

12.0 
12.  1 

25,194 
24,966 

24,740 

22.8 
22.6 
22.4 

14.9 
iS.o 
I5-I 

19,068 
18,886 
18,705 

18.2 

18.1 
18.0 

17-9 
18.0 
18.1 

14,070 
I3,9i8 
13,767 

15-2 
15.1 
15.0 

12.2 

24,516 

15.2 

18,525 

18.2 

13,617 

12.3 

24,294 

22.2 

15-3 

18,346 

17.9 

18.3 

13,468 

14-9 

12.4 

24,073 

22.1 

21.9 

15-4 

18,168 

17.8 
17.6 

18.4 

13,319 

14.9 
14-7 

12.5 

23,854 

15-5 

17,992 

18.5 

13,172 

12.6 

12.7 

23,637 
23,421 

21.7 
21.6 

15.6 
15-7 

17,817 
17,643 

17-5 
17-4 

18.6 
18.7 

13,025 
12,879 

14-7 
14.6 

21.4 

17.3 

14.6 

12.8 

23,207 

15.8 

17,470 

18.8 

12,733 

12.9 

22,995 

21.2 

15,9 

17,298 

17.2 

18.9 

12,589 

14.4 

13.0 

22,785 

21.  0 
2O.9 

16.0 

17,127 

17.1 
16.9 

19.0 

12,445 

14.4 
14.3 

13.  1 

13,2 

13  3 

22,576 
22,368 
22,162 

20.8 
20.6 

16.1 
16.2 
16.3 

16,958 
16,789 
16,621 

16.9 
16.8 

I9-I 
19.2 
19-3 

12,302 
12,160 
12,018 

14-2 
14.2 

20.4 

16.7 

14.  1 

13.4 
13.5 

13.6 

21,958 
21,757  ' 
21,557 

20.1 

20.  o 
19.9 

16.4 
16.5 
16.6 

16,454 
16,288 
16,124 

16.6 
16.4 
16.3 

19-4 
19-5 
19.6 

11,877 
11,737 
n,598 

14.0 
13  9 
13-9 

13-7 
13-8 
13-9 

21,358 
21,160 
20,962 

19.8- 
19.8 

—  19.7 

16.7 
'  16.8 
16.9 

I5,96i 
15,798. 
15,636 

16.3 
16.2 
—  16.0 

19.7 
19.8 
19-9 

11,459 
11,321 
11,184 

13-8 
13-7 
—13-7 

14.0 

20,765 

17.0 

15,476 

20.0 

11,047 

Taken  from  Appendix  10,  "  U.  S.  Coast  and  Geodetic  Survey  Report  "  for  1881. 


MISCELLANEOUS  TABLES 


329 


TABLE  LXXIX.  —  (Continued) 


B 

A 

Diff. 
for  o.oi 

B 

A 

Diff. 
for  o.oi 

B 

A 

Diff. 
for  o.oi 

Inches 

Feet 

Feet 

Inches 

Feet 

Feet 

Inches 

Feet 

Feet 

20.0 
2O.  I 

11,047 
10,911 

-13-6 

23-7 
23.8 

6,423 
6,308 

-ii.  5 

27.4 
27-5 

2,470 
2,371 

-9-9 

20.2 

10,776 

13  5 

' 

23-9 

6,194 

11.4 
11.4 

27.6 

2,272 

9-9 
9-9 

20.3 

10,642 

24-0 

6,080 

27.7 

2,173 

20.4 

10,508 

13-4 

24-1 

5,967 

II.  3 

27.8 

2,075 

9.8 

20.5 

10,375 

13  3 

24-2 

5,854 

II.  3 

27.9 

1,977 

9.8 

13-3 

11.3 

9.7 

20.6 

10,242 

24-3 

5,741 

28.0 

1,880 

20.7 

10,110 

13-2 

24-4 

5,629 

II.  2 

28.1 

1,783 

9-7 

20.8 

9,979 

13-  1 

T1    T 

24-5 

5,518 

II.  I 
II   I 

28.2 

1,686 

9-7 

20.9 

21.0 

9,848 
9-7i8 

J-,5-  •!• 
13-0 

24-6 
24-7 

5,407 
5,296 

II.  I 

28.3 
28.4 

1,589 
1,493 

9-7 
9-6 

21.  1 

9,589 

12.9 
12.9 

24.8 

5,i86 

II.  0 
10.9 

28.5 

1,397 

9-6 
9.5 

21.2 

9,46o 

24-9 

5,077 

28.6 

1,302 

21.3 

21.4 

9,332 
9,204 

12.8 
12.8 

25.0 
25.1 

4,968 
4,859 

IO.9 
10.9 

28.7 
28.8 

1,207 

1,112 

9-5 
9-5 

12.7 

10.8 

9.4 

21-5 
21.6 

9,077 
8,951 

12.6 

__      £ 

25-2 
25-3 

4,751 
4,643 

10.8 

28.9 
29.0 

1,018 
924 

9-4 

21.7 

8,825 

12.  0 
12.5 

25-4 

4,535 

10.8 
10.7 

29.1 

830 

9-4 
9.4 

21.8 

8,700 

25-5 

4,428 

29.2 

736 

21.9 

8,575 

12.5 

25.6 

4,321 

10.7 

29-3 

643 

93 

22.0 

8,451 

12.4 
12.4 

25-7 

4,215 

10.6 
10.6 

29.4 

550 

9-3 
9.2 

22.1 

8,327 

25-8 

4,109 

29-5 

458 

22.2 

8,204 

12.3 

25-9 

4,004 

10.5 

29.6 

366 

9.2 

22.3 

8,082 

12.2 

26.0 

3,899 

10.5 

29.7 

274 

9.2 

12.2 

10.5 

92 
•* 

22.4 

7,960 

26.1 

3,794 

29.8 

182 

22.5 

7,838 

12.2 

26.2 

3,690 

10.4 

29-9 

91 

9-1 

22.6 

7,717 

12.  1 
12  O 

26.3 

3,586 

10.4 

30.0 

00 

9-1 

22.7 

7,597 

26.4 

3,483 

10.3 

30.1 

-91 

9-1 

22.8 

7,477 

12.0 

26.5 

3,38o 

10.3 

30.2 

181 

9-0 

22.9 

7,358 

II-9 

26.6 

3,277 

10.3 

30-3 

271 

9-0 

II.9 

10.2 

9.0 

23-0 

7,239 

26.7 

3,175 

30.4 

36i 

23-1 

7,121 

ii.  8 

26.8 

3,073 

IO.2 

30-5 

45i 

9-0 

23-2 

7,004 

11.7 

TT    7 

26.9 

2,972 

IO.I 

30-6 

540 

8.9 

8n 

23  3 

6,887 

il  .  / 

27.0 

2,871 

' 

30-7 

629 

•9 

23.4 
23.5 

6,770 
6,654 

II.7 

ii.  6 

ii.  6 

27.1 
27.2 

2,770 
2,670 

IO.I 
IO.O 
IO.O 

30.8 
30-9 

717 
805 

8.8 
8.8 
—8.8 

23.6 

6,538 

27-3 

2,570 

31-0 

-893 

23.7 

6,423 

—  11.5 

27-4 

2,470 

—  IO.O 

330 


RAILROAD  FIELD  MANUAL 


TABLE  LXXX.  —  CORRECTION  COEFFICIENT  FOR  TEMPERATURE 
AND  HYGROMETRIC  CONDITIONS 

This  correction  is  used  when  no  hygrometric  observations  have 
been  made.  To  the  difference  in  altitude  found  in  Table  LXXIX 
for  the  given  barometer  readings  is  added  algebraically  the  product 
of  that  difference  and  the  correction  below  given,  according  to  the 
formula,  diff.  alt.  =  (diff.  by  Table  LXXIX)  (i  +  c). 


Sum  O.  T.i 

Corr. 
coeff. 

Sum  O.  T. 

Corr. 

Coeff. 

Sum  O.  T. 

Corr. 
coeff. 

0° 
10 
20 

30 
40 
So 
60 

—0.1024 
-0.0915 
—0.0806 
—0.0698 
-0.0592 
—0.0486 
—0.0380 

70° 
80 
90 

IOO 

no 

120 
130 

—0.0273 
—  0.0166 
—0.0058 
+0.0049 
+0.0156 
+0.0262 
+0.0368 

140° 
150 
160 

170 
180 

+0.0471 
+0.0575 
+0.0677 
+0.0779 
+0.0879 

»  Computed  from  Tables  I  and  IV,  Appendix  10,  "  U.  S.  Coast  Survey  Report  "  for  1881. 

TABLE  LXXXI.1  —  Volume  in  cubic  feet  per  second  discharging 
over  a  thin  plate  weir  one  foot  in  length  without  end  contractions2 
according  to  Francis'  Formula  Q  =  3.33  L,VH3. 


Head, 
H  ,  in 

ft. 

Cu.  ft. 
per  sec. 

Head, 
H,  in 
ft. 

Cu.  ft. 
per  sec. 

Head, 
H,  in 
ft. 

Cu.  ft. 
per  sec. 

Head, 
H,  in 

ft. 

Cu.  ft. 
per  sec. 

Head, 
H,  in 

ft. 

Cu.ft. 
per  sec. 

.01 

0.003 

•  Si 

.213 

.01 

3-380 

•  5i 

6.179 

2.01 

9.489 

.02 

0.009 

•  52 

-249 

.02 

3-430 

•52 

6.240 

2.02 

9.56o 

.03 

0.017 

•  53 

.285 

•03 

3-481 

•  53 

6.302 

2.03 

9  631 

.04 

0.027 

•  54 

.321 

.04 

3-532 

•  54 

6.364 

2.04 

9.703 

.05 

0.037 

•  55 

•  358 

•05 

3.583 

•  55 

6.426 

2.05 

9-774 

.06 

0.049 

•  56 

•  395 

.06 

3.634 

-56 

6.488 

2.06 

9-846 

.07 

0.062 

•  57 

•  433 

.07 

3.686 

•  57 

6-551 

2.07 

9.917 

.08 

0.075 

-58 

•  471 

.08 

3-737 

•  58 

6.613 

2.08 

9.989 

.09 

0.090 

•59 

•  509 

.09 

3-790 

•59 

6.676 

2.09 

10.062 

.10 

0.105 

.60 

•  548 

.10 

3-842 

.60 

6.739 

2.10 

10.134 

.11 

O.I2I 

.61 

.586 

.11 

3.894 

.61 

6.803 

2.  II 

10.206 

.12 

0.138 

.62 

.626 

.12 

3-947 

.62 

6.866 

2.12 

10.279 

.13 

0.156 

•  63 

.665 

•  13 

4.000 

.63 

6-930 

2.13 

10.352 

.14 

0.174 

.64 

•  70S 

.14 

4-053 

.64 

6.994 

2.14 

10.425 

•  IS 

0.193 

.65 

•  745 

•  IS 

4-107 

.65 

7-058 

2.15 

10.498 

.16 

0.213 

.66 

•  786 

.16 

4-160 

.66 

7.122 

2.16 

10.571 

.17 

0.233 

.67 

.826 

•  17 

4-214 

.67 

7-187 

2.17 

10.645 

.18 

0.254 

.68 

.867 

.18 

4.268 

.68 

7-251 

2.18 

10.718 

•  19 

0.276 

.69 

.909 

•19 

4.323 

-69 

7.316 

2.19 

10.792 

.20 

0.298 

•  70 

•  950 

.20 

4-377 

.70 

7.381 

2.  2O 

10.866 

.21 

0.320 

•  71 

•992 

.21 

4-432 

•  71 

7.446 

2.21 

10.940 

.22 

0.344 

•72 

2.034 

.22 

4.487 

•  72 

7-512 

2.22 

11.015 

.23 

0.367 

•  73 

2.077 

•23 

4-543 

•  73 

7-577 

2.23 

11.089 

•  24 

0-392 

•74 

2.I2O 

.24 

4-598 

•  74 

7-643 

2.24 

11.164 

.25 

0.416 

•  75 

2.163 

•25 

4.654 

•  75 

7.709 

2.25 

11.239 

.26 

0.441 

•  76 

2.206 

.26 

4-710 

•  76 

7-775 

2.26 

11.314 

.27 

0.467 

•  77 

2.250 

.27 

4.766 

•  77 

7-842 

2.27 

11.389 

.28 

0-493 

•  78 

2.294 

.28 

4.822 

-78 

7.908 

2.28 

11.464 

.29 

0.520 

•79 

2.338 

.29 

4.879 

•79 

7-975 

2.29 

11.540 

.30 

0-547 

.80 

2.383 

•  30 

4.936 

.80 

8.042 

2.30 

11.615 

.31 

0-575 

.81 

2.428 

•  31 

4-993 

.81 

8.109 

2.31 

11.691 

.32 

0.603 

.82 

2-473 

•32 

5.050 

.82 

8.176 

2.32 

11.767 

•  33 

0.631 

•83 

2.518 

•33 

5-108 

.83 

8.244 

2-33 

11.843 

•  34 

0.660 

.84 

2.564 

•34 

5.165 

.84 

8.311 

2-34 

11.920 

•  35 

0.690 

•  85 

2.610 

•  35 

5.223 

.85 

8-379 

2.35 

11.996 

.36 

0.719 

.86 

2.656 

•  36 

5.281 

.86 

8-447 

2.36 

12.073 

•  37 

0.749 

•  87 

2.702 

•  37 

5-340 

.8? 

8-515 

2-37 

12.150 

.38 

0.780 

.88 

2-749 

•  38 

5-398 

.88 

8.584 

2.38 

12.227 

•  39 

0.811 

.89 

2.796 

•39 

5-457 

.89 

8.652 

2.39 

12.304 

.40 

0.842 

.90 

2.843 

.40 

5-516 

.90 

8.721 

2.40 

12.381 

•  41 

0.874 

•91 

2.891 

.41 

5-575 

•91 

8.790 

2.41 

12.459 

•  42 

0.906 

•92 

2-939 

.42 

5.635 

•92 

8-859 

2.42 

12.536 

•  43 

0-939 

•  93 

2.987 

•  43 

5.694 

•93 

8-929 

2-43 

12.614 

•  44 

0.972 

•94 

3-035 

-44 

5-754 

•94 

8.998 

2.44 

12.692 

•  45 

1.005 

•95 

3-083 

•  45 

5.814 

•  95 

9.068 

2.45 

12.770 

.46 

1-039 

•96 

3.132 

.46 

5.875 

•96 

9.138 

2.46 

12.848 

•  47 

1.073 

•97 

3.181 

•  47 

5-935 

•97 

9.208 

2-47 

12.927 

.48 

1.107 

•98 

3-231 

.48 

5.996 

•98 

9.278 

2.48 

13  005 

•  49 

1.142 

•  99 

3-280 

•49 

6.057 

•99 

9-348 

2.49 

13-084 

•  50 

1.  177 

I.OO 

3-330 

•  50 

6.118 

.00 

9-419 

2.50 

13-163 

1  From  Trautwine's  Engineers'  Pocketbook. 

1  The  table  values  are  not  seriously  in  error  when  there  are  end  contractions  provided 
L  is  at  least  10  H.  The  original  formula  was  limited  to  heads,  H,  between  H  foot  and  2 
feet.  The  tabular  values  are  probably  not  seriously  in  error  for  the  range  given.  For  any 
weir  of  length  L  feet  multiply  the  tabular  values  by  L. 

(331) 


332 


RAILROAD   FIELD   MANUAL 


TABLE   LXXXII 
Feet  to  Meters 


0 

i 

2 

3 

4 

5 

6 

7 

8 

9 

Meters 

Meters 

Meters 

Meters 

Meters 

Meters 

Meters 

Meters 

Meters 

Meters 

0 

o.ooo 

0.305 

0.610 

0.914 

1.219 

1.524 

1.829 

2.134 

2-438 

2.743 

IO 

3.048 

3-353 

3.658 

3-962 

4.267 

4-572 

4.877 

5.182 

5-486 

5-791 

20 

6.036 

6.401 

6.706 

7.010 

7-315 

7.620 

7.925 

8.229 

8-534 

8.839 

30 

9.144 

9-449 

9-753 

10.058 

10.363 

10.668 

10.972 

11.277 

11.582 

11.887 

40 

12.192 

12.496 

12.801 

13-106 

13.411 

13.716 

14.020 

14.325 

14-630 

14-935 

So 

15.239 

15-544 

15.849 

16.154 

16.459 

16.763 

17.068 

17-373 

17-678 

17.983 

60 

18.287 

18.592 

18.897 

19  .  202 

19.507 

19.811 

20.116 

20.421 

20.726 

21.031 

70 

21.335 

21  .  640 

21.945 

22  .  250 

22.555 

22.859 

23.164 

23.469 

23-774 

24.079 

80 

24-383 

24.688 

24-993 

25.298 

25.602 

25-907 

26.212 

26.517 

26.822 

27  .  126 

90 

27.431 

27.736 

28.041 

28.346 

28.651 

28.955 

29.260 

29-565 

29.870 

30.174 

100 

30.479 

30.784 

31-089 

31-394 

31-698 

32.003 

32.308 

32-613 

32.918 

33-222 

Meters  to  Feet 


vr_i__- 

o 

i 

2 

3 

4 

5 

6 

7 

8 

9 

JvieLers 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

Feet 

o 

o.oo 

3.28 

6.56 

9.84 

13.12 

16.40 

19.69 

22.97 

26.25 

29.53 

IO 

32.81 

36.09 

39-37 

42.65 

45-93 

49-21 

52-49 

55.78 

59-06 

62.34 

20 

65.62 

68.90 

72.18 

75.46 

78.74 

82.02 

85.30 

88.58 

91-87 

95.15 

30 

98.43 

101.71 

104-99 

108.27 

111.55 

114.83 

118.11 

121.39 

124.67 

127.96 

40 

131.24 

134.52 

137.80 

141.08 

144.36 

147.64 

150.92 

154-20 

157.48 

160.76 

SO 

164.04 

167.33 

170.61 

173.89 

177.17 

180.45 

183.73 

187.01 

190.29 

193-57 

60 

196.85 

200.13 

203.42 

206.70 

209.98 

213.26 

216.54 

219.82 

223.10 

226.38 

70 

229.66 

232.94 

236.22 

239-51 

242.79 

246.07 

249-35 

252.63 

255.91 

259-19 

80 

262.47 

265.75 

269.03 

272.31 

275.60 

278.88 

282.16 

285.44 

288.72 

292.00 

90 

295.28 

298.56 

391.84 

305.12 

308.40 

3H.69 

314.97 

318.25 

321-53 

324-81 

100 

328.09 

331-37 

334-65 

337-93 

341-21 

344-49 

347.78 

35i.o6 

354-34 

357.62 

i  statute  mile  =  1.6093  kilometers, 
i  kilometer      =  0.6214  statute  mile. 


CHAPTER  X 
ADJUSTMENT  OF  INSTRUMENTS 

The  Transit.  —  The  adjustments  in  order  are: 

I.  Axis  of  plate  bubbles  perpendicular  to  vertical  axis  of  instrument. 

II.  Line  of  sight  perpendicular  to  and  presumably  coincident  with 
horizontal  axis  of  telescope. 

1.  Parallax. 

2.  Vertical  wire  perpendicular  to  horizontal  axis  of  telescope. 

3.  Intersection  of  wires  to  axis  of  telescope. 

4.  Objective  slide  coincident  with  axis  of  telescope. 

5.  Line  of  sight  perpendicular  to  horizontal  axis  of  telescope. 

6.  Eyepiece  to  center. 

III.  Horizontal  axis  of  telescope  truly  horizontal  (Standard). 

IV.  Axis  of  telescope  bubble  parallel  to  line  of  sight. 

V.  Error  of  vernier  of  vertical  circle. 
To  test  for  and  make  the  adjustments: 

1.  Set  up;    turn  the  alidade  through   180°;    if  the  plate  bubbles 
depart  from  the  centers  of  their  tubes,  bring  them  halfway  back  with 
the  adjusting  pin,   and  relevel.     Repeat  test  and  adjustment   until 
complete. 

II.  i.  Carefully  focus  the  eyepiece  on  the  wires  until  they  are  sharp 
and  there  is  no  apparent  motion  over  an  object  sighted  as  the  eye  is 
moved  a  little  sidewise  or  up  and  down. 

2.  Sight  a  minute  distant  point  and  note  whether  the  vertical  wire 
remains  on  the  point  as  the  telescope  is  slightly  revolved  on  its  hori- 
zontal axis.     If  not,  loosen  two  adjacent  capstan  screws  carrying  the 
wire  ring,  and  turn  the  ring  slightly  until  by  further  trial  the  adjustment 
is  complete. 

3.  Construct  a  pair  of  Y  standards  of  wood,  as  two  notches  cut  in 
opposite  sides  of  a  box,  that  will  support  the  telescope  near  the  two 
ends  after  it  has  been  removed  from  the  standards.     Remove  the 
telescope  and  place  it  in  the  Y's;  direct  the  line  of  sight  to  any  minute 
distant  point  and  revolve  the  telescope  in  the  Y's  180°;  notice  if  the 
intersection  of  the  wires  remains  on  the  point;  if  not,  bring  the  wires 
halfway  back  to  the  point  by  opposite  capstan  screws,  moving  first 

333 


334  RAILROAD   FIELD   MANUAL 

one  set  and  then  the  other.  Repeat  the  test  and  adjustment  until 
complete.  This  adjustment  is  not  often  made  but  should  be  made  if 
careful  leveling  is  to  be  done  with  the  transit. 

4.  Not  all  object  slides  are  adjustable.      If  the  slide  may  be  ad- 
justed, its  adjustment  may  be  tested  by  making  a  test  for  3  on  a  very 
near  object;    if  an  error  appears,  the  slide  may  be  moved  by  moving 
the  ring  carrying  it.     The  ring  is  often  concealed  by  a  band  around  the 
telescope.     After  adjusting  the  slide  a  test  should  be  made  again  for 
3,  and  both  tests  and  adjustments  repeated  until  complete. 

5.  Set  up;    sight  a  minute  distant  point,  or  set  a  pin  some  200  to 
400  feet  away;  transit  the  telescope  and  find  a  distant  point  in  the  line 
of  sight  or  set  a  pin  some  200  to  400  feet  away;    revolve  in  azimuth 
and  sight  the  first  point;   transit  and  see  whether  the  line  of  sight  falls 
on  the  second  point;    if  not,  move  the  vertical  wire  one-fourth  the 
apparent  distance  toward  the  second  point;  repeat  the  test  and  adjust- 
ment until  complete.     The  same  first  point  may  be  retained  but  new 
second  points  must  be  found  or  set  for  each  test. 

6.  If  the  wires  seem  to  be  to  one  side  of  the  field  of  view,  the  eyepiece 
is  not  centered.     This  need  not  cause  error  in  work.     To  correct  the 
condition,   if  the  eyepiece   is  adjustable,   move  the   ring  carrying   it 
between  the  eye  end  and  the  wire  ring  until  the  wires  appear  to  be  in 
the  center  of  the  field. 

III.  (a}  Hang  a  plumb  line  from  a  high  point  not  far  from  the 
transit,  turn  the  line  of  sight  on  the  line  near  its  top  and  plunge  the 
telescope  downward,  noting  if  the  intersection  of  the  wires  follows 
the  line;    if  not,  raise  or  lower  one  end  of  the  horizontal  axis  until  the 
required  condition  is  met. 

(6)  Sight  a  nearby  high  point,  say,  on  a  building,  plunge  the  telescope 
and  set  a  point  near  the  level  of  the  instrument  or  lower;  reverse  in 
azimuth,  transit,  and  sight  the  high  point;  plunge  again  and  note 
whether  the  line  of  sight  cuts  the  first  lower  point  set;  if  not,  raise 
or  lower  one  end  of  the  horizontal  axis  until  the  required  condition  is 
met.  A  new  lower  point  will  be  needed  for  each  test. 

IV.  Adjust  as  described  for  the  Y  level,  II  I  (6). 

V.  After  making  IV,  with  the  transit  carefully  leveled,  bring  the 
telescope  bubble  to  the  center  of  its  tube  and  note  the  reading  of  the 
vertical  arc  vernier.     If  it  is  not  zero,  either  move  the  vernier  till  it 
does  read  zero  or  note  the  error  as  an  index  error  to  be  applied  to  all 
vertical  angle  readings.     Care  must  be  taken  to  note  whether  the  error 
is  such  as  to  diminish  or  increase  angles  of  elevation;  angles  of  depres- 
sion will  be  affected  in  the  opposite  way. 


ADJUSTMENT  OF  INSTRUMENTS  335 

The  Y  Level.  —  The  adjustments  are: 

I.  Line  of  sight  coincident  with  axis  of  telescope. 

1.  Parallax. 

2.  Horizontal  wire  perpendicular  to  vertical  axis  of  instrument. 

3.  Intersection  of  wires  to  axis  of  telescope. 

4.  Objective  slide  coincident  with  axis  of  telescope. 

5.  Eyepiece  to  center. 

II.  Bubble  axis  parallel  to  line  of  sight. 

1.  Vertical  adjustment. 

2.  Lateral  adjustment. 

III.  Y  adjustment  —  bubble  axis  perpendicular  to  vertical  axis  of 
level. 

To  Make  the  Adjustment:       . 

1.  i.   Set  up;   «focus  the  eyepiece  on  the  wires  until  they  appear 
sharp  and  there  is  no  apparent  motion  over  the  field  as  the  eye  is 
moved  a  little  sidewise  or  vertically. 

2.  Sight  a  distant  point  near  one  end  of  the  horizontal  wire;   turn 
the  telescope  a  little  on  the  vertical  axis  and  note  if  the  point  remains 
covered  by  the  wire  from  one  end  to  the  other;   if  not,  loosen  two  ad- 
jacent screws  carrying  the  wire  ring  and  turn  the  ring  until  by  trial 
the  required  condition  is  met. 

3.  Loosen  the  clips  over  the  Y's  and  sight  a  distant  point,  clamping 
the  azimuth  motion;  revolve  the  telescope  in  the  Y's  upside  down,  and 
note  whether  the  intersection  of  the  wires  remains  on  the  point;    if 
not,  move  the  wire  ring  first  sidewise  and  then  vertically  about  half 
the  apparent  error  until  the  intersection  of  the  wires  will  remain  on  a 
point  through  a  complete  revolution  of  the  telescope. 

4.  If  the  object  slide  is  adjustable,  perform  the  same  test  on  a  very 
near  point  and  adjust  the  object  slide.     The  ring  carrying  the  object 
slide  when  it  is  adjustable  is  likely  to  be  concealed  beneath  a  band 
around  the  telescope  between  the  object  focusing  screw  and  the  wire 
adjusting  screws. 

5.  When  the  instrument  is  adjusted  the  wires  may  appear  to  be  out 
of  the  center  of  the  field  of  view;  if  so,  the  eyepiece  is  out  of  center  and 
may  be  centered  by  moving  the  ring  between  the  eye  end  and  the  wire 
ring  until  the  wires  appear  to  center  the  field. 

II.  i  (a)  Set  up  carefully,  loosen  the  clips  over  the  Y's,  remove  the 
telescope  and  replace  it  end  for  end;  if  the  bubble  does  not  return  to 
the  center  of  the  tube  bring  it  halfway  back  by  the  bubble  adjusting 
screws,  relevel,  and  test  and  adjust  again,  until  the  required  condition 
is  met.  A  better  method  is  the  following: 


336  RAILROAD  FIELD   MANUAL 

(b)  Set  up  midway  between  two  stakes  about  200  feet  apart;  read  a 
rod  on  the  two  stakes  and  get  their  difference  of  elevation;  set  up 
beyond  one  of  the  stakes  about  ^  the  distance  between  them;  read 
the  rod  on  the  near  stake,  apply  the  difference  in  level  and  add  a  cor- 
rection for  curvature,  =  o.ooi  ft.  for  220  feet,  for  a  trial  reading  on  the 
distant  stake;  read  the  rod  on  the  distant  stake  and  if  the  reading  is 
not  the  same  as  the  trial  reading,  move  the  target  up  or  down  {%  of 
the  apparent  error  according  as  the  instrument  is  pointing  low  or  high; 
set  the  line  of  sight  on  the  target  and  bring  the  bubble  to  the  center  by 
its  adjusting  screws.  Without  moving  the  instrument  make  another 
complete  test  on  near  and  far  rod  and  continue  until  the  required  con- 
dition is  met.  If  the  level  is  set  outside  one  stake  one-fourth  of  the 
distance  between  the  stakes  the  apparent  error  will  be  multiplied  by 
£  instead  of  ^,  and  similarly  for  other  proportions. 

2.  With  the  level  set  up  and  the  clips  loose,  turn  the  telescope  a 
little  in  the  Y's  and  note  whether  the  bubble  remains  centered;  if  not, 
adjust  it  by  the  lateral  adjusting  screws  at  one  end  until  it  will  so 
remain  when  the  telescope  is  turned  from  side  to  side. 

III.  Set  up  and  level  with  particular  care  over  one  set  of  leveling 
screws;  turn  on  the  vertical  axis  180°  and  note  whether  the  bubble 
remains  in  the  center  of  the  tube;  if  not,  bring  it  halfway  back  by  rais- 
ing or  lowering  one  Y  by  the  capstan  nuts  through  which  its  stem 
passes;  relevel  and  repeat  until  the  required  condition  is  met. 

The  Dumpy  Level. — The  adjustments  are: 

I.  Bubble  axis  perpendicular  to  vertical  axis  of  level. 

II.  Line  of  sight  parallel  to  bubble  axis. 

1.  Parallax. 

2.  Horizontal  wire  perpendicular  to  vertical  axis  of  instrument. 

3.  Line  of  sight. 

The  adjustments  are  made  as  follows: 

I.  Set  up  with  telescope  leveled  with  particular  care  over  one  set 
of  screws;    reverse  in  azimuth  and  note  whether  the  bubble  remains 
in  the  center  of  its  tube;   if  not,  bring  it  halfway  back  by  the  bubble 
adjusting  screws;   relevel  and  repeat  until  the  condition  is  met. 

II.  i  and  2  are  made  as  for  the  Y  level. 

3  is  made  as  for  Y  level  II  I  (6),  adjusting  the  wires  to  the  bubble 
rather  than  the  bubble  to  the  wires;  i.e.,  centering  the  bubble  and 
moving  the  horizontal  wire  to  the  computed  correct  reading  on  the 
distant  rod. 


CHAPTER  XI 
SEXAGESIMAL  TRIGONOMETRIC  FUNCTIONS 

TABLE  LXXXIII.  —  LOGARITHMIC  SINES,  COSINES,  TANGENTS,  AND 
COTANGENTS  FOR  EACH  MINUTE  OF  ARC 

To  interpolate  when  the  angles  are  less  than  3°,  the  quantities  5  and 
T  as  found  in  the  5th  and  6th  columns  of  the  first  three  pages  are  used 
as  follows: 

Log  sine  a  =  Log  a'  —  S, 
Log  tangent  or  =  Log  a'  —  T, 

Log  a'  =  Log  sine  a  +  5  =  Log  tangent  a  +  T. 

For  cosine  and  cotangent  of  angles  near  90°  use  the  sine  and  tangent 
of  the  complements. 


337 


0° 


179C 


/ 

/ 

LSin 

d 

S 

T 

LTan 

cd 

LCot 

LCos 

o 
~I~ 

2 

3 
4 

I 

I 

9 

0 

i 

2 

3 

4 

i 
J 

9 
10 

ii 

12 
13 
14 

15 
16 

3 

19 
20 

21 
22 
23 
24 
25 
26 
27 
28 
29 

30 

3i 

32 
33 
34 

s 

8 

39 
40 

41 
42 
43 
44 

8 

47 
48 
49 
50 

51 

52 
53 
54 

II 
11 

59 
60 



30103 
17609 
12494 

9691 
7918 
6694 
5800 
5"5 
4576 

4139 

3779 
3476 
3218 

2997 
2802 
2633 
2483 
2348 
2227 

2119 
202  1 
1930 
1848 

1773 
1704 
1639 
1579 
1524 
1472 
1424 

1379 
1336 
1297 

1259 
1223 
1190 
1158 
1128 

IIOO 

1072 
1046 

IO22 

999 
976 
954 
934 
914 
896 
877 
860 

843 
827 
812 

797 
782 
769 
755 
743 
730 







30103 
17609 
12494 
9691 
7918 
6694 
5800 
5"5 
4576 

4139 

3779 
3476 
3219 
2996 
2803 
2633 
2482 
2348 
2228 

2119 

2O20 
1931 

l848 

1773 
1704 
1639 
1579 
1524 
1473 
1424 

1379 
1336 
1297 

1259 
1223 
II9O 

"59 

1128 

IIOO 

1072 
1047 

1022 
998 
976 

955 
934 
915 

895 
878 

860 

843 
828 
812 

797 
782 
769 
756 
742 
730 



0.00  000 

60 

59 
58 
57 
56 
55 
54 
53 
52 
Si 
50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 

38 
37 
36 
35 
34 
33 

32 

31 
30 

29 
28 
27 
26 
25 
24 
23 

22 
21 

20 

19 
18 
17 
16 
IS 
14 
13 

12 
II 

10 

1 

7 
6 
5 
4 
3 

2 

I 
0 

6.46  373 
6.76476 
6.94  085 
7.06  579 
7.16  270 
7.24  188 
7.30  882 
7.36  682 
7.41  797 

3-53  627 
3-53  627 
3-53  627 
3-53  627 
3-53  627 
3-53  627 
3-53  627 
3-53  627 
3-53627 

3-53  627 
3-53  627 
3-53  627 
3-53  627 
3-53627 
3-53  627 
3-53  627 
3-53  627 
3-53  627 

6-46  373 
6.76  476 
6.94085- 
7.06  579 
7.16  270 
7.24  188 
7.30  882 
7.36  682 
7.41  797 

3-53627 
3-23  524 
3-05  915 
2.93  421 
2.83  730 
2.75812 

2.69  118 
2.63  318 
2.58  203 

0.00  000 
0.00000 

o.oo  ooo 
o.oo  ooo 

0.00  000 
0.00000 

o.oo  ooo 

0.00000 
0.00000 

10 

7-46  373 

3-53  627 

3-53  627 

7-46  373 

2.53  627 

0.00000 

ii 

12 

13 
14 
15 

16 

3 

19 
20 

21 
22 
23 
24 

11 
11 

29 
30 

31 
32 
33 

34 
35 
36 

11 

39 
40 

7-505I2 
7-54  291 
7-57  767 
7-6o  985 
7.63  982 
7.66  784 
7.69417 
7.71  900 
7-74  248 

3-53  627 
3-53  627 
3-53  627 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 

3-53  627 
3-53  627 
3-53  627 
3-53627 
3-53  627 
3-53627 
3-53  627 
3-53627 
3-53627 

7-50512 
7.5429I 
7-57  767 
7.60  986 
7-63  982 
7-66  785 
7.69  418 
7.71  900 
7-74  248 

2.49  488 
2-45  709 
2.42  233 
2-39014 
2.36  018 
2.33  215 
2.30  582 
2.28  100 
2.25  752 

0.00  000 
0.00000 

o.oo  ooo 

O.OO  000 
O.OO  000 
O.OO  000 

9.99  999 
9-99  999 
9-99  999 

7.76475 

3-53  628 

3-53  627 

7.76476 

2.23  524 

9-99  999 

7.78  594 
7.80615 
7-82  545 
7-84  393 
7.86  1  66 
7.87  870 

7.89  509 
7.91  088 
7.92  612 

3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 

3-53  627 
3-53  627 
3-53  627 
3-53627 
3-53  627 
3-53627 
3-53  626 
3-53  626 
3-53626 

7.78  595 
7.80615 
7.82  546 

7-84  394 
7.86  167 
7-87  871 
7.89  Sio 
7.91  089 
7.92  613 

2.21  405 
2.19385 

2.17  454 
2.15  606 
2.13  833 

2.12  129 
2.IO  490 
2.089II 
2.07  387 

9-99  999 
9-99  999 
9-99  999 
9-99  999 
9-99  999 
9-99  999 
9-99  999 
9-99  999 
9.99  998 

7-94  084 

3-53  628 

3-53  626 

7.94086 

2.05  914 

9-99  998 

7-95  5o8 
7.96  887 
7-98  223 
7-99  520 
8.00  779 

8.O2  002 
8.03  192 
8.04  350 

8.05  478 

3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 
3-53  628 

3-53  626 
3-53  626 
3-53  626 
3-53  626 
3-53  626 
3-53  626 
3-53  626 
3-53  626 
3-53  626 

7-95  Sio 
7.96  889 
7.98  225 
7-99  522 
8.00  781 
8.  02  004 
8.03  194 
8.04  353 
8.05  481 

2.04  490 

2.03  in 
2.01  775 
2.00478 
1.99219 
1.97  996 
1.96806 
i-95  647 
1-94  519 

9-99  998 
9-99  998 
9-99  998 
9-99  998 
9-99  998 
9-99  998 
9-99  997 
9-99  997 
9-99  997 

8.06  578 

3-53  628 

3-53  625 

8.06  581 

1-93  419 

9-99  997 

4i 
42 
43 
44 

8 

47 
48 
49 
5° 

8.07  650 
8.08  696 
8.09  718 
8.10717 
8.  1  1  693 
8.12  647 
8.13  581 
8.14  495 
8.15  39i 

3-53  628 
3-53  628 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 

3-53  625 
3-53  625 
3-53  625 
3-53  625 
3-53  625 
3-53  625 
3-53  625 
3-53  625 
3-53  624 

8.07  653 
8.08  700 
8.09722 
8.10720 
8.  1  1  696 
8.12651 
8.13  585 
8.14  500 
8.15  395 

1.92  347 
1.91  300 
1.90  278 
1.89  280 
1.88304 
1-87  349 
1.86415 
1.85  500 
1.84605 

9-99  997 
9-99  997 
9-99  997 
9-99  996 
9.99  996 
9-99  996 
9.99  996 
9-99  996 
9-99  996 

8.16  268 

3-53  629 

3-53  624 

8.16  273 

1.83  727 

9-99  995 

5i 
52 
53 
54 

II 
11 

59 
60 

8.17  128 
8.17  971 
8.18  798 
8.19  610 
8.20407 
8.21  189 
8.21  958 

8.22  713 

8.23  456 

3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  629 
3-53  630 

3-53  624 
3-53  624 
3-53  624 
3-53  624 
3-53  624 
3-53  624 
3-53  623 
3-53  623 
3-53  623 

8.17  133 
8.17  976 
8.18  804 
8.19616 
8.20413 
8.21  195 
8.21  964 

8.22  72O 

8.23  462 

1.82  867 
1.82  024 
1.81  196 
1.80384 
1-79  587 
1.78  805 
1.78  036 
1.77  280 
1.76  538 

9-99  995 
9-99  995 
9-99  995 
9-99  995 
9-99  994 
9-99  994 
9-99  994 
9-99  994 
9.99  994 

8.24  186 

3-53  630 

3-53  623 

8.24  192 

1.75  808 

9-99  993 

LCos 

d 

LCot 

cd 

LTan 

LSin 

t 

90° 


(338) 


89° 


178C 


t 

/ 

LSin 

d 

S 

T 

LTan 

cd 

LCot 

LCos 

60 

0 

8.24186 

3-53  630 

3-53623 

8.24  192 

7lH 

1.75  808 

9-99  993 

60 

61 
62 
63 
64 

% 

67 
68 
69 

i 

2 
3 

4 

7 
8 
9 

8.24903 
8.25609 
8.26  304 
8.26988 

8.27  661 
8.28324 

8.28977 
8.29621 
8.30  255 

706 

684 

6p 
663 
653 
644 
634 

3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 
3-53  630 

3.53623 
3-53623 
3-53  623 
3-53622 
3.53622 
3-53622 
3-53622 
3-53622 
3.53622 

8.24910 
8.25616 
8.26312 
8.26996 
8.27  669 
8.28332 
8.28986 
8.29629 
8.30  263 

706 
696 

684 

673 

663 

654 

643 
634 

•74  384 
.73  688 
.73004 
•72331 
.71  668 
.71014 
-70371 
•69  737 

9-99  993 
9-99  993 
9-99  993 
9-99  992 
9-99  992 
9-99  992 
9-99  992 
9-99  992 
9-99  99i 

59 
58 
57 
56 
55 
54 
53 
52 
51 

70 

10 

8.30879 

firfi 

3-53  630 

3-53621 

8.30  888 

6t7 

1.69  112 

9-99  99i 

50 

7i 
72 
73 
74 
75 
76 
77 
78 
79 

n 

12 
13 
14 

3 

17 
18 
19 

8.31  495 
8.32  103 
8.32  702 
8.33  292 
8.33  875 
8.34450 
8.35018 
8.35  578 
8.36  131 

608 

599 
590 
583 

fa 

560 

553 

3-53  630 
3-53  631 
3-53  631 
3-53  631 
3.53631 
3-53  631 
3-53  631 
3-53631 
3-53631 

3-53621 
3-53621 
3-53621 
3.53621 
3-53620 
3-53620 
3.53620 
3.53  620 
3-53620 

8.31  505 
8.32  112 
8.32711 
8.33  302 
8.33886 
8.34461 
8.35029 
8-35  590 
8.36  143 

607 

599 
591 

584 
575 
568 

56l 
553 

1.68495 

1.67  888 
1.67  289 
1.66  698 
1.66  114 
1.65539 
1.64971 
1.64410 
1-63857 

9-99  99i 
9-99  990 
9-99  990 
9-99  990 
9-99  990 
9-99  989 
9-99  989 
9-99  989 
9-99  989 

49 
48 
47 
46 
45 
44 
43 
42 
41 

80 

20 

8.36  678 

3-53  631 

3-53  620 

8.36  689 

1.63311 

9-99  988 

40 

81 
82 
83 
84 
85 
86 

87 
88 
89 

21 

22 
23 
24 

11 

27 
28 
29 

8.37217 
8.37  750 
8.38  276 
8.38  796 
8.39310 
8.39818 
8.40320 
8.40  816 
8.41  307 

539 

533 
526 
520 

5U 
508 
502 
496 
491 

Age 

3-53631 
3-53  632 
3-53632 
3-53632 
3-53  632 
3-53  632 
3.53632 
3-53632 
3-53632 

3-536I9 
3.53619 
3.53619 
3.S36I9 
3.536i9 
3.536i8 
3.536i8 
3.536i8 
3.53618 

8.37  229 
8.37  762 
8.38  289 
8.38  809 
8.39323 
8.39  832 
8.40  334 
8.40  830 
8.41  321 

533 
527 
520 

514 
509 
502 

496 
49i 
486 

1.62  771 
1.62  238 
1.61  711 
1.61  191 
1.60677 
i.  60  168 
1.59666 
1.59170 
1.58679 

9-99  988 
9.99  988 
9-99  987 
9-99  987 
9-99  987 
9-99  986 
9-99  986 
9-99  986 
9-99  985 

39 
38 
37 
36 
35 
34 
33 
32 
31 

90 

30 

8.41  792 

AQQ 

3-53632 

3.53617 

8.41  807 

AgQ 

1.58193 

9-99  985 

30 

9i 
92 
93 
94 
95 
96 
97 
98 
99 

3i 
32 
33 

34 
35 
36 

s 

39 

8.42  272 
8.42  746 
8.43  216 
8.43  680 
8.44  139 
8.44  594 
8.45  044 
8.45  489 
8.45  930 

474 
470 
464 
459 
455 
450 
445 
441 

3-53632 
3-53  633 
3-53  633 
3-53  633 
3-53  633 
3.53633 
3.53633 
3-53  633 
3-53  633 

3.53617 
3536i7 
3.53617 
3.53617 
3.536i6 
3.536i6 
3-536I6 
3.536i6 
3-536I5 

8.42  287 
8.42  762 
8.43  232 
8.43696 
8.44  156 
8.44611 
8.45061 
8-45  507 
8.45  948 

475 
470 
464 
460 
455 
450 
446 
441 

I.577I3 
1-57  238 
1.56768 

1-56304 
1-55844 
1.55389 
1-54939 
1-54493 
1-54052 

9-99  985 
9-99  984 
9-99  984 
9-99  984 
9-99  983 
9-99  983 
9-99  983 
9-99  982 
9-99  982 

29 
28 
27 
26 
25 
24 
23 

22 
21 

100 

40 

8.46  366 

3-53  634 

3.536I5 

8.46  385 

1.53615 

9.99  982 

20 

IOI 
102 

103 
104 
105 
106 
107 
108 
109 

4i 
42 
43 
44 
45 
46 

8 

49 

8.46  799 
8.47  226 
8.47  650 
8.48  069 
8.48  485 
8.48  896 
8.49  304 
8.49  708 
8.50  108 

427 
424 
419 
416 
411 
408 

404 
400 

3-53  634 
3-53  634 
3-53  634 
3-53  634 
3-53  634 
3-53  634 
3-53  634 
3-53  635 
3.53635 

3.53615 
3.53615 
3.53614 
3.53614 
3-53614 
3-53614 
3-53613 
3-53613 
3.53613 

8.46817 
8.47  245 
8.47  669 
8.48  089 
8.48  505 
8.48917 
8.49325 
8.49729 
8.50130 

428 
424 
420 
416 
412 
408 
404 
401 

1.53183 
1.52755 
1-52331 
1.51911 
I.  Si  495 
1.51  083 
1.50675 
1.50271 
1.49  870 

9.99981 
9-99  98i 
9-99  98i 
9-99  98o 
9-99  98o 
9-99  979 
9-99  979 
9-99979 
9.99  978 

:i 

17 

16 
15 
14 
13 
12 
II 

no 

60 

8.50  504 

390 

3-53  635 

3.53613 

8.50527 

397 

1.49473 

9-99  978 

10 

III 

112 
"3 
114 

"5 
116 
117 
118 
119 

Si 
52 
53 
54 
55 
56 

% 

59 

8.50  897 
8.51  287 
8.51  673 
8.52055 
8-52  434 
8.52  810 

8.53  183 
8.53  552 
8.53919 

390 
386 
382 

379 
376 
373 
369 
367 
•*6a 

3.53635 
3.53635 
3.53635 
3-53  635 
3.53635 
3-53636 
3-53  636 
3-53  636 
3-53  636 

3.53612 
3-53612 
3.53612 
3.536II 
3.536II 
3.536n 
3.536ii 
3.536io 
3.536io 

8.50920 
8.51310 
8.51  696 
8.52079 
8.52459 
8.52835 
8.53  208 
8.53  578 
8.53  945 

393 
390 
386 
383 
380 
376 
373 
370 

$ 

i  .49  080 
1.48690 
1.48304 
1.47921 
I.4754I 
1.47  165 
1.46792 
1.46422 
1.46055 

9-99977 
9-99977 
9-99977 
9-99  976 
9.99976 
9-99  975 
9-99975 
9-99  974 
9-99974 

9 

8 
7 
6 

5 
4 
3 

2 

I 

120 

60 

8.54  282 

3-53636 

3.53610 

8.54  308 

1.45692 

9-99  974 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

t 

(339) 


88C 


2° 


177C 


1 

/ 

LSin 

d 

S 

T 

LTan 

cd 

LCot 

LCos 

120 

0 

2 

3 
4 
5 
6 

I 

9 
10 

ii 

12 
13 

14 

IS 

16 

17 
18 
19 
20 

21 
22 
23 

24 

11 

27 
28 
29 

30 

3i 
32 
33 
34 

11 

11 

39 
40 

41 

42 
43 
44 
45 
46 

47 
48 
49 
50 

51 

52 
53 

54 

Ii 
11 

59 
60 

8.54282 

360 

357 
355 
35i 
349 
346 
343 
341 
337 
336 

332 

330 
328 
325 
323 
320 
3i8 
316 
313 
3" 
309 
307 
305 
302 
301 
298 
296 
294 
293 
290 

288 
287 
284 
283 
281 
279 
277 
276 
274 
272 

270 
269 
267 
266 
263 
263 
260 

256 
254 
253 
252 
250 
249 
247 
246 
244 
243 
242 

3-53636 

3-53610 

8.54308 

361 
358 

355 
352 
349 
346 
344 
341 
338 
336 

333 
330 
328 
326 
323 
321 
319 
3i6 
314 
3" 
310 

307 
305 
303 
301 
299 
297 
295 
292 
291 
289 
287 
285 
284 
281 
280 
278 
276 
274 
273 
271 

269 
268 
266 
264 
263 
261 
260 
258 
257 
2SS 

254 
252 
251 
249 
248 
246 

245 
244 
243 

1.45692 

9-99  974 

60 

59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 
28 
27 
26 
25 
24 
23 

22 
21 

20 

19 
18 
17 
16 
IS 
14 
13 

12 

II 
10 

1 

7 
6 
5 
4 
3 

2 

I 
0 

121 
122 
123 
124 

I25 

126 
127 
128 
129 

8.54642 

8.54  999 
8.55  354 
8.55  70S 
8.56054 
8.56400 

8.56743 
8.57084 
8.57421 

3-53  636 
3.53637 
3-53  637 
3-53  637 
3-53637 
3-53  637 
3-53  637 
3.53637 
3-53  638 

3-53  609 
3-53  609 
3-53  609 
3-53  609 
3-53  608 
3-53  608 
3-53  608 
3-53  607 
3-53  607 

8.54669 
8.55027 
8.55  382  , 

8.55  734 
8.56083 
8.56429 
8.56773 
8.57  "4 
8.57452 

1.45331 

1-44973 
1.44618 
1.44  266 
I.439I7 
I-4357I 
1.43  227 
1.42886 
1.42548 

9-99973 
9-99  973 
9.99972 

9.99972 
9-99971 
9.99971 

9-99  970 
9.99970 
9.99  969 

130 

8.57  757 

3-53  638 

3-53  607 

8.57  788 

1.42  212 

9-99  969 

131 
132 
133 
134 
135 
136 

137 
138 
139 

8.58089 
8.58419 
8.58  747 
8.59072 
8-59395 
8.59715 
8.60033 
8.60349 
8.60  662 

3-53  638 
3-53638 
3-53  638 
3.53638 
3-53  639 
3.53639 
3-53  639 
3-53  639 
3-53  639 

3-53606 
3.536o6 
3-53  606 
3-53  605 
3-53  605 
3-53  605 
3-53  604 
3-53  604 
3-53604 

8.58  121 
8.584SI 
8.58779 
8.59105 
8.59428 

8.59749 
8.60068 
8.60  384 
8.60  698 

1.41879 

1.41  549 

I.4I  221 

1.40895 
1.40572 
I.4025I 
1-39932 
I.396l6 
1.39302 

9-99  968 
9-99  968 
9-99  967 
9-99  967 
9-99  967 
9-99  966 
9-99  966 
9-99965 
9-99  964 

140 

8.60  973 

3-53  639 

3-53  603 

8.61  009 

I.3899I 

9.99  964 

141 
142 
143 
144 
!45 
146 

147 
148 
149 

8.61  282 
8.61  589 
8.61  894 
8.62  196 
8.62497 
8.62  795 
8.63  091 
8.63  385 
8.63  678 

3-53  640 
3-53  640 
3-53  640 
3-53  640 
3-53  640 
3-53  640 
3-53641 
3-53  641 
3-53  641 

3-53  603 
3-53603 
3-53  602 
3-53  602 
3-53  602 
3.536oi 
3-53  601 
3-53  601 
3.53  600 

8.61319 
8.61  626 
8.61  931 
8.62  234 
8.62  535 
8.62  834 
8.63  131 
8.63  426 
8.63718 

I.3868I 
1.38374 
1.38069 
1.37766 
I-37465 

1.37  166 
1.36869 
1.36574 
1.36282 

9-99  963 
9-99  963 
9-99  962 
9.99962 
9.99961 
9.99961 
9.99  960 
9-99  96o 
9-99959 

ISO 

8.63  968 

3-53  641 

3-53  600 

8.64009 

1-35  99i 

9-99959 

151 
152 
153 
154 
155 
156 
157 
158 
159 

8.64256 
8.64  543 
8.64827 
8.65  no 
8.65  391 
8.65  670 
8.65  947 
8.66  223 
8.66  497 

3-53  641 
3-53  642 
3-53  642 
3-53642 
3-53  642 
3-53642 
3-53  642 
3-53  643 
3-53  643 

3-53  599 
3-53  599 
3-53  599 
3-53  598 
3-53  598 
3-53  598 
3-53  597 
3-53  597 
3^3596 

8.64  298 
8.64585 
8.64870 

8.65  154 
8.65435 
8.65715 
8.65  993 
8.66  269 
8.66  543 

1-35702 
I-354I5 
1-35  130 
1.34846 
1.34565 
1-34285 
1.34007 
I-3373I 
1.33457 

9-99  958 
9.99958 
9-99957 
9-99  956 
9.99956 
9-99955 
9-99  955 
9-99954 
9-99954 

1  60 

8.66  769 

3-53  643 

3-53  596 

8.66816 

1-33  184 

9-99953 

161 
162 
163 
164 
165 
166 
167 
1  68 
169 

8.67  039 
8.67  308 
8.67  575 
8.67  841 
8.68  104 
8.68367 
8.68627 
8.68  886 
8.69  144 

3-53  643 
3-53  643 
3-53  644 
3-53  644 
3-53  644 
3-53  644 
3.53644 
3-53  645 
3.53645 

3-53  596 
3-53595 
3-53  595 
3-53594 
3-53  594 
3-53  594 
3-53  593 
3-53  593 
3-53592 

8.67  087 
8.67356 
8.67624 
8.67  890 
8.68154 
8.68417 
8.68678 
8.68  938 
8.69  196 

1.32913 
1.32  644 
1.32376 
1.32  no 
1.31  846 
1-31  583 
1.31322 
1.31062 
1.30804 

9-99952 
9-99952 
9-99951 
9-99951 
9-99950 
9-99  949 
9-99  949 
9-99  948 
9-99  948 

170 

8.69  400 

3-53  645 

3-53592 

8.69453 

1-30547 

9-99  947 

171 
172 
173 
174 
175 
176 

177 
178 
179 

8.69654 
8.69  907 
8.70159 
8.70  409 
8.70658 
8.70905 
8.71  151 
8.71  395 
8.71  638 

3.53645 
3-53  646 
3-53  646 
3-53  646 
3-53  646 
3-53  646 
3-53  647 
3-53  647 
3-53647 

3-53592 
3.53591 
3-53591 
3-53  590 
3-53  590 
3-53  589 
3-53  589 
3-53  589 
3-53  588 

8.69  708 
8.69  962 
8.70214 
8.70465 
8.70714 
8.70962 
8.71  208 
8.71453 
8.71  697 

1.30292 
1.30038 
1.29786 

1.29535 
1.29286 
1.29038 
1.28  792 
1.28547 
1.28303 

9-99  946 
9-99  946 
9-99  945 
9-99  944 
9.99  944 
9-99  943 
9-99  942 
9-99  942 
9-99  941 

180 

8.71  880 

3-53  64? 

3-53  588 

8.71940 

1.28060 

9.99  940 

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8.71  880 

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1.28060 

9.99  940 

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241   239   237   235   234 

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5.72  I2O 

8.72  339 

240 

239 

8  72  181 
8.72  420 

241 
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1.27  819 
1.27  580 

9.99  940 

9-99  939 

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24.1   23.9   23-7   23.6   23.4 
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8-72  597 
8.72  834 
8.73  069 
8.73  303 

238 
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235 
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8.72  659 
8.72  896 
8.73  132 
8.73  366 

239 
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1.27  341 

1.27  104 
1.26  868 
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9-99  938 
9-99  938 
9-99  937 
9-99  936 

57 
56 
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144.6  143-4  142.2  141.6  140.4 
168.7  167.3  165.9  165.2  163.8 

7 
8 
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8.73  535 
8.73  767 
8.73  997 

232 
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8.73600 
8.73  832 
8-74  063 

232 
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1.26  400 
1.26  168 
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9-99  936 
9-99  935 
9-99  934 

53 
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8 
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192.8  191.2  189.6  188.8  187.2 
216.9  215.1  213.3  212.4  210.6 

131   831   229   237   126 

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8.74  226 

8  74  292 

1.25  708 

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8  74  454 

228 

8.74  521 

229 

1.25  479 

9-99  933 

40 

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69.6   69-3   68.7   68.1   67.8 

12 
13 

8.74  680 
8.74  906 

226 

8  74  748 
8.74  974 

227 
226 

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1.25  026. 

9-99  932 
9-99  932 

48 
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92.8   92.4   91.6   90.8   90.4 
116.0  115.5  H4-5  "3-5  "3-o 

14 

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8  75  130 
8.75  353 
8  75  575 

224 
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222 
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8-75  '99 
8-75  423 
8-75  645 

225 
224 
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1.24  801 
1.24  577 
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9-99  931 
9-99  930 
9-99  929 

46 
45 
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139.2  138.6  137.4  136.2  135.6 
162.4  161.7  160.3  158.9  158.2 
185.6  184.8  183.2  181.6  180.8 
208.8  207.9  206.1  204.3  203.4 

11 

8.75  795 
8.76013 

220 

8.75  867 
8.76  087 

220 

1.24  133 
1.23  913 

9.99  929 
9-99  928 

43 

42 

224   222   220   219   217 

19 

8.76  234 

219 

8.76  306 

1.23  694 

9-99  927 

41 

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22.4    22.2    22.O    21.9    21.7 

20 

8.76  451 

217 

8.76  525 

219 

1-23  475 

9-99  926 

40 

3 

67.2   66.6   66.0   65.7   65.1 

21 
22 
23 

8.76  667 
8.76  883 
8.77  097 

216 
216 

214 
213 

8.76  742 
8.76  958 
8-77  173 

217 
216 

215 
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1.23  238 
1.23  042 

1.22  827 

9-99  926 
9-99  925 
9-99  924 

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37 

4 
5 
6 
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89.6   88.8   88.0   87.6   86.8 
112.0  ni.o  no.o  109.5  108.5 
134-4  133-2  132-0  131.4  130.2 
156.8  155.4  154-0  153-3  i5i-9 

24 
25 

8.77  3io 
8.77  522 

212 

8.77  387 
8.77  600 

213 

1.22  613 
1.22  4OO 

9-99  923 
9-99  923 

36 

35 

8 
9 

179.2  177.6  176.0  175.2  173.6 
201.6  199.8  198.0  197  i  195.3 

26 

8-77  733 

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8.77811 

211 

1.22  189 

9-99  922 

34 

216   214   213   211   209 

28 

8-77  943 
8.78  152 

209 

8.78  022 
8.78  232 

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1-21  978 
1.  21  768 

9-99  921 
9.99  920 

33 

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21.6    21.4    21.3    21.  1    20.9 

29 

8.78  360 

8.78  441 

209 

I-  21  559 

9-99  920 

31 

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64.8   64.2    63.9    63.3    62.7 

30 

8.78  568 

8.78  649 

1-21  351 

9  99  919 

30 

4 
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86.4   85.6   85.2    84.4   83.6 
108.0  107.0  106.5  105.3  104-5 

32 
33 
34 
35 

8.78  774 
8.78979 
8.79  183 
8.79  386 
8.79  588 

205 
204 
203 

202 

8.78  855 
8.79061 

8.79  266 
8.79  470 
8.79  673 

206 
203 
204 
203 

1-21  I4S 
1.20  939 

1.20  734 

1.20  530 

9.99  918 
9-99  917 
9-99  917 
9.99916 
9-99  915 

29 

28 

27 

26 

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7 
8 
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129.6  128.4  127.8  126.6  125.4 
151.2  149.8  149.1   147.7  146.3 
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194.4  192.6  191.7  189.9  188.1 

208   206   203   201   199 

36 

8.79  789 

8-79  875 

1.20  123 

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2O.8    2O.6    2O.3    2O.I    19.9 

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39 

8.79  990 
8.80  189 
8.80  388 

199 
199 

8.80  076 
8.80  277 
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201 
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l.I9924 

1.19  723 
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9-99  913 
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83.2   82.4   81.2   80.4   79-6 
104.0  103.0  101.5  100.5   99-5 

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8.80  583 

8.80  674 

198 

1,19326 

9.99911 

20 

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124.8  123.6  121.  8  120.6  119.4 

41 
42 

8.80  782 
8.80  978 

197 
196 

8.80  872 
8.8  1  068 

198 
196 

1.19  128 
1-18932 

9-99  9io 
9.99  909 

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8 
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166.4  164.8  162.4  160.8  159.2 
187.2  185.4  182.7  180.9  I79-I 

43 
44 
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8.81  173 
8.81  367 
8.  8  1  360 
8.81  752 

195 
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193 
192 
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8.81  264 

8.81  459 
8.81  653 
8.8  1  846 

196 
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1.18  736 

1-18  541 
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9-99  909 
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7 
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198   196   194   192   190 

19.8   19.6   19.4   19.2   19.0 
39-6   39-2   38.8   38.4   38.0 
59.4   38.8   58.2   57.6   57.0 

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8.81  944 

8.82  038 

1.17  962 

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79.2   78.4   77.6   76.8   76.0 

48 

8.82  134 

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1-17  770 

9.99  904 

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99.0   98.0   97-0   96.0   95.0 

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8.82  324 

190 

8.82  420 

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1-17  380 

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118.8  117.6  116.4  115.2  114.0 

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8.82  313 

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8.83  075 

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8.63  261 

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8.83  630 

184 

8.83  732 

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1.16  268 

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75.2   74.4   73.6   72.8   72.4 

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8.83  813 
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1.16084 
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130.4  148.8  147.2  145.6  144.8 

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8.84  358 

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182 

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8.84  646 
8.84  826 
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8.85  363 
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36.4   36.2   36.0   33.8   35.6 
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72.8   72.4   72.0   71.6   71.2 
91.0   90.5   90.0   89.5   89.0 
109.2  108.6  108.0  107.4  106.8 

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8.85  780 
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163.8  162.9  162.0  161.1  160.2 
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8.86  128 

8.86  243 

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17.7   17-6   17.5   17.4   17.3 

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8.86  301 
8.86  474 
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169 
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8.86417 
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8.86  763 

8.86  93  S 
8.87  106 
8.87  277 

8.87  447 
8.87  616 
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174 
172 
172 
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1-12  553 
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9-99  884 
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9.99  88  1 
9.99  880 
9-99  879 

9-99  879 
9.99  878 
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46 
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43 
42 
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4 
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6 
7 
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3S-4   3S-2   35-0   34-8   34-6 
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70.8   70.4   70.0   69.6   69.2 
88.5   88.6   87.5   87.0   86.5 
106.2  105.6  105.0  104.4  103.8 

123.9   123-2   122.5   121.8   121.  1 

141.6  140.8  140.0  139.2  138.4 
159-3  158.4  157.5  1566  155.7 

172   171   170   169   108 

17.2   17.1   17.0   16.9   16.8 

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1.  12  047 

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8.88  326 
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164 
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8.88  453 
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8.89  in 
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167   166   106   164   163 

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33-4   33-2   33-0   32.8   32.6 
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8.89  464 

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1.10402 

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160 
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48.6  48.3  48.0  47.7  47.4 
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8.91  185 

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8.91  195 
8.91  349 
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8.92  262 
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147    146    145    144 

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58.8    58.4    58.0    57.6 
73-5    73-0    72-S    72.0 
88.2    87.6    87.0    86.4 

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117.6   116.8   116.0   115.2 
132.3   131.4   I30.S   "9.6 

148    14*    141    140 

14.3    14.2    14.1    14.0 
28.6   28.4   28.2    28.0 
42.9   42.6   42.3   42.0 
57.2    56.8   56.4   56.0 
71.5    71.0   70.5    70.0 
85.8   85.2   84.6   84.0 
100.1    99.4   98.7   98.0 

II4.4    II3.6    112.  8    II2.O 
128.7    127.8    126.9    126.0 

139    138    137    136 
13.9    13-8    13-7    13-6 
27.8    27.6    27.4    27.2 
41.7    41.4    41.1    40.8 
55-6    5S-2    S4-8    54-4 
69.5    69.0    68.5    68.0 
83.4   82.8    82.2    81.6 
97.3    96.6    95.9    95-2 

8.94  174 
8.94  317 

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8.94  603 
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8.94  340 
8.94  485 
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8-95  344 
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1.05  660 
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9.99  833 
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8.97  363 
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8.97  285 
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1.02  850 
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9-99  810 
9-99  809 
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9-99  807 
9.99  806 
9.99  804 

9-99  803 
9.99  802 
9.99  801 

125.1   124.2   123.3   122.4 
135    134    133    131 

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27.0    26.8    26.6    26.4 
40.5    40.2    39.9    39.6 
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67.5    67.0    66.5    66.0 
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8.98  157 

8.98  358 

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8.98  288 
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8.98  679 
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8-99  275 
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65.5    65.0    64.5    64.0 
78.6    78.0    77-4    76.8 
91.7    91.0    90.3    89.6 
104.8   104.0   103.2   102.4 

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36.9   36.6   36.3   36.0 
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61.5    61.0    60.5    60.0 
73-8   73-2    72.6   72.0 
86.1   85.4   84.7   84.0 
98.4    97.6    96.8    96.0 
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9-99  768 
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9-99  765 
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48.4    48.0    47.6    47.2 
60.5    60.0    59.5    59.0 
72.6    72.0    71.4    70.8 
84.7    84.0    83.3    82.6 

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9-03  109 

9-03  361 

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0.96  639 

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9-03  342 

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0.96  403 

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9-03  458 

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0.96  286 

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9-03  574 

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0.96  168 

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117   116   115   114 

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9-03  690 

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9-99  74i 

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9.03  920 

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9.04  181 

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9-99  738 

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35.1    34.8    34.5    34.2 

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9.04  034 

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9.04  297 

0.95  703 

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46.8    46.4    46.0    45.6 

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0.95  587 

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58.5   58.0   57.5   57.0 

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0.95  472 

9-99  734 

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70.2   69.6   69.0   68.4 
81.9   81.2   80.5   79.8 
93.6   92.8   92.0   91.2 
105.3  IO4-4  103.5  102.6 

9.04376 
9.04  490 
9.04  603 

9.04  643 
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9.05  101 
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9-05  164 

9.05  441 

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9-05  553 

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0.94  447 

9-99721 

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33-9   33-6   33-3   33-0 

45.2  44.8  44.4  44.0 
56.5   56.0   55.5   55.0 

9-05  386 

9.05  666 

0.94  334 

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9.05  778 

0.94  222 

9-99  7i8 

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67.8   67.2   66.6   66.0 

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101.7  100.8   99.9   99.0 

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9-99  693 
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9-08  795 
9.08  897 
9.08  999 
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9.09  202 
9.09  304 
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9-09  123 
9.09  227 
9-09  330 

9-09  434 
9-09  537 
9.09  640 
9-09  742 
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105 
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0.90  981 
0.90877 
0.90773 
0.90670 
0.90  566 
0.90  463 
0.90  360 
0.90  258 
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9-99  674 
9-99672 

9-99  670 
9-99  669 
9-99  667 
9-99  666 
9-99  664 
9-99  663 
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105         104         103 

10.5        10.4        10.3 

21.0            20.8            20.6 
31-5            31-2            30.9 

42.0        41.6        41.2 

52.5      52.0      51.5 

63.0        62.4        61.8 
73.5         72.8        72.1 

10 

9.09  606 

9.09  947 

0.90  053 

9-99  659 

50 

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84.0       83.2       82.4 

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12 
13 
14 
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16 

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9.09  707 
9.09  807 
9.09  907 
9.10006 
9.10  106 
9.10  205 

9-10304 
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100 
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99 
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9.10  049 
9.10  150 
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0.89  748 
0.89  647 
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0.89  445 
0.89  344 
0.89  244 
0.89  144 

9-99  658 
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94-5         93-6         92.7 
102         101          99 

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30.6             30.3             29.7 
40.8             40-4             39.6 
51.0             50.5             49-5 

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9.10956 

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9.11  184 
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98 
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97 
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97 

9.11  056 
9-11155 
9.11  254 

9-II353 
9.11452 
9U  55i 
9.11  649 
9.11747 
9.11845 

99 
99 
99 
99 
99 
98 

98 
98 
08 

0.88  944 
0.88  845 
0.88  746 
0.88  647 
0.88  548 
0.88  449 
0.88351 
0.88  253 
0.88  155 

9-99  642 
9.99  640 
9-99  638 
9-99  637 
9-99  635 
9-99  633 
9.99632 
9-99  630 
9-99  629 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

8 
9 

i 

2 

3 

81.6         80.8         79.2 
91.8         90.9         89.1 

98           97           96 

9-8          9-7          9-6 
19.6        19.4        19.2 
29.4        29.1         28.8 

30 

9.11  570 

06 

9-  1  1  943 

0.88057 

9-99627 

30 

5 

49.0        48.5        48.0 

3i 
32 
33 

34 
35 
36 

11 

39 

9.11  666 
9.11  761 
9."  857 
9.11952 
9.12047 
9.12  142 
9.12  236 
9-12331 
9-12425 

95 

96 
95 
95 
95 
94 
95 
94 

9.12  040 
9-12138 
9-12  235 
9-12332 
9.12428 
9-12525 
9.12  621 
9.12  717 
9.12813 

98 
97 
97 
96 
97 
96 

96 
96< 

0.87  960 
0.87  862 
0.87  765 
0.87  668 
0.87  572 
0.87475 
0.87379 
0.87  283 
0.87  187 

9-99625 
9-99  624 
9-99  622 
9.99  620 
9.99618 
9-996i7 
9.99615 
9.99613 
9.99612 

29 
28 
27 
26 
25 
24 
23 

22 
21 

6 
7 
8 
9 

58.8        58.2         57.6 
68.6         67.9         67.2 
78.4         77.6         76.8 
88.2        87.3        86.4 

95           94           93 

9-5           9-4           9-3 
190        18  8        18  6 

40 

9.12519 

9.12909 

0.87  091 

9.99610 

20 

3 

28.5         28.2         27.9 

41 

42 
43 
44 
45 
46 

47 
48 
49 

9.12  612 
9.12  706 
9.12  799 
9.12  892 
9.12985 
9.13078 
9-13  i?i 
9-13  263 
9-13355 

94 
93 
93 
93 
93 
93 
92 
92 

9-13004 
9.13099 
9.13  194 
9-13  289 
9-13384 
9.13478 
9-13573 
9-13  667 
9.13  76i 

95 
95 
95 
95 
94 
95 
94 
94 

0.86  996 
0.86  901 
0.86  806 
0.86711 
0.86616 
0.86522 
0.86427 
0.86  333 
0.86  239 

9.99  608 
9-99  607 
9-99  605 
9-99  603 
9.99  601 
9.99  600 
9-99  598 
9-99  596 
9-99  595 

19 

18 
17 
16 
15 
14 
13 

12 
II 

4 

1 

9 

38.0        37.6        37.2 
47-5         47-0        46.5 
57.0         56.4         55.8 
66.5         65.8         65.1 
76.0         75.2         74.4 
85.5         84.6         83.7 

92           91           90 

50 

9-13447 

9-13854 

0.86  146 

9-99  593 

10 

i 

9.2          9.1          9.0 

5i 

52 

53 
54 
55 
56 
57 
58 
59 

9-13  539 
9-13  630 
9.I3722 

9-13  813 
9.13904 
9-13994 
9-14085 
9.I4I75 
9.14  266 

9i 
92 
91 
9i 
90 
91 
90 
9i 

9.13948 
9.14041 
9.I4I34 
9.14227 
9-14320 
9.14412 
9.14504 
9-14597 
9.14688 

94 
93 
93 
93 
93 
92 
92 
93 
91 

0.86052 
0.85959 
0.85  866 
0-85  773 
0.85  680 
0.85  588 
0.85  496 
0.85  403 
0.85312 

9-99  59i 
9-99  589 
9-99  588 
9-99  586 
9-99  584 
9-99  582 
9-99  581 
9-99  579 
9-99577 

1 

7 
6 
5 
4 
3 

2 

I 

2 

3 
4 
5 
6 

1 

9 

18.4        18.2         18.0 
27.6        27.3         27.0 
36.8        36.4        36.0 
46.0        45.5        45.0 
55.2         54.6        54.0 
64.4        63.7        63.0 
73.6        72.8        72.0 
82.8        81.9        81.0 

60 

9.U356 

9.14780 

0.85  220 

9-99575 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

/ 

P  P 

(345) 


8° 


171C 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

P  P 

0 

9.14356 

0Q 

9.14780 

0.85  220 

9-99575 

60 

I 

2 

3 
4 
5 
6 

i 

9 

9-14445 
9-14535 
9.14624 
9.14714 
9.14803 
9.14891 
9.14980 
9.15069 
9.15157 

90 
89 
90 
89 
88 
89 

88 

9.14872 
9.14963 
9.15054 
9.15  145 
9-15  236 
9-15327 
9-15417 
9-15  508 
9-15  598 

91 
91 
91 
91 
91 
90 
91 
90 

0.8S  128 
0.85037 
0.84  946 
0.84855 
0.84  764 
0.84673 
0.84  583 
0.84492 
0.84  402 

9-99  574 
9-99572 
9-99  570 
9-99  568 
9-99  566 
9-99  565 
9-99  563 
9.99561 
9-99559 

59 

58 
57 
56 
55 
54 
53 
52 
5i 

I 

2 

3 

4 

I 

9 

9 

18 
27 
3J 
46 

55 

X           91           90 

.2               9.1               9.O 

.4         18.2         18.0 
.6         27.3         27.0 
.8         36.4         36.0 
.0        45.5         45.0 
.2         54.6         54.0 

10 

9-15  245 

88 

9.15  688 

go 

0.84312 

9-99  557 

50 

8 

i~\ 

.6         72.8         72.0 

it 

12 
13 

14 
15 

16 

11 

19 

9.15333 
9.15421 
9-is  508 
9-15596 
9-15683 
9.15  770 
9-15857 

9-iS  944 
9.16030 

88 
87 
88 

87 
87 
87 
87 
86 
86 

9-15  777 
9-15867 
9.15956 
9.16046 
9-16135 
9.16  224 
9.16312 
9.16401 
9.16489 

90 
89 
90 

89 
89 
88 

88 

0.84  223 
0.84  133 
0.84  044 

0.83  954 
0.83  865 
0.83  776 
0.83  688 
0.83  599 
0.83511 

9-99556 
9-99  554 
9-99552 
9-99  550 
9-99  548 
9-99  546 
9-99  545 
9-99  543 
9-99  54i 

4J 

47 
46 
45 
44 
43 
42 
41 

9 

82 

I 
2 
3 
4 

C 

.8         81.9        81.0 

89               88 

8.9              8.8 
17.8             17.6 
26.7             26.4 
35-6             35-2 
44.5             44-O 

20 

9.16  116 

87 

9.16577 

88 

0.83  423 

9-99  539 

40 

6 

53-4             52.8 

21 
22 
23 
24 
25 
26 
27 
28 
29 

9.16  203 
9.16  289 
9-16374 
9.16460 
9-16545 
9.16631 
9.16716 
9.16801 
9.16886 

86 
85 
86 

85 
86 
85 
85 

H 

9.16665 
9-16753 
9.16841 
9.16928 
9.17016 
9.17  103 
9.17  190 
9.17  277 
9.17363 

88 
88 
87 
88 
87 
87 
87 
86 
8? 

0.83  335 
0.83  247 
0.83  159 
0.83072 
0.82  984 
0.82  897 
0.82  810 
0.82  723 
0.82  637 

9-99  537 
9-99535 
9-99  533 
9-99532 
9-99  530 
9.99528 
9-99  526 
9-99  524 
9.99522 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

i 

2 

3 

7 
8 
9 

8 

8 
17 

2t 

62.3             61.6 
71.2             70.4  ' 
80.1             79.2 

7           86           85 

.7           8.6           8.5 
.4         17.2         17.0 
.1         25.8         25.5 

30 

9.16970 

Of 

9-17  450 

86 

0.82  550 

9-99  520 

30 

4 

34 

.8         34.4        34.0 

3i 

32 
33 
34 

II 

3 

39 

9.17055 
9-17  139 
9.17223 
9.17307 
9.I739I 
9-17474 
9.17558 
9.17641 
9.17724 

84 
84 
84 
84 
83 
84 
83 

83 
g. 

9-17  536 
9.17  622 
9.17  7o8 
9.17  794 
9.17  880 
9.17965 
9.18051 
9-18136 

9.l8  221 

86 

86 
86 
86 

Si 

85 
8S, 

0.82  464 
0.82  378 
0.82  292 
0.82  206 

O.82  I2O 
0.82  035 

0.8  1  949 
0.81  864 
0.81  779 

9.995i8 
9.99517 
9.99515 
9-99513 
9-995" 
9-99  509 
9-99  507 
9-99  505 
9-99  503 

29 
28 
27 
26 
25 
24 
23 

22 
21 

6 

7 
8 
9 

52 
6c 

3 

I 

.2             51.6             SI.O 

.9       60.2       59.5 
.6         68.8         68.0 
•3         77-4         76.5 

84              83 

8.4              8.3 
16  8             16  6 

40 

9.17807 

Q- 

9.18306 

°5 

0.8  1  694 

9-99  SGI 

20 

^ 

25.2             24.9 

41 
42 
43 
44 
45 
46 

47 
48 
49 

9.17890 
9-17973 
9-18055 
9.18137 

9.l8  220 
9.18302 

9.18383 
9-18465 

9-i8  547 

83 

82 
82 

83 
82 

81 
82 
82 
81 

9.18391 
9.18475 
9.18560 
9.18644 
9.18728 
9.I88I2 
9.18896 
9.18979 
9.19063 

oS 
84 

85 
84 
84 
84 
84 

s 

Q, 

0.8  1  609 
0.81  525 
0.81  440 
0.81  356 
0.81  272 
0.81  188 
0.81  104 
0.81  021 
0.80937 

9-99  499 
9-99  497 
9-99  495 
9.99  494 
9-99  492 
9-99  490 
9-99  488 
9.99  486 
9-99  484 

i9 
18 
17 
16 

is 

14 
13 

12 

ii 

4 

1 

I 

9 
8 

33-6             33-2 
42.0             41.5 
50.4             49.8 
58.8             58.1 
67.2             66.4 
75-6             74-7 

2          81          80 

50 

9.18628 

81 

9.I9I46 

Q, 

0.80854 

9-99  482 

10 

i 

1 

!.2           8.1           8.0 

5i 

52 
53 
54 

II 

57 
58 
59 

9.18  709 
9.18  790 
9.18871 
9-18952 
9.19033 
9.19113 
9.19193 
9^9273 
9-19353 

81 
81 
81 

81 
80 
80 
•80 
80 

9.19229 
9.I93I2 
9-19395 
9.19478 
9.I956I 
9.19643 

9.19725 
9.19807 
9.19889 

83 
83 
83 
83 
82 
82 
82 
82 

0.80771 
0.80  688 
0.80  605 
0.80522 
0.80  439 
0.80357 
0.80  275 
0.80  193 
0.80  in 

9-99  480 
9.99478 
9-99  476 
9-99474 
9-99472 
9-99  470 
9.99  468 
9-99  466 
9-99  464 

i 

7 
6 
S 
4 

3 

2 

I 

2 

3 

4 
5 
6 

I 

9 

2i 

3 
4' 
4< 

£ 

7C 

Jo       24.3       24.0 
.8         32.4        32.0 
.0        40.5         40.0 

).2             48.6            48.0 

.4       56.7       56.0 
.6         64.8         64.0 
.8        72.6        72-0 

60 

9-19433 

9.I997I 

0.80  029 

9-99  462 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

t 

P  P 

98C 


(346) 


170° 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

P  P 

0 

9-19433 

9.19971 

82 

0.80029 

9.99462 

60 

I 

2 

3 

4 
5 
6 

I 

9 

9-19513 
9.19592 
9.19672 

9-19751 
9.19830 
9.19909 
9.19988 
9.20067 
9.20  145 

79 
80 
79 
79 
79 
79 
79 
78 

9.20053 

9-20134 
9.20  216 
9.20  297 
9.20378 
9.20459 
9-20  540 
9.20621 
9.20701 

81 
82 
81 
81 
81 
81 
81 
80 
81 

0.79947 
0.79866 
0.79784 
0.79  703 
0.79622 
0.79541 
0.79460 
0.79379 
0.79  299 

9-99  460 
9-99  458 
9-99  456 
9-99454 
9-99452 
9-99  450 
9-99  448 
9-99  446 
9.99  444 

59 
58 
57 
56 
55 
54 
53 
52 
Si 

I 

2 

3 

4 

82           81           80 

8.2          8.1          8.0 
16.4        16.2         16.0 
24.6         24.3         24.0 
32.8        32.4        32.0 
41.0        40.5        40.0 

10 

9.20  223 

7° 

9.20782 

80 

0.79  218 

9-99  442 

50 

6 

49.2        48.6        48.0 

ii 

12 
13 

14 
15 

16 

17 
18 
19 

9.20302 
9.20380 
9-20458 

9-20535 
9.20613 
9.20691 
9.20  768 
9-20845 
9.20922 

79 

78 
78 
77 
78 
78 
77 
77 
77 

9.20862 
9.20942 
9.21022 

9.21  IO2 
9.21  l82 
9.21  26l 
9-21  341 

9.21  420 
9-21  499 

80 
80 
80 
80 
79 
80 

79 
79 

0.79  138 
0.79058 
0.78978 
0.78  898 
0.78818 
0.78739 
0.78659 
0.78  580 
0.78  501 

9.99440 
9-99  438 
9-99  436 
9-99  434 
9-99432 
9.99429 

9-99427 
9-99425 
9-99  423 

49 

48 
47 
46 
45 
44 
43 
42 
4i 

7 
8 
9 

57-4         56.7         56.0 
65.6         64.8         64.0 
73.8         72.9         72.0 

79           78           77 

20 

9.20999 

77 

9-2I578 

0.78422 

9-99421 

40 

i 

7-9           7-8           7-7 

21 
22 
23 

24 
25 
26 

27 
28 
29 

9.21  076 
9-21153 
9.21  229 
9.21  306 
9.21382 
9.21458 

9-21  534 
9.21  610 
9.21  685 

77 
76 
77 
76 
76 
76 
76 
75 

9-21  657 

9-21  736 

9.21  814 
9-2i  893 
9.21971 
9.22049 
9.22  127 
9.22  205 
9.22  283 

79 

78 
79 

78 
78 
78 
78 
78 

*?8 

0.78343 
0.78  264 
0.78186 
0.78  107 
0.78029 
0.77951 
0.77873 
0.77795 
0.77  717 

9.99419 
9.99417 
9.99415 
9.99413 
9.99411 
9-99  409 
9.99  407 
9-99  404 
9-99  402 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

3 
4 
5 
6 
7 
8 
9 

23.7         23.4         23.1 
31.6         31.2         30.8 
39-5         39-0        38.5 
47.4         46.8         46.2 
55-3         54-6         53-9 
63.2         62.4         61.6 
71.1         70.2         69.3 

30 

9.21  761 

9.22  361 

0.77  639 

9.99  400 

30 

3i 
32 
33 
34 
35 
36 
37 
38 
39 

9.21836 
9.21  912 
9.21987 
9.22  062 

9-22  137 
9.22  211 
9.22  286 
9.22361 
9.22435 

76 
75 
75 
75 
74 
75 
75 
74 

9-22438 
9.22  516 
9.22593 
9.22  670 
9-22747 
9.22824 
9.22  901 
9.22977 
9-23054 

78 

77 
77 
77 
77 
.77 
76 
77 
76 

0.77  562 
0.77484 
0.77  407 
0.77  330 
0.77  253 
0.77  176 
0.77099 
0.77023 
0.76  946 

9-99  398 
9-99  396 
9-99  394 
9.99392 
9-99  390 
9-99  388 
9-99  385 
9.99383 
9.9938i 

29 
28 

27 
26 
25 
24 
23 

22 
21 

I 

2 

3 
4 
5 
6 

76           75           74 

7-6           7-5           7-4 
15.2         15.0         14.8 

22.8             22-5             22.2 
30.4            3O.O             29.6 

38.0        37-5         37-0 
45.6         45.0        44.4 

40 

9-22  509 

9-23  130 

76 

0.76870 

9-99379 

20 

i 

S3-2         52.5         51-8 
60.8         60.0         59.2 

4i 
42 
43 
44 
45 
46 

8 

49 

9-22  583 
9.22657 
9.2273I 
9.22805 
9.22878 
9.22952 
9.23025 
9.23098 
9-23  171 

74 
74 
74 
73 
74 
73 
73 
73 

9.23  206 
9-23  283 
9-23359 
9-23  435 
9-23  5io 
9-23  586 
9.23  661 
9-23737 
9.23812 

77 

7f 
76 

75 
76 
75 
76 
75 

0.76  794 
0.76717 
0.76641 
0.76  565 
0.76  490 
0.76414 
0.76339 
0.76  263 
0.76188 

9-99377 
9-99375 
9.99372 
9.99370 
9-99  368 
9.99366 

9-99  364 
9.99362 
9-99  359 

19 

18 
I? 
1  6 

is 

M 

n 

12 
II 

9 

i 

68.4         67.5         66.6 

73           72           71 

7-3           7-2            7-1 

50 

9.23  244 

9-23  887 

0.76  113 

9-99357 

10 

3 

21.9         21.6         21.3 

51 
52 
53 
54 

11 
% 

59 

9.233I7 
9.23  390 
9-23  462 

9-23  535 
9-23  607 
9.23679 
9-23752 
9-23823 
9-23  895 

73 
72 
73 
72 
72 
73 
7i 
72 

9-23  962 
9.24037 
9.24112 
9.24186 
9.24  261 
9-24335 
9.24410 
9-24484 
9-24  558 

75 
75 
74 
75 
74 
75 
74 
74 

0.76038 
0.75963 
0.75  888 
0.75814 
0-75739 
0.75  665 
0.75  590 
0.75516 
0-75  442 

9-99355 
9-99353 
9-99351 
9-99  348 
9-99  346 
9-99  344 
9-99  342 
9-99  340 
9-99337 

I 

7 
6 
5 
4 
3 

2 

I 

4 
5 
6 
7 
8 
9 

29.2       28.8       28.4 
36.5      36.0      35.5 
43.8       43.2       42.6 
51.1       50.4       49.7 
58.4         57-6         56.8 
65.7         64.8         63.9 

60 

9.23  967 

9-24632 

0.75368 

9-99335 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

t 

P   P 

99° 


(347)      80° 


10° 


169° 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9.23  967 

9-24632 

0.75368 

9-99  335 

60 

I 
1 
3 
4 
5 
6 

7 
8 
9 

9.24039 
9.24110 

9.24  181 

9-24253 
9.24324 
9-24395 
9.24466 
9-24  536 
9.24607 

71 

71 
72 

71 
71 
71 
70 
71 

9.24  706 
9-24779 
9-24853 
9.24926 

9.25  ooo 
9.25073 
9.25  146 
9.25  219 
9.25  292 

73 
74 
73 
74 
73 
73 
73 
73 

0.75  294 

0.75  221 
0.75  147 
0.75074 

0.75  ooo 

0.74927 
0.74854 
0.74781 
0.74708 

9-99333 
9-99331 
9-99328 
9.99326 
9-99  324 
9.99322 

9-99319 
9-99317 
9.99315 

2 

3 

2 
2 

2 

3 

2 
2 

59 
58 
57 
56 
55 
54 
53 
52 
51 

I 

2 

3 

4 

74         73         72 

7-4         7-3         7-2 
14.8       14.6       14.4 

22.2         21.9         21.6 
29.6         29.2         28.8 

10 

9.24677 

9.25365 

0.74635 

9.99313 

50 

i 

44.4       43-8       43-2 

ii 

12 
13 
14 

;i 

17 

18 
19 

9.24748 
9.24818 
9.24888 
9.24958 
9.25028 
9-25  098 
9.25  168 
9-25  237 
9-25307 

70 
70 
70 
70 
70 
70 
69 

70 

6Q 

9.25437 
9.25  510 
9.25  582 
9.25655 
9.25727 

9-25  799 
9.25871 
9-25  943 
9.26015 

73 
72 
73 
72 
72 
72 
72 
72 

0.74563 
0.74  490 
0.74418 

0-74345 
0.74273 
O.74  2OI 
0.74129 
0.74057 
0.73985 

9-99310 
9-99  308 
9-99  306 

9-99  304 
9.99301 
9-99  299 
9-99  297 
9-99  294 
9-99  292 

3 

2 
2 
2 

3 

2 
2 

3 

2 

49 

48 
47 
46 
45 
44 
43 
42 
4i 

7 
8 
9 

51.8       51.1       50.4 
59.2       58.4       57.6 
66.6       65.7       64.8 

71         70         69 

30 

9.25376 

60 

9.26086 

0.739U 

9-99  290 

40 

i 

7.1        7.0        6.9 

21 

22 
23 

24 

!l 

27 
28 
29 

9-25  445 
9.25514 
9-25  583 
9-25652 
9.25721 
9.25  790 
9-25858 
9.25927 
9-25  995 

69 
69 
69 
69 
69 
68 

69 

68 
68 

9.26158 
9.26  229 
9.26301 
9-26372 
9.26443 
9-26514 
9-26585 
9-26655 
9.26  726 

71 
72 
71 
7i 
?i 
71 
70 
7i 

0.73  842 
0.73771 

0.73  699 
0.73628 
0.73  557 
0.73  486 
0.73415 
0-73345 
0.73  274 

9.99  288 
9-99  285 
9-99  283 
9.99  281 
9.99278 
9-99  276 
9-99  274 
9.99271 
9-99  269 

3 

2 
2 

3 
2 
2 

3 

2 

39 

38 
37 
36 
35 
34 
33 
32 
3i 

3 

4 

1 

7 
8 
9 

21.3          21.0          20.7 
28.4          28.O          27.6 

35-5       35-0      34-5 
42.6       42.0      41.4 
49.7       49.0      48.3 
56.8       56.0       55.2 
63.9       63.0      62.1 

30 

9.26063 

68 

9.26  797 

0.73  203 

9-99  267 

30 

3i 

32 
33 
34 

11 

8 

39 

9.26131 
9.26  199 
9.26  267 

9.26335 
9-26  403 
9.26470 
9-26  538 
9.26605 
9.26672 

68 
68 
68 
68 
67 
68 
67 
67 
6? 

9.26867 
9.26937 
9.27008 
9.27078 
9.27  148 
9.27  218 
9.27  288 
9-27357 
9.27427 

70 
7i 
70 
70 
70 
70 

69 
70 
fia 

0.73  133 
0.73  063 
0.72  992 
0.72  922 
0.72852 
0.72  782 
0.72  712 
0.72  643 
0.72573 

9.99  264 
9.99  262 
9.99  260 
9.99257 
9-99  255 
9-99252 
9-99  250 
9-99  248 
9-99  245 

2 
2 
3 
2 

3 

2 

2 

3 

29 

28 
27 
26 
25 
24 

23 

22 
21 

I 

2 

3 

4 

I 

7 

68         67         66 

6.8        6.7        6.6 
13.6       13.4      13-2 
20.4       20.  i       19.8 
27.2       26.8      26.4 
34-0       33-5       33-0 
40.8       40.2       39.6 
47.6       46.9       46.2 

40 

9.26739 

67 

9-27  496 

0.72  504 

9-99  243 

2 

20 

8 

54-4       53-6       52.8 

4i 

42 
43 
44 

9 

3 

49 

9.26806 
9-26873 
9.26940 
9.27007 
9.27073 
9.27  140 
9.27  206 
9-27273 
9-27339 

6? 
67 
67 
66 
67 
66 

67 
66 
66 

9-27  566 
9-27635 
9.27  704 

9-27773 
9.27  842 
9.27911 
9.27  980 
9.28049 
9.28  117 

69 
69 
69 
69 
69 
69 

60 

0.72  434 
0.72365 
0.72  296 
0.72  227 
0.72  158 
0.72089 
0.72020 
0.71951 
0.7.1  883 

9-99  241 
9-99  238 
9-99  236 
9-99  233 
9-99  231 
9-99  229 
9.99  226 
9-99  224 
9.99  221 

2 

3 

2 

3 

2 
2 

3 

2 

3 

19 
18 
i7 
16 
15 
14 
13 

12 
II 

9 

61.2       60.3       59.4 

65           3 

i      6.5        0.3 
2     13.0        0.6 

50 

9-27  405 

9.28  186 

0.71  814 

9-99  219 

2 

10 

4     26.0         1.2 

51 
52 
S3 
54 
55 
56 

Ii 

59 

9.27471 
9-27537 
9.27  602 
9.27  668 
9-27  734 
9.27  799 

9.27  864 
9.27930 
9-27  995 

66 
65 
66 
66 
65 
65 
66 
65 

9-28254 
9-28323 
9-28391 

9-28459 
9-28527 
9-28595 
9.28662 
9-28730 
9.28798 

69 
68 
68 
68 
68 
67 
68 
68 
67 

0.71  746 
0.71  677 
0.71  609 
0.71  541 
0.71  473 
0.71  405 

0.71  338 
0.71  270 
0.71  202 

9-99  217 
9-99  214 
9.99212 

9-99  209 
9-99  207 
9-99  204 
9.99  202 
9.99  200 
9-99  197 

2 

3 

2 

3 

2 

3 

2 

2 

3 

I 

7 
6 
5 
4 
3 

2 

I 

5     32.5         1-5 
6     39.0         1.8 
7     45-5         2.1 
8     52.0         2.4 
9     58.5         2-7 

60 

9.28060 

9.28865 

0.71  135 

9-99  195 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

r 

P  P 

100° 


(348) 


79° 


11 


168C 


T 

i 

2 

3 
4 

I 

7 
8 
9 
10 
ii 

12 
13 

U 
15 

16 

11 

19 
20 

21 

22 
23 
24 
25 
26 

27 
28 
29 

30 

32 
33 
34 
35 
36 

9 

39 
40 

41 
42 
43 

44 

J3 
8 

49 
50 

Si 
52 
S3 
54 
55 
56 

g 

59 
60 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

60 

59 
58 
57 
56 
55 
54 
53 
52 
Si 
50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 

38 
37 
36 
35 
34 
33 
32 

30 

29 

28 
27 
26 

25 
24 
23 

22 
21 

20 

19 
18 
17 
16 
IS 
14 
13 

12 
II 

10 

9 
8 
7 
6 

5 
4 
3 

2 

0 

p  p 

9.28060 

65 

65 
64 
65 
65 
64 
64 
65 
64 
64 

64 
64 
63 
64 
64 

63 
64 
63 
63 
63 
63 

62 

63 
62 
63 
62 
62 
63 
62 
62 
61 
62 
62 
61 
62 
61 
62 
61 
61 
61 
61 
61 
61 
60 
61 
60 
61 
60 
61 
60 
60 
60 
60 

g 

60 
59 
60 

9.28865 

68 

67 
67 
67 
67 
67 
67 
67 

66 
67 
66 

67 
66 
66 
66 
66 
66 
66 
66 
65 
66 

65 
66 

65 
65 
65 
65 
65 
64 
65 
64 
65 
64 
64 
65 
64 
64 
64 
64 
63 
64 
63 
64 
63 
64 
63 
63 

63 
63 
63 
63 
62 

63 
62 
63 
62 
62 
62 

0.71  135 

9-99  195 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 

2 

3 
2 

3 

2 
3 

2 

3 

2 

3 

2 

3 

2 

3 
3 

2 

3 

2 

3 

2 

3 
3 

2 

3 

2 

3 
3 

2 

3 

2 

3 
3 

2 

3 
3 

2 

3 
3 

2 

3 
3 

2 

3 
3 
2 
3 
3 

I 

2 

3 
4 
5 
6 

I 

9 

i 

2 

3 
4 
5 
6 
7 
8 
9 

i 

2 

3 

4 
5 
6 

I 

9 

68         67         66 

6.8         6.7         6.6 
13.6       13.4       13.2 

2O.4          20.1           19.8 
27.2          26.8          26.4 

34-0       33-5       33-0 
40.8       40.2       39.6 
47.6       46.9       46.2 
54.4       53.6       52.8 
61.2       60.3       59-4 

65         64         63 

6.5        6.4        6.3 
13.0       12.8       12.6 
19.5      19.2      18.9 
26.0       25.6       25.2 
32.5      32.0     31.5 
39.0       38.4       37.8 
45.5       44.8       44.1 
52.0       51.2       50.4 
S8.S       57-6       56.7 

62         61         60 

6.2        6.1         6.0 

12.4         12.2          I2.O 

18.6       18.3       18.0 
24.8       24.4       24.0 
31.0      30.5       30.0 
37.2       36.6      36.0 
43.4      42.7      42.0 
49.6      48.8      48.0 
55-8       54.9       54-0 

59           3 

i       5-9        0.3 
2     ii.  8        0.6 
3     17.7         0.9 
4     23.6         1.2 
5     29.5         1.5 
6     35-4         1.8 
7     41.3         2.1 
8     47.2         2.4 
9     53-1         2-7 

9.28  125 
9.28  190 
9-28254 
9.28319 
9-28384 
9.28448 
9.28512 
9.28577 
9.28641 

9-28933 
9.29000 
9.29067 
9.29134 

9.29  2OI 
9.29  268 

9-29335 
9.29402 
9.29468 

0.71067 

0.71  ooo 
0.70  933 
0.70866 
0.70  799 
0.70732 
0.70665 
0.70  598 
0.70532 

9.99192 
9-99  190 
9-99  187 
9-99  185 
9.99  182 
9.99  1  80 
9.99177 
9-99175 
9.99172 

9.28705 

9-29535 

0.70465 

9.99170 

9.28  769 
9-28833 
9.28896' 
9.28  960 
9.29024 
9.29087 
9-29150 
9.29214 
9.29277 

9.29601 
9.29668 
9-29734 
9.2980O 
9.29866 
9.29932 
9.29998 
9.30  064 
9.30130 

0.70399 
0.70332 
0.70  266 
0.70  200 
0.70134 
0.70068 
0.70002 
0.69936 
0.69870 

9-99  167 
9-99  165 
9.99162 
9.99  160 
9-99157 
9-99155 
9.99152 
9-99  ISO 
9-99  147 

9.29340 

9-30  195 

0.69  805 

9-99  145 

9.29403 
9.29466 
9.29529 
9.29591 
9-29654 
9.29716 
9.29779 
9.29841 
9.29903 

9.30261 
9-30326 
9.30391 
9.30457 
9.30522 
9.30587 
9-30652 
9.30717 
9.30782 

0.69739 
0.69  674 
0.69  609 
0.69  543 
0.69478 
0.69413 
0.69348 
0.69  283 
0.69  218 

9-99  142 
9-99  140 
9-99  137 
9-99  135 
9-99  132 
9-99  130 
9.99127 
9.99124 
9.99122 

9.29966 

9-30  846 

0.69154 

9.99119 

9.30028 
9.30090 
9-30151 
9.30213 
9-30275 
9-30336 
9.30398 
9-30459 
9.30521 

9.309II 
9-30975 
9.31  040 
9.31  104 

9-31  168 
9-31  233 
9.31  297 
9-31361 
9.3i  425 

0.69  089 
0.69025 
0.68  960 
0.68  896 
0.68832 
0.68  767 
0.68  703 
0.68  639 
0.68575 

9.99117 
9.99114 

9-99  109 
9.99  106 
9-99  104 
9.99  101 
9-99  099 
9-99  096 

9.30582 

9.31  489 

0.68511 

9-99  093 

9.30  643 
9.30  704 
9-30  765 
9.30826 
9-30887 
9.30947 
9.31008 
9.31  068 
9-31  129 

9-3i  552 
9.31  616 
9.31  679 
9-31  743 
9-31  806 
9-31  870 
9-31  933 
9.31996 
9-32059 

0.68  448 
0.68  384 
0.68321 
0.68  257 
0.68  194 
0.68  130 
0.68  067 
0.68  004 
0.67  941 

9.99091 
9.99  088 
9.99  086 
9.99  083 
9.99  080 
9.99078 

9-99075 
9.99072 
9.99070 

9.31  189 

9.32  122 

0.67878 

9-99  067 

9-31  250 
9.31310 
9.31370 
9-31  430 
9.31  490 

9-31  549 
9-31  609 
9-31  669 
9.31728 

9-32  185 
9-32  248 
9-323II 
9-32373 
9-32  436 
9-32  498 
9-32  561 
9-32  623 
9-32  685 

0.67  815 
0.67  752 
0.67  689 
0.67  627 
0.67  564 
0.67  502 
0.67  439 
0.67377 
0.67315 

9.99  064 
9.99062 
9-99059 
9.99056 
9-99  054 
9.99051 
9.99  048 
9.99  046 
9.99  043 

9-31  788 

9-32  747 

0.67  253 

9.99040 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

' 

P  P 

xor 


(349) 


12° 


167° 


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LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9.31  788 

9-32  747 

A? 

0.67  253 

9.99  040 

60 

I 

2 
3 
4 
5 
6 

I 

9 

9-31  847 
9.31  907 
9-31  966 
9-32025 
9-32084 
9-32  143 

9.32  202 
9.32  26l 
9.32319 

60 

59 
59 
59 
59 
59 

11 

9.32  810 
9-32872 
9-32  933 
9-32995 
9.33057 
9.33H9 
9-33  180 
9-33  242 
9-33  303 

62 
61 
62 
62 
62 
61 
62 
61 
62 

0.67  190 
0.67128 
0.67  067 
0.67  005 

0.66  943 
0.66881 
0.66820 
0.66758 
0.66  697 

9.99038 
9.99035 
9.99032 
9.99030 
9.99027 
9.99024 
9.99022 
9.99019 
9.99016 

3 
3 

2 

3 
3 

2 

3 
3 

59 
58 
57 
56 
55 
54 
53 
52 
51 

6 

i       ( 

2       12 

3      ii 
4     2; 
5     33 

3         62         61 

.3         6.2         6.1 

.6         12.4         12.2 

i-9       18.6       18.3 

.2          24.8          24.4 

•  5       3i.o       30.5 

10 

9-32378 

9-33365 

61 

0.66635 

9-99013 

50 

6     37 

-8       37-2       36.6 

ii 

12 
13 
U 

IS 

16 
17 
18 
19 

9.32437 
9.32495 

9-32  553 
9.32  612 
9-32670 
9-32728 
9-32  786 
9.32  844 
9-32  902 

58 
58 
59 
58 
58 
58 
58 

II 

9-33426 
9-33  487 
9-33  548 
9.33  609 
9-33  670 
9-33  731 
9-33  792 
9-33  853 
9-33  913 

61 
61 
61 
61 
61 
61 
61 
60 

fir 

0.66  574 
0.66513 
0.66452 
0.66391 
0.66  330 
0.66  269 
0.66  208 
0.66  147 
0.66087 

9.99011 
9.99  008 

9-99  005 
9.99  002 
9.99  ooo 
9.98  997 
9.98  994 
9.98  991 
9.98  989 

3 
3 
3 

2 

3 
3 
3 

2 

49 
48 
47 
46 
45 
44 
43 
42 
4i 

8     5c 
9     S< 

.4       49-6       48.8 
•7       55-8       54.9 

60           59 

20 

9-32  960 

-Q 

9-33  974 

fin 

0.66  026 

9.98  986 

3 

40 

6.0           5.9 

21 

22 
23 

24 
25 
26 

27 
28 
29 

9.33018 
9.33075 
9-33  133 
9-33  190 
9-33  248 
9-33  305 
9-33  362 
9-33  420 
9-33  477 

57 
58 
57 
58 
57 
57 
58 
57 

9.34034 
9.34095 
9-34  155 
9.342I5 
9.34276 
9-34336 
9-34  396 
9-34456 
9-345i6 

6l 
60 
60 
6l 
60 
60 
60 
60 
60 

0.65  966 
0.65  905 
0.65  845 
0.65  785 
0.65  724 
0.65  664 
0.65  604 
0.65  544 
0.65  484 

9.98  983 
9.98  980 
9.98978 

9.98975 
9.98972 
9.98  969 
9-98  967 
9.98  964 
9.98961 

3 

2 

3 
3 
3 

2 

3 
3 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

3 
4 
5 
6 
7 
8 
9 

18.0         17.7 
24.0         23.6 
30.0         29.5 
36.0         35.4 
42-0        41.3 
48.0        47.2 
54-0         53.1 

30 

9-33  534 

9-34576 

0.65  424 

9.98  958 

30 

3i 

32 
33 

34 

11 

a 

39 

9-33  591 
9-33  647 
9-33  704 
9-33  76i 
9.338i8 
9-33  874 
9-33931 
9-33  987 
9-34043 

56 

57 
57 

11 

57 
56 
56 

9.34635 
9.34695 
9-34755 
9.34814 
9.34874 
9-34933 
9-34992 
9-35051 
9-35  in 

60 
60 
59 
60 
59 
59 
59 
60 

0.65365 
0.65  305 
0.65  245 
0.65  186 
0.65  126 
0.65  067 
0.65  008 
0.64  949 
0.64  889 

9.98955 
9.98  953 
9.98  950 
9.98  947 
9.98  944 
9.98941 
9.98  938 
9.98  936 
9.98  933 

2 

3 
3 
3 
3 
3 

2 

3 

29 
28 

27 
26 
25 
24 

23 

22 
21 

i 

2 

3 
4 
5 
6 

58           67 

5-8           5-7 
11.  6        11.4 
17.4        17.1 

23.2            22.8 
29.0            28.5 
34-8            34.2 

40 

9-34  ioo 

efi 

9-35  170 

0.64  830 

9.98  930 

30 

8 

46.4         45-6 

4i 

42 
43 

44 
45 
46 

3 

49 

9.34156 
9-34212 
9-34  268 
9-34324 
9-34  380 
9.34436 
9-34491 
9-34  547 
9.34602 

56 
56 
56 
56 
56 
55 
56 
55 
sfi 

9-35  229 
9-35  288 
9-35  347 
9.35405 
9-35  464 
9-35  523 
9.35581 
9-35  640 
9-35  698 

59 
59 
58 
59 
59 
58 
59 
58 

0.64771 
0.64  712 
0.64653 
0.64  595 
0.64  536 
0.64477 
0.64419 
0.64  360 
0.64  302 

9.98927 
9.98924 
9.98921 
9.98919 
9.98916 
9.98913 
9.98910 
9.98  907 
9.98  904 

3 
3 

2 

3 
3 
3 
3 
3 

19 
18 
i7 
16 
IS 
14 
13 

12 
II 

9 

1 

i 

52.2         51-3 

6         55         3 

5-6        5.5      0.3 

50 

9-34  658 

9-35757 

eg 

0.64  243 

9.98  901 

10 

3     K 

i.8       16.5      0.9 

51 
52 
53 
54 
55 
56 

11 

59 

9.34713 
9-34  769 
9.34824 

9.34879 
9-34934 
9-34  989 
9-35  044 
9-35  099 
9-35  154 

56 

55 
55 
55 
55 
55 
55 
55 

9.35815 
9.35873 
9-35931 
9-35  989 
9.36  047 
9-36  105 
9-36163 
9.36221 
9.36279 

58 
58 
58 
58 
58 
58 
58 
58 

0.64  185 
0.64  127 
0.64  069 
0.64011 
0.63  953 
0.63  895 
0.63  837 
0.63  779 
0.63  721 

9-98  898 
9.98  896 
9-98  893 
9.98  890 
9.98887 
9.98  884 
9.98  881 
9.98878 
9-98875 

2 

3 
3 
3 
3 
3 
3 
3 

9 
8 
7 
6 
5 
4 
3 

2 
I 

4     2 
5     2! 
6     3 
7     3< 
8     4' 
.9     5< 

2.4          22.0          1.2 

?.o       27.5       1.5 
5.6       33.0       1.8 

).2          38.5          2.1 

^8       44.0       2.4 
5.4      49.5       2.7 

60 

9.35  209 

9-36336 

0.63  664 

9.98872 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

/ 

P  P 

102° 


(350) 


13C 


166C 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

p  p 

0 

I 

2 

3 
4 
5 
6 
7 
8 
9 
10 
it 

12 
13 
14 

11 

17 

18 
19 
20 

21 
22 
23 
24 
25 
26 
27 
28 
29 

30 

31 
32 
33 

34 
35 
36 

a 

39 
40 

41 
42 
43 
44 
45 
46 
47 
48 
49 
50 

5i 

52 
53 
54 
55 
56 

11 

59 
60 

9-35  209 

54 
55 
55 
54 
54 
55 
54 
54 
54 
54 
54 
54 
54 
54 
54 
53 
54 
53 
54 
53 
53 
53 
54 
53 
53 
53 
52 
53 
53 
53 
52 

53 
52 
52 
53 
52 
52 
52 
52 
52 
52 
52 
52 
52 
Si 
52 
Si 
52 
Si 
52 

51 
5i 
Si 
Si 
5i 
51 
Si 
Si 
51 
51 

9-36336 

58 
58 

57 
57 
58 
57 
57 
57 
57 
57 
57 
57 
57 
57 
56 

3 

57 
56 
57 
56 

56 
56 
56 
56 
56 
56 

56 
56 
55 
56 
56 
55 
55 
56 
55 
55 
56 
55 
55 
55 
55 
55 
54 
55 
55 
54 
55 
55 
54 
54 
55 
54 
54 
54 
54 
54 
54 
54 
54 

cd 

0.63  664 

9.98872 

3 

2 
3 
3 

3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
3 
4 
3 
3 
3 
3 
3 
3 
3 
3 
3 
4 
3 
3 
3 
3 
3 
3 
3 
4 

60 

59 
58 
57 
56 
55 
54 
53 
52 
SI 
50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
3i 
30 

3 

27 
26 
25 
24 
23 

22 
21 

20 

19 
18 
17 
16 
15 
U 
13 

12 
II 

10 

9 

8 
7 
6 
5 
4 
3 

2 
I 

0 

6 
i 

2       I] 
3     ii 
4     2; 
5     2C 
6     31 
7     4C 

8    4e 

9     52 

5 

I       S 
2      II 
3     16 

4       22 

5     27 
6     33 
7     38 
8     44 
9     49 

I 

2 

3 

4 

! 

7 
8 
9 

I 

2 

3 

4 

I 

7 
8 
9 

8         57         56 

'.8        5-7         5-6 
.6      11.4      n.2 
.4       17.1       16.8 

.2          22.8         22.4 

.0       28.5       28.0 
^.8       34-2       33-6 
•6       39-9       39-2 
.4       45.6       44.8 
•2       51-3       50.4 

5         54         53 

•5         5-4         5-3 
.0       10.8       10.6 
.5       16.2       15.9 

.0         21.6         21.2 
.5          27.0         26.5 
.O         32.4         31.8 

•5       37-8       37.1 
.0       43.2       42.4 
.5       48.6       47-7 

52           61 

5-2           5-i 

10.4            10.2 

15.6      15.3 

20.8         20.4 
26.0        25.5 
31.2       30.6 

36.4     35.7 

41.6        40.8 

46.8      45.9 

4              3 

0.4           0.3 
0.8            0.6 

1.2                O-9 
1.6                1.2 
2.O                  I.S 

2.4           1.8 

2.8                2.1 
3-2             2.4 
3.6           2.7 

9-35  263 
9.35318 
9-35373 
9-35427 
9.35481 
9-35  536 
9-35  590 
9-35  644 
9-35  698 

9-36394 
9-36452 
9-36  509 
9-36  566 
9.36624 
9.36681 
9-36  738 

9.36  795 
9-36852 

0.63  606 
0.63  548 
0.63  491 

0-63  434 
0.63  376 
0.63319 
0.63  262 
0.63  205 
0.63  148 

9.98  869 
9.98  867 
9.98  864 
9.98861 
9-98858 
9-98855 
9-98852 
9.98  849 
9.98  846 

9-35752 

9.36  909 

0.63  091 

9.98  843 

9-35  806 
9-35  860 
9-35914 
9-35  968 
9.36022 
9-36075 
9-36  129 
9-36182 
9-36  236 

9.36  966 
9-37023 
9.37080 
9-37  137 
9-37  193 
9-37  250 
9-37  306 
9-37  363 
9.37419 

0.63  034 
0.62977 
0.62  920 
0.62863 
0.62  807 
0.62  750 
0.62  694 
0.62  637 
0.62  581 

9.98  840 
9.98837 
9.98  834 
9-98831 
9.98828 
9-98  825 
9.98822 
9.98  819 

9.98  816 

9-36  289 

9.37476 

0.62  524 

9-98813 

9.36342 
9.36395 
9.36  449 
9.36  502 
9.36S5S 
9.36  608 
9.36  660 
9-367I3 
9-36766 

9-37  532 
9-37  588 
9-37  644 
9.37  700 
9.37756 
9.37812 
9.37868 
9.37924 
9-37  98o 

0.62  468 
0.62  412 
0.62  356 
0.62  300 
0.62  244 
0.62  188 
0.62  132 
0.62  076 
0.62  020 

9.98810 
9.98  807 
9.98  804 
9.98  801 
9.98  798 
9.98  795 
9.98  792 
9.98  789 
9.98  786 

9-36819 

9-38035 

0.61  965 

9.98  783 

9-36871 
9-36924 
9-36976 
9-37028 
9-37  081 
9-37  133 
9-37  185 
9-37  237 
9-37  289 

9-38091 
9.38  147 

9.38  202 
9.38  257 
9.38313 
9.38368 

9.38423 
9.38479 

9.38  534 

0.61  909 
0.61  853 
0.61  798 
0.61  743 
0.61  687 
0.61  632 
0.61  577 
0.61  521 
0.61  466 

9-98  780 
9.98777 
9.98774 
9.98771 
9.98  768 
9.98  765 
9.98  762 
9.98  759 
9.98  756 

9-37341 

9.38  589 

0.61  411 

9.98  753 

9-37  393 
9-37  445 
9-37497 
9-37  549 
9.37  600 
9.37652 
9-37  703 
9-37  755 
9-37  806 

9.38  644 
9.38  699 
9.38  754 
9.38  808 
9.38  863 
9-38918 
9.38972 
9.39027 
9.39082 

0.61356 
0.61  301 
0.61  246 
0.61  192 
0.61  137 
0.61  082 
0.61  028 
0.60  973 
0.60918 

9.98  750 
9.98  746 
9-98  743 
9-98  740 
9.98  737 
9.98  734 
9.9873I 
9.98728 
9.98725 

9-37858 

9-39  136 

0.60  864 

9.98722 

9-37  909 
9-37  96o 
9.38011 
9.38062 
9-38113 
9-38  164 
9-38215 
9.38  266 
9-38317 

9-39  190 
9-39  245 
9-39  299 
9-39353 
9-39  407 
9-39  461 
9.39515 
9-39  569 
9.39623 

0.60  810 
0.60755 
0.60  701 
0.60  647 
0.60  593 
0.60  539 
0.60  485 
0.60431 
0.60377 

9.98719 
9.98715 
9.98712 
9.98  709 
9.98  706 
9.98  703 
9.98  700 
9-98  697 
9.98  694 

9.38368 

9.39677 

0.60323 

9.98  690 

LCos 

d 

LCot 

LTan 

LSin 

d 

/ 

P  P 

103C 


(351) 


76° 


14C 


166C 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9-38  368 

9-39677 

0.60323 

9.98  690 

(JO 

I 

2 

3 

4 
5 
6 

7 
8 
9 

9-38418 
9.38  469 
9-38  519 
9-38  570 
9.38620 
9-38  670 
9-38721 
9-38771 
9.38821 

51 

5° 
Si 
50 
So 
Si 
So 
So 

9-39731 

9-39  785 
9-39838 
9-39  892 
9-39  945 
9-39  999 
9-40052 
9.40  106 
9.40  159 

54 
53 
54 
53 
54 
S3 
54 
53 

0.60  269 
0.60  215 
0.60  162 

0.60  108 
0.60055 
0.60001 
0.59  948 
0-59  894 
0.59841 

9.98  687 
9.98  684 
9.98  681 
9.98678 
9.98675 
9.98671 
9.98  668 
9-98  665 
9.98  662 

3  - 
3 
3 
3 
4 
3 
3 
3 

59 

58 
57 
56 
55 
54 
53 
52 
5i 

I 

2 

3 

4 
5 

64    63 

5-4    5-3 
10.8    10.6 
16.2    15.9 

21.6     21.2 

27.0    26.5 

10 

9.38871 

9.40  212 

0.59  788 

9-98659 

50 

6 

32.4   31.8 

ii 

12 
13 

U 

15 

16 

11 

19 

9-38921 
9.38971 
9-39021 
9.39071 
9-39121 
9.39  170 

9-39  220 
9-39  270 
9.393I9 

50 
50 
So 
So 
49 
50 
50 
49 

9.40  266 
9.40319 
9.40372 
9.40425 
9.40  478 
9-40  531 
9.40  584 
9.40  636 
9.40  689 

53 
53 
53 
53 
53 
53 
52 
53 

0.59  734 
0.59  681 
0.59  628 

0-59575 
0.59522 
0.59  469 
0.59416 
0.59364 
0-593II 

9.98656 
9-98652 
9.98  649 
9.98  646 
9.98  643 
9.98  640 
9.98  636 
9.98  633 
9.98  630 

4 
3 
3 
3 
3 
4 
3 
3 

49 

48 
47 
46 
45 
44 
43 
42 
41 

9 
K 

37-8    37.1 
43-2    42.4 
48.6    47.7 

I    51    60 

20 

9.39369 

9.40  742 

0-59  258 

9.98627 

40 

i   5 

.2    5-1    5-0 

21 
22 
23 
24 
25 
26 
27 
28 
29 

9.39418 
9-39467 
9.39517 
9-39  566 
9-396I5 
9-39  664 
9-39713 
9-39762 
9.39811 

49 
50 
49 
49 
49 
49 
49 
49 

9-40  795 
9.40  847 
9.40  900 
9.40952 
9-4i  005 
9-4i  057 
9.41  109 
9.41  161 
9.41  214 

52 
53 
52 
53 
52 
52 
52 
53 

0.59  205 
0-59  153 
0.59  loo 
0.59  048 
0.58995 
0.58  943 
0.58891 
0.58839 
0.58  786 

9-98  623 
9.98  620 
9.98617 
9.98614 
9.98610 
9.98  607 
9.98  604 
9.98  601 
9.98  597 

3 
3 
3 
4 
3 
3 
3 
4 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

3  15 
4  20 
5  26 
6  31 
7  36 
8  41 
9  46 

.6   15.3   15.0 
8   20.4   20.0 
o   25.5   25.0 

2    30.6    30.0 

4   35-7   35-0 
6   40.8   40.0 
8   45.9   45.0 

30 

9.39  860 

9.41  266 

0.58734 

9-98  594 

30 

3i 
32 

33 
34 
35 
36 
37 
38 
39 

9-39  909 
9.39958 
9.40  006 
9.40055 
9-40  103 
9-40152 
9.40  200 
9.40  249 
9.40  297 

49 
48 
49 
48 
49 
48 

49 
48 

9-41  3i8 
9.41  370 
9.41  422 
9.41  474 
9-41  526 
9-41  578 
9.41  629 
9.41  681 
9-41  733 

52 

52 
52 
52 
52 
Si 
52 
52 

0.58682 
0.58  630 
0.58578 
0.58  526 
0.58474 
0.58  422 

0.58371 
0.58319 
0.58  267 

9.98  591 
9.98  588 
9.98  584 
9-98581 
9.98  578 
9.98  574 
9.98571 
9.98  568 
9.98  565 

3 

4 
3 
3 
4 
3 
3 
3 

29 

28 
27 
26 
25 
24 

23 

22 
21 

i 

I   4 
2   9 
3  14 
4  19 
5  24 
6  29 

>    48    47 

9    4-8    4-7 
8    9.6    9.4 
7   14-4   I4-I 
6   19.2   18.8 
5   24.0   23.5 
4   28.8   28.2 

40 

9.40  346 

AQ 

9.41  784 

0.58  216 

9.98  561 

20 

8  39 

2   38.4   37.6 

4i 
42 
43 
44 
45 
46 
47 
48 
49 

9.40  394 
9.40  442 
9-40  490 
9-40  538 
9.40  586 
9.40  634 
9.40  682 
9.40  730 
9.40778 

48 
48 
48 
48 
48 
48 
48 
48 

9-41  836 
9.41  887 
9-41  939 
9.41  990 
9.42  041 
9.42  093 
9.42  144 
9-42  195 
9.42  246 

Si 
52 
51 
Si 
52 
51 
Si 
Si 

0.58  164 
0.58  113 
0.58061 
0.58010 
0.57959 
0.57  907 
0.57856 
0.57  805 
0.57754 

9.98  558 
9-98  555 
9.98551 
9.98  548 
9.98  545 
9.98  541 
9.98  538 
9-98  535 
9.98  531 

3 
4 
3 
3 
4 
3 
3 
4 

19 
18 
17 
16 
15 
U 
13 

12 
II 

9  44 

i 

I   43.2   42.3 

4      3 

0.4    0.3 

50 

9-40825 

j.8 

9-42  297 

0-57  703 

9.98  528 

10 

3 

1.2       0-9 

Si 
52 
53 
54 
55 
56 

11 

59 

9.40  873 
9.40921 
9.40  968 
9.41  016 
9-4i  063 
9.41  "I 
9-41  158 
9.41  205 
9-41  252 

48 

s 
» 

47 

47 

47 
Ac 

9-42  348 
9-42  399 
9.42  450 

9-42  501 
9-42  552 
9-42  603 
9-42  653 
9.42  704 
9-42  755 

51 
Si 
51 
Si 
Si 
50 
Si 
51 

0.57  652 
0.57  601 
0.57  550 
0-57  499 
0.57  448 
0.57  397 
0-57  347 
0.57  296 
0.57  245 

9-98525 
9-98  521 
9-98518 

9.98515 
9.98511 
9.98  508 
9.98  505 
9-98  501 
9.98  498 

4 
3 
3 
4 
3 
3 
4 
3 

9 

8 
7 
6 
5 
4 
3 

2 

I 

4 

1 
I 

9 

1.6       1.2 
2.0       1.5 

2.4     1.8 

2.8       2.1 
3-2       2.4 

3-6    2.7 

60 

9-41  3oo 

9.42  805 

0.57  195 

9.98  494 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

t 

P  P 

104C 


(352) 


76° 


15C 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

p  p 

0 

I 

2 

3 
4 
5 
6 

7 
8 
9 
10 

ii 

12 
13 

14 
15 

16 

17 
18 
i9 
20 

21 
22 
23 
24 
25 
26 
27 
28 
29 

30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

41 
42 
43 
44 
45 
46 

47 
48 
49 
50 

Si 
52 
53 

54 

11 

57 
58 
59 
60 

9-41  300 

47 
47 
47 
47 
47 
47 
46 
47 
47 
46 

47 
46 
47 
46 

47 
46 
46 
47 
46 
46 

46 

46 
46 
46 
45 
46 
46 
46 

S 

45 
46 
45 
46 
45 

8 

45 
45 
45 
45 
45 
45 
45 
44 
45 
45 
45 
44 
45 
44 
45 
44 
45 
44 
44 
44 
45 
44 
44 

9.42  805 

Si 

SO 
Si 
50 
So 
Si 
50 
So 
So 
SO 
50 
So 
50 
50 
So 
49 
50 
50 
49 
SO 

49 
So 
49 
So 
49 
49 
49 
So 
49 
49 
49 
49 
49 
49 
49 
48 
49 
49 
48 
49 
49 
48 
49 
48 
48 
49 
48 
48 
48 
49 
48 
48 
48 
48 
48 
48 
47 
48 
48 
48 

o-57  195 

9.98  494 

3 
3 
4 
3 
4 
3 
3 
4 
3 
4 
3 
4 
3 
3 
4 
3 
4 
3 
4 
3 
4 
3 
4 
3 
3 
4 
3 
4 
3 
4 
3 
4 
3 
4 
4 
3 
4 
3 
4 
3 
4 
3 
4 
3 
4 
4 
3 
4 
3 
4 
3 
4 
4 
3 
4 
3 
4 
4 
3 
4 

60 

59 
58 
57 
56 
55 
54 
53 
52 
5i 
50 

49 
48 
47 
46 
45 
44 
43 
42 
4i 
40 

39 
38 
37 
36 
35 
34 
33 
32 
3> 
30 

29 

28 
27 
26 
25 
24 
23 

22 
21 

20 

19 
18 
17 
16 
i5 
14 
13 

12 
II 

10 

I 

7 
6 
5 
4 
3 

2 

I 

0 

6 

i       S 

2       IO 

3     IS 
4     20 
5     25 
6    30 
7     35 
8    40 
9     45 

4) 

I       4 

2         9 

3     14 
4     19 
S     24 
6     28 
7     33 
8     38 
9     43 

I 

2 

3 
4 

7 
8 
9 

I 

2 

3 

4 

I 

7 
8 
9 

L         60         49 

.1         5-0         4-9 

.2          10.0            9.8 

-3       15-0       14-7 
4       20.0       19.6 
5       25.0       24.5 
6       30.0       29.4 
7       35-0       34-3 
.8       40.0       39.2 
.9       45.0       44.1 

}         47         46 

8        4.7        4.6 
6        9.4        9-2 
4       14.1       13.8 
2       18.8       18.4 
o       23.5       23.0 
8       28.2       27.6 
6      32.9      32.2 
4       37.6       36.8 
2       42.3       41-4 

46           44 

4-S            4-4 
9.0           8.8 
13-5         13-2 
18.0         17.6 

22.5            22.O 
27.0            26.4 
31-5            30.8 

36.0         35-2 
40.5        39-6 

4             3 

0.4           0.3 
0.8           0.6 
1.2           0.9 

1.6                 1.2 
2.0                I.S 

2.4            1.8 

2.8                 2.1 

3-2             2.4 
3-6            2.7 

9-41  347 
9-41  394 
9.41  441 
9.41  488 
9-41  535 
9-41  582 
9.41  628 
9-41  675 
9.41  722 

9.42  856 
9.42  906 

9-42  957 
9-43  007 
9.43057 
9-43  108 
9-43  158 
9-43  208 
9-43  258 

0.57  144 
0.57  094 
o-57  043 
0.56993 
0.56  943 
0.56892 
0.56842 
0.56792 
0.56  742 

9.98  491 
9.98  488 
9.98  484 
9.98  481 
9.98477 
9.98474 
9.98471 
9.98  467 
9.98  464 

9.41  768 

9-43  308 

0.56692 

9.98  460 

9.41815 
9.41  861 
9.41  908 

9-41  954 
9.42001. 
9.42  047 
9.42  093 
9.42  140 
9.42  186 

9-43  358 
9.43  408 
9-43  458 
9-43  5o8 
9-43  558 
9-43  607 
9-43  657 
9-43  707 
9-43  756 

0.56642 
0.56592 
0.56542 
0.56492 
0.56442 
0.56393 
0.56343 
0.56  293 
0.56  244 

9.98457 
9.98  453 
9.98  450 
9.98  447 
9.98  443 
9.98  440 
9.98  436 
9.98  433 
9.98429 

9.42  232 

9-43  806 

0.56  194 

9.98426 

9.42  278 
9-42324 
9.42370 
9.42  416 
9.42461 
9.42  507 
9-42  553 
9-42  599 
9.42  644 

9-43  855 
9-43  90S 
9-43  954 
9.44  004 
9-44  053 
9.44  102 

9-44I5I 
9.44  201 
9-44  250 

0.56  145 
0.56095 
0.56  046 
0-55  996 
0.55947 
0.55  898 
0.55  849 
0.55  799 
0-55  750 

9.98422 
9.98419 
9.98415 
9.98412 
9.98  409 
9.98  405 
9.98  402 
9.98  398 
9.98395 

9.42  690 

9-44  299 

0.55  70i 

9-98  391 

9-42  735 
9.42  781 
9.42  826 
9.42  872 
9.42917 
9.42  962 
9.43  008 
9-43  053 
9-43  098 

9-44  348 
9-44  397 
9.44  446 

9-44  495 
9.44  544 
9-44592 
9-44  641 
9.44  690 
9-44  738 

0-55  652 
0.55  603 
0-55554 
0.55  505 
o.SS  456 
0.55  408 
0-55359 
o.553io 
0.55  262 

9-98388 
9.98  384 
9-98381 
9-98377 
9.98373 
9.98370 
9.98  366 
9.98  363 
9-98359 

9-43  143 

9-44  787 

0.55213 

9.98356 

9-43  1  88 
9-43  233 
9-43  278 
9-43  323 
9-43  367 
9.43412 
9-43  457 
9-43  502 
9-43  546 

9.44836 
9.44  884 
9-44  933 
9.44  981 
9.45029 
9-45  078 
9-45  126 
9-45  174 
9-45  222 

0.55  164 
0.55  116 
0.55  067 
0.55019 
o.5497i 
0.54922 
0.54874 
0.54826 
0.54778 

9.98352 
9.98  349 
9.98  345 
9.98  342 
9-98338 
9-98334 
9.98331 
9-98327 
9-98324 

9-43  59i 

9-45  271 

0.54729 

9.98  320 

9-43  635 
9-43  680 
9-43  724 
9-43  769 
9-43  813 
9-43  857 
9-43  9oi 
9-43  946 
9-43  990 

9-45319 
9-45  367 
9.45415 
9-45  463 
9-455" 
9-45  559 
9-45  606 
9-45  654 
9-45  702 

0.54681 
0.54633 
0-54  585 
0-54537 
0.54  489 
0.54  441 
0-54394 
0.54346 
0.54  298 

9.98317 
9-98313 
9.98  309 

9-98  306 
9.98302 
9.98  299 
9.98  295 
9.98  291 
9.98  288 

9.44  034 

9-45  750 

0.54250 

9.98  284 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

t 

P  P 

105C 


(353) 


16C 


163C 


' 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

944034 

9-45  750 

0.54  205 

9.98  284 

60 

I 

2 

3 
4 

I 

9 

9-44  o?8 
9.44122 
9.44166 
9.44210 
9-44  253 
9-44  297 
9-44341 
9.44385 
9.44428 

44 
44 
44 
43 
44 
44 
44 
43 

9-45  797 
9-45  845 
9-45  892 
9.45  940 
9-45  987 
9-46035 
9.46  082 
9-46  130 
9-46  177 

48 

47 
48 

47 
48 
47 
48 
47 

0.54  203 
0.54155 
0.54  108 
0.54060 
0-54013 
0-53  965 
0.53  9i8 
0.53  870 
0.53  823 

9.98  281 
9.98  277 
9-98  273 
9.98  270 
9.98  266 
9.98  262 
9.98  259 
9-98  255 
9-98  251 

3 
4 
4 
3 

4 
4 
3 
4 
4 

59 
•58 
57 
56 
55 
54 
5,3 
52 
5i 

4 

i   i 

2    C 

3  14 
4  IS 

5  24 

18    47    46 

l.B    4-7    4-6 
.6    9.4    9.2 
•4   14-1   13-8 
.2   18.8   18.4 
.0   23.5   23.0 

10 

9-44472 

9.46  224 

0-53  776 

9.98  248 

3 

50 

6   2? 

.8   28.2   27.6 

ii 

12 
13 
14 
15 

16 

11 

19 

9.44516 
9-44559 
9.44  602 
9-44  646 
9-44  689 
9-44  733 
9.44  776 
9.448i9 
9-44  862- 

43 

43 
44 
43 
44 
43 
43 
43 

9.46  271 
9.46319 
9-46  366 
9.46  413 
9.46  460 
9.46  507 
9.46  554 
9.46  601 
9.46  648 

48 
47 
47 
47 
47 
47 
47 
47 

0.53  729 
0.53  68  1 
0-53  634 
0-53  587 
0-53  540 
0.53  493 
0-53  446 
0-53  399 
0-53352 

9.98  244 
9.98  240 
9.98  237 
9-98  233 
9.98  229 
9.98  226 

9.98  222 

9.98  218 

9-98215 

4 
3 
4 
4 
3 
4 
4 
3 

49 

48 
47 
46 
45 
44 
43 
42 
4i 

i!  Si 

9  43 
4 

.6   32.9   32.2 
•4   37-6   36.8 
.2   42.3   41.4 

5    44    43 

20 

9-44  905 

9.46  694 

0.53  3o6 

9.982II 

40 

i   4 

-5    4-4    4-3 

21 
22 
23 
24 

3 

27 
28 
29 

9-44  948 
9-44  992 
9-45  035 
9.45077 
9-45  120 
9-45  163 
9-45  206 
9-45  249 
9-45  292 

44 
43 
42 
43 
43 
43 
43 
43 

9.46  741 
9.46  788 
9-46  835 
9.46  881 
9.46928 
9-46975 
9.47021 
9.47  068 
9.47114 

47 
47 
46 
47 
47 
46 
47 
46 

Aft 

0.53  259 

0.53  212 
0.53  165 

0-53  "9 
0.53072 
0.53025 
0.52  979 
0.52932 
0.52886 

9.98  207 

9.98  204 
9.98  200 
9.98  196 
9.98  192 
9.98  l89 
9.98  185 

9.98  181 
9-98  177 

3 
4 
4 
4 
3 
4 
4 
4 

39 

38 
37 
36 
35 
34 
33 
32 
31 

2   £ 
3  13 
4  18 
5  22 
6  27 
7  3i 
8  36 
9  40 

.5   13.2   12.9 
.0   17.6   17.2 

.5    22.0    21.5 

.0   26.4   25.8 

•  5    30.8    30.1 

.0   35.2   34.4 
-5   39-6   38.7 

30 

9-45  334 

9.47  160 

0.52  840 

9.98174 

3 

30 

3i 

32 
33 

34 
35 
36 

s 

39 

9-45377 
9-45  419 
9.45  462 

9-45  504 
9-45  547 
9-45  589 
9-45  632 
9-45  674 
9-45  7i6 

42 

43 
42 
43 
42 
43 
42 
42 

9-47  207 
9-47  253 
9-47  299 
9-47  346 
9-47  392 
9-47  438 
9-47  484 
9-47  530 
9-47  576 

46 
46 

47 
46 
46 
46 
46 

$ 

0.52  793 
0.52  747 
0.52  701 
0.52654 
0.52608 
0.52  562 
0.52  516 
0.52  470 
0.52424 

9.98  170 
9.98  166 
9.98  162 
9-98  159 
9.98155 
9.98151 
9.98  147 
9.98  144 
9.98  140 

4 
4 
3 

4 

4 
4 
3 

4 

29 

28 
27 
26 
25 
24 

23 

22 
21 

i 

2 

3 

4 
5 
6 

42     41 

4.2    4.1 
8.4    8.2 
12.6    12.3 
16.8    16.4 

2I.O     2O-5 
25.2      24.6 

40 

9-45  758 

9.47  622 

.f. 

0.52378 

9.98  136 

4 

20 

7 
g 

29.4     28.7 

3^6    ^28 

41 
42 
43 
44 

if 

47 
48 
49 

9-45  801 
9-45  843 
9-45  885 
9-45927 
9-45  969 
9.46011 
9-46053 
9.46  095 
9-46  136 

42 
42 
42 
42 
42 
42 
42 
41 

9-47  668 
9-47  714 
9-47  76o 
9-47  806 
9-47852 
9-47  897 
9-47  943 
9-47  989 
9-48035 

46 
46 
46 
46 
45 
46 
46 
46 

0.52332 
0.52  286 
0.52  240 
0.52  194 
0.52  148 
0.52103, 
0.52057 
0.52  on 
0.51  965 

9-98  132 
9.98  129 
9.98125 

9.98  121 
9.98  117 
9.98II3 
9.98IIO 

9.98  106 

9.98  102 

3 
4 
4 
4 
4 
3 
4 
4 

19 
18 
17 
16 
15 
14 
13 

12 

II 

9 
i 

37-8    36-9 

4      3 

0.4     0.3 

50 

9.46  178 

9.48  080 

0.51  920 

9.98  098 

10 

51 

52 
53 
54 

56 

11 
59 

9.46  220 
9.46  262 
9.46  303 

9.46  345 
9-46  386 
9.46428 
9.46  469 
9-46511 
9-46  552 

42 
41 
42 
41 
42 
41 
42 
41 

9.48  126 
9.48171 
9.48217 
9.48  262 
9.48  307 
9.48353 
9.48  398 
9-48  443 
9.48  489 

8 

45 

s 

45 

8 

0.51  874 
0.51  829 
0.51  783 
0-51  738 
0.51  693 
0.51  647 
0.51  602 
0.51557 
0.51  5ii 

9.98  094 

9.98  090 

9.98  087 
9.98  083 
9.98079 
9.98075 
9.98071 
9.98067 
9.98  063 

4 
3 
4 

4 
4 
4 
4 
4 

9 

8 
7 
6 
5 
4 
3 

2 

I 

4 
5 
6 
7 
8 
9 

1.6       1.2 
2.0       1.5 

2.4     1.8 

2.8       2.1 

3-2      2.4 
3-6     2.7 

60 

9.46  594 

9-48  534 

0.51  466 

9.98  060 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

' 

P  P 

106C 


(354) 


73° 


17C 


162° 


1 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9-46  594 

9.48  534 

0.51466 

9.98  060 

60 

I 

2 

3 

4 

7 
8 
9 

9-46635 
9.46676 
9.46717 
9.46  758 
9.46  800 
9.46  841 
9.46  882 
9.46  923 
9.46  964 

41 
41 
41 
42 
41 
41 
41 
41 

9.48  579 
9.48  624 
9.48  669 
9.48714 
9-48  759 
9.48  804 
9.48  849 
9.48  894 
9.48  939 

45 
45 
45 
45 
45 
45 
45 
45 

0.51421 
0.51  376 
0.51331 
0.51  286 
0.51  241 
0.51  196 
0.51151 

0.51  106 
0.51  061 

9.98056 
9.98052 
9.98  048 
9.98  044 
9.98  040 
9.98  036 
9-98032 
9.98029 
9-98025 

4 
4 
4 
4 
4 
4 
3 
4 

59 

58 
57 
56 
55 
54 
53 
52 
5i 

45         44         43 

10 

9.47  005 

9-48  984 

0.51  016 

9.98021 

50 

2 

9.0         8.8         8.6 

it 

12 
13 
14 
15 

16 

17 
18 
19 

9-47  045 
9.47  086 
9-47  127 
9.47  168 
9-47  209 
9.47  249 
9-47  290 
9-47  330 
9-47371 

41 
41 
41 
41 
40 
41 
40 
41 

9-49  029 
9-49  073 
9.49118 
9-49  163 
9-49  207 
9.49252 
9-49  296 
9-49341 
9-49385 

44 
45 
45 
44 
45 
44 
45 
44 

0.50971 
0.50927 
0.50  882 
0.50837 
0.50793 
0.50  748 
0.50  704 
0.50659 
0.50615 

9.98017 
9.98013 
9.98  009 
9-98005 

9.98  ooi 
9-97  997 
9-97  993 
9-97  989 
9-97  986 

4 
4 
4 
4 
4 
4 
4 
3 

49 
48 
47 
46 
45 
44 
43 
42 
4i 

3 
4 

1 

7 
8 
9 

13.5       13-2       12.9 
18.0       17.6       17.2 

22.5          22.O         21-5 
27.0         26.4         25.8 
31.5         30.8         30.1 
36.0         35.2         34-4 

40-5       39-6       38.7 

20 

9.47411 

9.49  430 

0.50570 

9-97  982 

40 

21 

22 
23 
24 
25 
26 

27 
28 
29 

9-47  452 
9-47  492 
9-47  533 
9-47  573 
9-476i3 
9-47  654 
9-47  694 
9-47  734 
9-47  774 

40 
41 
40 
40 
41 
40 
40 
40 

9.49  474 
9-495I9 
9-49  563 
9-49  607 
9-49652 
9-49  696 
9.49  740 
9-49  784 
9.49828 

45 
44 
44 
45 
44 
44 
44 
44 

0.50526 
0.50481 
0.50437 
0.50393 
0.50348 
0.50304 
0.50  260 
0.50  216 
0.50  172 

9-97  978 
9-97  974 
9.97970 
9.97  966 
9-97  962 
9-97  958 
9-97  954 
9-97950 
9-97  946 

4 
4 
4 
4 
4 
4 
4 
4 

39 
38 
37 
36 
35 
34 
33 
32 
31 

I 

2 

3 

4 

42         41         40 

4.2        4.1        4.0 
8.4         8.2         8.0 

12.6         12.3          I2.O 

16.8       16.4       16.0 

30 

9-47  814 

9.49872 

0.50  128 

9-97  942 

30 

5 

2I.O          20-5           20.0 

31 

32 
33 
34 

31 
8 

39 

9-47  854 
9-47  894 
9-47  934 
9-47  974 
9.48014 
9-48054 
9.48  094 
9-48  133 
9-48  173 

40 
40 
40 
40 
40 
40 

39 

40 

9.49916 
9-49  96o 
9.50004 
9.50048 
9-50092 
9.50  136 
9.50  180 
9-50223 
9.50267 

44 
44 
44 
44 
44 
44 
43 
44 

0.50084 
0.50040 
0.49  996 
0.49952 
0.49  908 
0.49  864 
0.49  820 
0-49  777 
0-49  733 

9-97  938 
9-97  934 
9-97  930 
9.97926 
9.97922 
9.97918 
9-97  914 
9-97  9io 
9.97  906 

4 
4 
4 
4 
4 
4 
4 
4 

29 
28 
27 
26 
25 
24 

23 

22 
21 

6 
7 
8 
9 

25.2       24.6       24.0 
29.4       28.7       28.0 
33-6       32-8       32.0 
37-8       36.9       36.0 

40 

9-48213 

9-503II 

0.49  689 

9-97  902 

20 

41 

42 
43 
44 
45 
46 
47 
48 
49 

9-48  252 
9.48  292 
9-48332 
9-48371 
9.48411 
9.48  450 
9.48  490 
9.48  529 
9-48  568 

40 
40 
39 
40 
39 
40 

39 
39 

9-50355 
9.50398 
9.50  442 
9-50485 
9-50529 
9-50572 
9.50616 
9-50659 
9-50  703 

44 
43 
44 
43 
44 
43 
44 
43 
44 

0.49  645 
0.49  602 
0-49  558 
0.49515 
0.49471 
0.49  428 
0.49  384 
0-49  341 
0-49  297 

9-97  898 
9-97  894 
9-97  890 
9.97  886 
9-97  882 
9-97  878 
9-97  874 
9-97  870 
9-97  866 

4 
4 
4 
4 
4 
4 
4 
4 
4 

19 

18 
i7 
16 
15 
14 
13 

I  2 
II 

i 

2 

3 
4 
5 
6 
7 

39         5         4        3 

3.9      0.5      0.4      0.3 
7.8      i.o      0.8      0.6 
11.7      1.5      1.2      0.9 

15.6         2.0        1.6         1.2 
19.5         2.5         2.0        1.5 

23.4      3.0      2.4      1.8 

27.3        3.5         2.8         2.1 

50 

9.48  607 

9.50  746 

43 

0-49  254 

9-97  861 

5 

10 

8 

31.2     4.0     3.2     2.4 

Si 

52 
53 
54 

II 

57 
58 
59 

9.48  647 
9.48  686 
9.48725 
9.48  764 
9-48  803 
9.48  842 
9.48  881 
9.48920 
9-48  959 

39 
39 
39 
39 
39 
39 
39 
39 

9-50789 
9-50833 
9.50876 
9.50919 
9.50962 
9-51005 
9-51  048 
9-5i  092 
9.5H35 

43 
44 
43 
43 
43 
43 
43 
44 
43 

0.49  211 

0.49  167 
0.49124 
0.49081 
0.49  038 
0.48  995 
0.48952 
0.48  908 
0.48  865 

9-97  857 
9-97  853 
9-97  849 
9-97  845 
9-97  841 
9-97  837 
9-97  833 
9-97  829 
9-97  825 

4 
4 
4 
4 
4 
4 
4 
4 
4 

9 
8 
7 
6 
5 

4 
3 

2 
I 

60 

9-48  998 

9-Si  178 

0.48822 

9.97821 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

f 

P  P 

107C 


(355) 


18C 


1 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

o 

9-48  998 

9-51178 

0.48822 

9.97821 

60 

I 

2 

3 

4 

I 

7 
8 
9 

9-49  037 
9-49  076 
9-49II5 
9-49  153 
9-49  192 
9-49  231 
9-49  269 
9.49  308 
9-49  347 

39 
39 
38 
39 
39 
38 
39 

*8 

9-51221 
9-51  264 
9.51  306 

9-51  349 
9-51  392 
9-Si  435 
9-51  478 
9-Si  520 
9-Si  563 

43 
42 
43 
43 
43 
43 
42 
43 

0.48  779 
0.48  736 
0.48  694 
0.48  651 
0.48  608 
0.48  565 
0.48  522 
0.48  480 
0.48  437 

9.97817 
9.97812 
9.97  808 

9-97  804 
9.97  800 
9-97  796 
9-97  792 
9-97  788 
9.97  784 

5 
4 
4 
4 
4 
4 
4 
4 

59 
5? 

57 
56 
55 
54 
53 
52 
5i 

43    42    41 

10 

9-49  385 

9.51  606 

0.48  394 

9-97  779 

50 

2 

8.6    8.4    8.2 

ii 

12 
13 
14 

15 

16 

17 
18 
19 

9.49  424 
9-49  462 
9.49  500 

9-49  539 
9-49  577 
9.49615 

9-49  654 
9.49  692 
9-49  730 

38 
38 
39 
38 
38 
39 
38 

s 

9-51  648 
9.51691 
9-51  734 
9.51  776 
9.51819 
9.51  861 
9-51  903 
9.51  946 
9-51  988 

43 
43 
42 

43 
42 
42 
43 
42 

0.48352 
0.48  309 
0.48  266 
0.48  224 
0.48  181 
0.48  139 
0.48  097 
0.48  054 

0.48  OI2 

9-97  775 
9-97  77i 
9.97  767 

9-97  763 
9-97  759 
9-97  754 
9-97  750 
9-97  746 
9.97  742 

4 
4 
4 
4 
5 
4 
4 
4 

49 

48 
47 
46 
45 
44 
43 
42 
4i 

3 

4 

I 
i 

9 

12.9   12.6   12.3 
17.2   16.8   16.4 
21.5   21.0   20.5 
25.8   25.2   24.6 
30.1   29.4   28.7 
34.4   33.6   32.8 
38.7   37-8   36.9 

30 

9.49  768 

30 

-0 

9-52031 

43 

0.47  969 

9-97  738 

40 

21 
22 
23 

24 
25 
26 

27 
28 
29 

9.49  806 
9-49  844 
9.49  882 
9-49  920 
9-49  958 
9.49  996 
9-50034 
9.50072 
9.50  no 

38 
38 
38 
38 
38 
38 
38 

35 

9-52073 
9.52II5 
9.52157 
9.52  200 
9-52  242 
9.52  284 
9-52326 
9-52368 
9.52410 

42 
42 
43 
42 
42 
42 
42 
42 

0.47  927 
0.47  885 
0.47  843 
0.47  800 
0.47  758 
0.47  716 
0.47  674 
0.47  632 
0.47  590 

9-97  734 
9-97  729 
9.97725 
9-97  721 
9-97  717 
9-97  713 
9-97  7o8 
9-97  704 
9.97  700 

5 
4 
4 
4 
4 
5 
4 
4 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

i 

2 

3 

39    38    37 

3-9    3-8    3-7 
7-8    7-6    7-4 
ii.  7   11.4   n.  i 

30 

9.50  148 

9.52452 

0.47  548 

9-97  696 

30 

4 

15.6   15.2   14.8 

3i 
32 
33 

34 

II 

37 
38 
39 

9-50  185 
9-50223 
9.50261 
9-50  298 
9.50336 
9.50374 
9.50411 
9.50449 
9.50486 

38 
38 

37 
38 
38 
37 
38 
37 

9-52  494 
9-52  536 
9.52578 
9.52  620 
9.52  661 
9-52  703 
9-52  745 
9.52  787 
9-52829 

42 
42 
42 
41 
42 
42 
42 
42 

0.47  506 
0.47  464 
0.47  422 
0.47  380 
0-47  339 
0.47  297 
0.47  255 
0.47  213 
0.47  171 

9.97  691 
9-97  687 
9.97  683 
9.97  679 
9-97  674 
9-97  670 
9.97  666 
9.97  662 
9.97657 

4 
4 
4 
5 
4 
4 
4 
5 

29 

28 
27 
26 
25 
24 

23 

22 
21 

5 
6 

I 

9 

19-5   19-0   18.5 

23.4    22.8    22.2 
27.3    26.6    25.9 
31.2    30.4    29.6 

35-1   34.2   33-3 

40 

9-50523 

37 

9-52870 

41 

0.47  130 

9-97  653 

20 

4i 

42 
43 
44 
45 
46 

47 
48 
49 

9-50  561 
9-50  598 
9-50  635 
9-50673 
9.50710 
9-50  747 
9.50  784 
9.50821 
9-50858 

3° 
37 
37 
38 
37 
37 
37 
37 
3 

9-52912 
9-52953 
9-52  995 
9-53037 
9-53078 
9-53120 
9-53  161 
9-53  202 
9-53  244 

42 

41 
42 
42 
41 
42 
41 
41 
42 

0.47  088 
o.47  047 
0.47  005 
0.46  963 
0.46922 
0.46  880 
0.46  839 
0.46  798 
0.46  756 

9-97  649 
9-97  645 
9.97  640 
9-97  636 
9.97  632 
9.97  628 
9-97  623 
9.97  619 
9.976i5 

4 
5 

4 
4 
4 
5 
4 
4 

19 
18 
i7 
16 
IS 
14 
13 

12 
II 

i 

2 

3 

4 
5 

36     5     4 

3.6   0.5    0.4 
7.2    i.o    0.8 
10.8    1.5    1.2 
14.4    2.0    1.6 
18.0    2.5    2.0 

50 

9.50896 

9-53  285 

0.46715 

9.97  610 

10 

6 

21.6    3.0    2.4 

Si 
52 
53 
54 
55 
56 

3 

59 

9.50933 
9.50970 
9-51007 
9-51  043 
9.51  080 
9-Si  "7 
9-51  154 
9-51  191 
9.51  227 

37 

% 

37 

37 
37 

11 

9.53327 
9.53368 
9-53  409 
9-53  450 
9-53  492 
9-53  533 
9-53  574 
9.53615 
9-53656 

41 
4i 
41 
42 
41 
41 
41 
41 

0.46  673 
0.46632 
0.46  591 
0.46  550 
0.46  508 
0.46  467 
0.46  426 
0.46385 
0.46  344 

9.97  606 
9.97  602 
9-97  597 
9-97  593 
9-97  589 
9-97  584 
9.97  58o 
9-97  576 
9-97571 

4 
5 
4 
4 
5 
4 
4 
5 

1 

7 
6 

5 
4 
3 
2 

I 

28.8    4.0   3.2 

32.4   4.5   3.6 

60 

9.51  264 

37 

9-53  697 

0.46  303 

9-97  567 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

t 

P  P 

108° 


(356) 


71° 


19° 


160° 


' 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9.51  264 

9.53  697 

0.46  303 

9-97  567 

60 

I 

2 

3 

4 

J 

7 
8 
9 

9-Si  30i 
9.51338 
9-51374 
9-514" 
9-51447 
9.51  484 
9-51520 
9.51557 
9-Si  593 

37 
36 
37 
36 

11 

37 

9-53  738 
"9-53779 
9-53820 
9.53861 
9-53  902 
9-53  943 
9.53984 
9.54025 
9-54065 

41 
41 
41 
41 
41 
41 
41 
40 

0.46  262 

0.46  221 

0.46  180 

0.46  139 
0.46  098 
0.46057 
0.46016 

o-45  975 
0.45  935 

9-97  563 
9-97  558 
9-97  554 
9-97  550 
9-97  545 
9-97  54i 
9-97  536 
9-97  532 
9-97  528 

5 
4 
4 
5 
4 
5 
4 
4 

59 
58 
57 
56 
55 
54 
5,5 
52 
SI 

I 

41         40         39 

10 

9.51  629 

36 

9.54106 

0.45  894 

9-97  523 

50 

2 

8.2        8.0        7.8 

ii 

12 
13 
14 

15 

16 

;; 

19 

9.51  666 
9-Si  702 
9-51  738 
9-Si  774 
9.51  811 
9-51847 
9-51883 
9.5I9I9 
9-51955 

37 
36 
36 
36 
37 
36 
36 
36 

3,6 

9-54  147 
9.54187 
9-54228 
9-54  269 
9-54309 
9-54350 
9-54390 
9-54  431 
9-54471 

40 
41 
41 
40 
41 
40 

41 
4o 

0.45  853 
0.45813 
0-45  772 
0-45  731 
0.45  691 
0.45  650 
0.45  610 
0.45  569 
0.45  529 

9-97519 
9-97  515 
9-97  5io 
9-97  506 
9-97  501 
9-97497 
9-97  492 
9-97  488 
9-97  484 

4 
5 
4 
5 

4 
5 
4 
4 

49 
48 
47 
46 
45 
44 
43 
42 
4i 

3 

4 

I 

7 
8 
9 

12.3          I2.O          II.7 

16.4       16.0       15.6 

20-5          20.0         19.5 

24.6     24.0     23.4 

28.7       28.0      27.3 
32.8     32.0     31.2 
36.9     36.0     35.1 

20 

9-51  99i 

30 

9-54512 

41 

0.45  488 

9-97  479 

40 

21 
22 
23 

24 
25 
26 
27 
28 
29 

9-52027 
9-52063 
9-52099 
9.52135 
9.52171 
9-52  207 
9-52  242 
9.52  278 
9-52314 

30 
36 
36 
36 
36 
36 
35 
36 

36 

9-54552 
9-54  593 
9.54633 
9-54673 
9.547I4 
9-54754 
9-54  794 
9.54835 
9.54875 

40 

41 
40 
40 

4i 
40 
40 
4i 
40 

0.45  448 
0-45  407 
0-45  367 
0.45327 
0.45  286 
0.45  246 
0.45  206 
0-45  165 
0.45  125 

9-97  475 
9-97470 
9.97  466 
9.9746i 
9-97457 
9-97  453 
9-97  448 
9-97  444 
9-97  439 

5 
4 
5 
4 
4 
5 
4 
5 

39 
38 

37 
36 
35 
34 
33 
32 
3i 

I 

2 

3 

37         36         35 

3-7         3-6         3-5 
7.4         7.2         7.0 
ii.  i       10.8       10.5 

30 

9.52350 

9.549IS 

0.45  085 

9-97  435 

30 

4 

14.8       14.4       14.0 

31 
32 
33 
34 
35 
36 

a 

39 

9-52385 
9-52421 
9.52456 
9-52492 
9-52527 
9-52  563 
9-52  598 
9-52634 
9-52  669 

35 
36 
35 
36 
35 
36 
35 
36 
35 

9-54955 
9-54995 
9-55035 
9-55075 
9.55H5 
9.55155 
9-55  195 
9-55235 
9-55275 

4O 

40 
40 
40 
40 
40 
40 
40 
40 

0-45  045 
0.45  005 
0.44965 
0.44925 
0.44  885 
0.44  845 
0.44  805 
0.44  765 
0.44725 

9-97  430 
9-97  426 
9-97421 
9.97417 
9-97412 
9.97  408 

9-97  403 
9-97  399 
9-97  394 

5 

4 
5 
4 
5 
4 
5 
4 
5 

29 

28 
27 
26 

25 
24 

23 

22 
21 

6 

8 

9 

22.2          21.6          2I.O 

25.9    25.2     24.5 

29.6      28.8      28.0 
33.3     32.4     31-5 

40 

9-52  705 

9-55315 

0.44  685 

9-97  390 

20 

41 

42 
43 
44 

45 
46 

47 
48 
49 

9-52  740 
9-52775 
9.52811 

9-52  846 
9.52881 
9-52916 
9-5295I 
9-52  986 
9.53021 

35 
36 
35 
35 
35 
35 
35 
35 

9-55355 
9-55395 
9-55  434 
9-55474 
9.55514 
9-55554 
9-55  593 
9.55633 
9-55673 

40 
39 
40 
40 
40 
39 
40 
40 

0-44  645 
0.44  605 
0.44  566 
0.44526 
0.44  486 
0.44  446 
0.44  407 
0.44367 
0.44327 

9-97  385 
9-97  381 
9.97376 
9-97372 
9-97367 
9-97  363 
9-97  358 
9-97  353 
9-97  349 

4 
5 
4 
5 
4 
5 
5 
4 

19 
18 
17 
16 
15 
14 
13 

12 
II 

i 

2 
3 

4 

1 

34           5           4 

3.4        0.5        0.4 
6.8        i.o        0.8 

10.2             1.5             1.2 

13.6         2.0         1.6 

17.0             2.5             2.O 

20.4        3.0        2.4 

50 

9-53  056 

35 

,A 

9-55  712 

39 

0.44  288 

9-97  344 

5 

10 

7 

23.8         3.5         2.8 

51 
52 
53 
54 
55 
56 

a 

59 

9-53  092 
9-53  126 
9-53  161 
9-53  196 
9-53  231 
9-53  266 
9-53  301 
9-53  336 
9-53370 

34 
35 
35 
35 
35 
35 
35 
34 

9-55752 
9-55791 
9-55831 
9-55870 
9-55910 
9-55  949 
9-55  989 
9.56028 
9-56067 

39 
40 
39 
40 
39 
40 

39 
39 

0.44  248 
0.44  209 
0.44  169 

0.44  130 
0.44  090 
0.44051 
0.44011 
0.43972 
0.43  933 

9-97  340 
9-97  335 
9-97331 
9.97326 
9-97322 
9.973I7 
9.97312 
9-97  308 
9-97  303 

5 
4 
5 
4 
5 
5 
4 
5 

I 

7 
6 

5 

4 

3 

2 
I 

8 
9 

27.2      4.0      3.2 
30.6       4.5       3.6 

60 

9-53  405 

9-56  107 

0-43  893 

9-97  299 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

/ 

P  P 

109C 


(357) 


70° 


20° 


159° 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9-53  405 

9.56  107 

0.43  893 

9-97  299 

60 

I 

2 

3 
4 
S 
6 

7 
8 
9 

9.53  440 
9-53475 
9-53  509 
9-53  544 
9-53578 
9-536I3 
9-53  647 
9-53  682 
9.53716 

35 
34 
35 
34 
35 
34 
35 
34 

9.56  146 
9-56  185 
9-56  224 
9.56264 
9.56303 
9-56342 
9-56381 
9-56420 
9-56459 

39 

39 
40 

39 
39 
39 
39 
39 

0.43  854 
0.43815 
0.43  776 
0.43  736 
0.43  697 
0.43  658 
0.43  619 
0.43  580 
0.43  541 

9.97  294 
9-97  289 
9.97  285 
9.97  280 
9-97  276 
9-97  271 
9.97  266 
9.97  262 
9-97  257 

5 
5 
4 
5 
4 
5 
5 
4 
5 

59 

1? 

56 
55 
54 
53 
52 
Si 

40         39         38 

10 

9-53  751 

9.56498 

0.43  502 

9-97  252 

50 

2 

8.0         7.8         7.6 

ii 

12 
13 
14 
15 

16 

17 
18 
19 

9-53  785 
9.53819 
9-53  854 
9-53  888 
9-53922 
9-53957 
9-53  99i 
9-54025 
9-54059 

34 
35 
34 
34 
35 
34 
34 
34 

9.56537 
9-56576 
9.56615 
9.56654 
9.56693 
9.56732 
9.56771 
9.56810 
9-56  849 

39 
39 
39 
39 
39 
39 
39 
39 

0.43  463 
0.43  424 
0.43  385 
0.43  346 
0.43  307 
0.43  268 

0.43  229 
0.43  190 
0.43  151 

9-97  248 
9-97  243 
9-97  238 
9-97  234 
9-97  229 
9-97  224 
9-97  220 
9-97  215 
9.97  210 

5 
5 
4 
5 
5 
4 
5 
5 

49 

48 
47 
46 
45 
44 
43 
42 
41 

3 
4 

J 

7 
8 
9 

12.0         II.?          II.4 

16.0       15.6       15.2 

20.0         19.5          19.0 
24.0          23.4          22.8 
28.0          27.3          26.6 
32.0         31.2          30.4 
36.0         35.1          34.2 

20 

9-54093 

9-56887 

0.43  "3 

9.97  206 

40 

21 
22 
23 

24 
25 
26 

27 
28 
29 

9-54127 
9-54  161 
9-54  195 
9-54229 
9-54  263 
9.54297 
9-54331 
9-54365 
9-54399 

34 
34 
34 
34 
34 
34 
34 
34 
34 

9.56926 
9-56965 
9.57004 
9.57  042 
9.57081 

9-57  120 
9-57  158 
9.57197 
9-57  235 

39 
39 
39 
38 
39 
39 
38 
39 
38 

0.43  074 

0-43  035 
0.42  996 
0.42  958 
0.42919 
0.42  880 
0.42  842 
0.42  803 
0.42  765 

9.97  201 
9-97  196 
9.97  192 

9-97  187 
9.97  182 
9-97  178 
9-97  173 
9.97  168 
9-97  163 

5 
4 
5 
5 
4 
5 
5 
5 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

z 

2 
3 

37         35         34 

3-7         3-5         3-4 
7.4         7-0         6.8 

II.  I          IO.5          10.2 

30 

9-54  433 

33 

9.57274 

,Q 

0.42  726 

9-97  159 

30 

4 

14.8         14.0         13.6 

3i 

32 
33 
34 

$ 

11 

39 

9-54  466 
9-54  500 
9-54  534 
9-54  567 
9-54601 
9.54635 
9.54668 
9-54  702 
9-54735 

34 
34 
33 
34 
34 
33 
34 
33 
34 

9-57312 
9-57351 
9.57389 
9.57428 
9.57466 
9-57  504 
9-57  543 
9-57  58i 
9.57619 

39 

38 
39 
38 
38 
39 
38 
38 

0.42  688 
0.42  649 
0.42  611 
0.42572 
0.42  534 
0.42  496 
0.42  457 
0.42419 
0.42  381 

9-97  154 
9-97  149 
9-97  US 
9-97  140 
9-97  135 
9-97  130 
9-97  126 
9.97  121 
9.97  116 

5 
4 
5 
5 
5 
4 
5 
5 

29 

28 
27 
26 
25 
24 
23 

22 
21 

6 
7 
8 
9 

22.2         2I.O         20.4 
25.9         24.5          23.8 
29.6         28.O         27.2 

33-3       31-5       30.6 

40 

9-54  769 

33 

9-57  658 

39 

-0 

0.42  342 

9-97  in 

5 

20 

41 

42 
43 
44 
45 
46 
47 
48 
49 

9-54802 
9-54836 
9.54869 
9-54903 
9^4936 
9.54969 
9-55  003 
9.55036 
9-55  069 

34 
33 
34 
33 
33 
34 
33 
33 
33 

9-57  696 
9-57  734 
9-57772 
9.57810 
9-57  849 
9.57887 
9.57925 
9-57  963 
9.58001 

3° 
38 
38 
38 
39 
38 
38 
38 

388 

0.42  304 
0.42  266 
0.42  228 
0.42  190 
0.42  151 
0.42  113 
0.42075 
0.42  037 
0.41  999 

9.97  107 
9.97  102 
9-97  097 
9-97  092 
9-97  087 
9-97  083 
9-97  078 
9-97  073 
9.97  068 

5 
5 
5 
5 
4 
5 
5 
5 

19 
18 
i7 
16 
15 
14 
13 

12 
II 

i 

2 

3 

4 

33           5           4 

3.3        0.5        0.4 
6.6         i.o        0.8 
9-9         i.S         1-2 
13.2         2.0         1.6 

16.5             2.5             2.0 
19.8             3.0             2.4 

50 

9-55  102 

34 

9-58039 

_0 

0.41  961 

9-97  063 

10 

7 

23-1         3-5         2.8 

5i 

52 
53 
54 
55 
56 

11 

59 

9-55  136 
9-55  169 
9-55  202 
9-55  235 
9-55  268 
9-55  301 
9-55334 
9-55367 
9.55  400 

33 
33 
33 
33 
33 
33 
33 
33 
33 

9.58077 
9-58115 
9.58  153 
9.58  191 
9.58  229 
9-58267 
9.58304 
9-58342 
9.58  380 

3° 

| 

38 
38 
38 
37 

I 

0.41  923 
0.41  885 
0.41  847 
0.41  809 
0.41  771 
0.41  733 
0.41  696 
0.41  658 
0.41  620 

9-97  059 
9-97  054 
9.97  049 
9-97  044 
9-97  039 
9-97  035 
9-97  030 
9-97025 
9.97  020 

5 
5 
5 
5 
4 
5 
5 
5 

9 
8 
7 
6 
5 
4 
3 

2 

I 

8 
9 

26.4        4.0         3-2 
29-7         4-5         3-6 

60 

9-55433 

9-58418 

0.41  582 

9.97015 

• 

L  Cos 

d 

LCot 

cd 

LTan 

L  Sin 

d 

/ 

P  P 

110° 


(358) 


69° 


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LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9-55  433 

9-58418 

0.41  582 

9.97015 

60 

I 

2 

3 

4 

7 
8 
9 

9-55  466 
9-55  499 
9-55  532 
9-55  564 
9-55  597 
9-55  630 
9-55  663 
9-55  695 
9.55728 

33 
33 
33 
32 
33 
33 
33 
32 
33 

9.58  455 
9-58493 
9-5853I 
9-58569 
9.58606 
9.58  644 
9.58681 
9.587I9 
9.58757 

38 
38 
38 

37 
38 
37 
38 
38 

0.41  545 
0.41  507 
0.41  469 
0.41431 
0.41  394 
0.41  356 
0.41  319 
0.41  281 
0.41  243 

9.97  oio 
9-97  005 
9.97  ooi 
9.96  996 
9.96  991 
9.96  986 
9.96  981 
9-96976 
9.96971 

5 
4 
5 
5 
5 
5 
5 
5 

59 
58 
57 
56 
55 
54 
53 
52 
5i 

38         37         36 

10 

9.5576i 

9-58  794 

,Q 

0.41  206 

9.96  966 

50 

I 

3-8         3-7         3-6 

ii 

12 
13 

14 
15 

16 

II 

iQ 

9-55  793 
9-55826 
9.55858 
9-55  891 
9-55  923 
9.55956 
9-55  988 
9.56021 
9-56053 

33 
32 
33 
32 
33 
32 
33 
32 

9-58832 
9.58  869 
9-58907 
9-58  944 
9-58981 
9.59019 
9.59056 
9-59094 
9-59I3I 

8 

37 

11 

37 
38 

37 

0.41  168 
0.41  131 
0.41  093 
0.41  056 
0.41  019 
0.40981 
0.40  944 
0.40  906 
0.40  869 

9.96  962 
9.96957 
9.96952 

9.96  947 
9.96  942 
9.96937 
9.96932 
9.96927 
9.96922 

5 
5 
5 
5 
5 
5 
5 
5 

49 
48 
47 
46 

45 
44 
43 
42 
4i 

3 

4 

I 

7 
8 
9 

11.4       n.  i       10.8 

15.2       14.8       14.4 
19.0       18.5       18.0 

22.8          22.2          21.6 
26.6          25.9          25.2 
30.4          29.6          28.8 

34-2       33-3       32.4 

20 

9.56085 

9.59168 

0.40832 

9.96917 

40 

21 
22 
23 
24 
25 
26 
27 
28 
29 

9.56118 
9-56  150 
9.56  182 
9-56215 
9.56  247 
9.56279 
9-56311 
9.56343 
9.56375 

32 
32 
33 
32 
32 
32 
32 
32 

9-59  205 
9-59  243 
9-59  280 
9.59317 
9-59354 
9-59391 
9.59429 
9.59466 
9-59  503 

38 
37 
37 
37 
37 
38 
37 
37 

0.40  795 
0.40757 
0.40720 
0.40  683 
0.40  646 
0.40  609 
0.40  571 
0.40  534 
0.40  497 

9.96912 
9.96  907 
9.96  903 
9.96  898 
9.96  893 
9.96  888 
9.96  883 
9.96878 
9-96873 

5 
4 
5 
5 
5 
5 
5 
5 

39 
38 
37 
36 
35 
34 
33 
32 
31 

i 

2 

3 

33         32         31 

3-3         3-2         3-1 
6.6         6.4         6.2 
9.9         9.6         9.3 

30 

9.56  408 

9-59  540 

0.40  460 

9.96  868 

30 

4 

13.2       12.8       12.4 

3i 

32 
33 
34 
35 
36 
37 
38 
39 

9.56  440 
9.56472 
9.56  504 
9.56536 
9.56568 
9.56  599 
9-56631 
9.56  663 
9-56695 

32 
32 
32 
32 
31 
32 
32 
32 

9-59577 
9.59614 
9-59651 
9-59688 
9-59725 
9.59762 

9-59  799 
9.59835 
9.59872 

37 
37 
37 
37 
37 
37 
36 
37 

0.40  423 
0.40  386 
0.40  349 
0.40312 
0.40  275 
0.40  238 

O.4O  201 

0.40  165 
0.40  128 

9.96  863 
9.96  858 
9-96853 
9.96  848 
9.96  843 
9-96  838 
9.96  833 
9.96828 
9-96823 

5 
5 
5 
5 
5 
5 
5 
5 

3 

27 
26 
25 
24 
23 

22 
21 

f 

7 
8 
9 

16.5       16.0       15.5 
19.8       19.2       18.6 
23.1       22.4       21.7 
26.4       25.6       24.8 
29.7       28.8       27.9 

40 

9-56727 

9-59  909 

0.40  091 

9.96818 

20 

4i 

42 
43 
44 
45 
46 

47 
48 
49 

9.56759 
9.56  790 
9.56822 
9-56854 
9.56  886 
9.56917 
9.56  949 
9.56  980 
9.57012 

31 

32 
32 
32 
31 
32 
31 
32 

9-59  946 
9-59  983 
9.60019 
9.60056 
9-6o  093 
9.60  130 
9.60  1  66 
9.60  203 
9.60  240 

37 
36 
37 
37 

11 

37 
3;6 

0.40054 
0.40017 

0.39981 

0-39  944 
0.39  907 
0.39870 

0.39834 
0.39  797 
0.39  760 

9-96813 
9.96  808 
9-96  803 
9.96  798 
9.96  793 
9.96  788 
9.96  783 
9.96  778 
9-96772 

5 
5 
5 
5 
5 
5 
5 
6 

19 
18 
17 
16 
15 
14 
13 

12 
II 

i 

2 

3 
4 

5 

654 

0.6        0.5        0.4 

1.2             1.0             O.8 

1.8         1.5         1.2 
2.4         2.0        1.6 

3.O            2.5             2.O 

50 

9-57044 

9.60  276 

0.39724 

9.96  767 

10 

7 

3.6        3.0        2.4 
42         35          28 

5i 
52 
53 
54 
55 
56 

11 

59 

9.57075 
9-57  107 
9-57  138 
9-57  169 
9-57  201 
9-57  232 
9-57  264 
9-57  295 
9-57326 

32 
31 
31 
32 
31 
32 
31 
31 

9-60313 
9.60  349 
9.60  386 
9.60  422 
9.60  459 
9.60  495 
9-6o  532 
9.60  568 
9.60  605 

36 

9 

37 
36 
37 
36 

f6 

0.39  687 
0.39651 
0.39614 
0.39578 
0-39  541 
0.39  505 
0.39  468 
0-39432 
0-39395 

9.96  762 
9.96757 
9.96752 
9.96  747 
9.96  742 
9.96  737 
9-96  732 
9.96727 
9-96722 

5 
5 
5 
5 
5 
5 
5 
5 

9 

8 
7 
6 
5 
4 
3 

2 

I 

8 
9 

4.8       4.0       3.2 
5-4         4'5         3-6 

60 

9.57358 

9.60  641 

0-39359 

9.96717 

0 

LCos 

d 

LCot 

cd 

LTan 

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d 

/ 

P  P 

nr 


(359) 


68C 


157 


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d 

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cd 

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9.57358 

9.60  641 

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0.39359 

9.96717 

6 

60 

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2 

3 

4 

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7 
8 
9 

9-57389 
9.57420 
9-57451 
9.57482 

9-57  514 
9-57545 
9.57576 
9-57  607 
9-57  638 

31 
31 
31 
32 
31 
31 
31 
31 

9.60677 
9.60714 
9-60  750 
9.60  786 
9.60823 
9-60859 
9-60  895 
9-60931 
9.60  967 

37 
36 
36 
37 
36 
36 
36 
36 

0.39323 
0.39  286 
0.39  250 
0.39214 
0.39177 
0.39  141 
0.39  105 
0.39  069 
0.39033 

9.96711 
9.96  706 
9.96  701 
9.96  696 
9.96  691 

9.96  686 
9.96681 
9.96676 
9.96  670 

5 
5 
5 
5 
5 
5 

59 
58 
57 
56 
55 
54 
53 
52 
SI 

I 

37         36         35 

3-7         3-6         3  5 

10 

9-57  669 

9.61  004 

ifi 

0.38  996 

9.96665 

5 

50 

2 

7-4             7-2             7-0 

ii 

12 
13 

U 
15 

16 
17 
18 
19 

9-57  7oo 
9-57731 
9-57  762 
9-57  793 
9-57824 
9.57855 
9-57  885 
9.57916 
9-57  947 

31 
31 
31 
31 
31 
30 
31 
31 

9.61  040 
9.61  076 

9.6l  112 
9.6l  148 
9.6l  184 
9.6l  22O 
9.6l  256 
9.6l  292 
9.61328 

36 
36 
36 
36 
36 
36 
36 
36 
?6 

0.38  960 
0.38924 

0.38  888 
0.38852 
0.38816 
0.38  780 
0.38  744 
0.38  708 
0.38672 

9.96  660 
9-96655 
9.96650 
9-96645 
9.96  640 
9.96  634 
9.96629 
9.96624 
9.96619 

5 
5 
5 
5 
5 
6 
5 
5 
5 

49 
48 
47 
46 
45 
44 
43 
42 
4i 

3 
4 
5 
6 

I 

9 

ii.  i       10.8       10.5 
14.8      14.4       14.0 
18.5       18.0       17.5 

22.2          21.6          21.0 
25.9          25.2          24.5 
29.6          28.8          28.0 

33-3       32-4       31-5 

20 

9.57978 

9-6l  364 

?6 

0.38636 

9.96614 

g 

40 

21 
22 
23 
24 
25 
26 

27 
28 
29 

9.58008 
9-58039 
9-58070 
9.58  101 
9-58  131 
9.58  162 
9-58  192 
9-58223 
9.58  253 

31 
31 
31 
30 
31 
30 
31 
30 

9.6l  400 
9-6l  436 
9.61472 
9.6l  508 

9.61  544 
9.61  579 
9.6i  615 
9.61  651 
9.61  687 

36 
36 
36 
36 
35 
36 
36 
36 

0.38  600 
0.38  564 
0.38528 
0.38  492 
0.38456 
0.38421 
0.38385 
0.38  349 
0.38313 

9.96  608 
9-96  603 
9.96  598 
9.96  593 
9-96588 
9-96582 
9.96577 
9.96572 
9.96  567 

5 
5 

5 

i 

5 
5 
5 

39 
38 
37 
36 
35 
34 
33 
32 
Si 

i 

2 

3 

32         31         30 

3-2         3-1         3-0 
6.4         6.2         6.0 
9-6        9-3         9-0 

30 

9.58  284 

9.61  722 

,A 

0.38  278 

9-96562 

f. 

30 

4 

3i 
32 
33 
34 
35 
36 

a 

39 

9-58314 
9.58345 
9.58375 
9-58406 
9-58436 
9.58467 
9-58497 
9-58527 
9.58557 

31 

30 
31 
30 
31 
30 

3° 
30 

9.61  758 
9.61  794 
9.61  830 
9.61  865 
9.61  901 
9.61  936 
9.61  972 
9.62008 
9.62  043 

36 

36 

35 
36 
35 
36 
36 
35 

0.38  242 
0.38  206 
0.38  170 

0.38135 
0.38  099 
0.38  064 
0.38028 
0.37  992 
0-37957 

9-96556 
9.96551 
9.96  546 

9.96  54i 
9.96535 
9.96  530 
9-96525 
9-96520 
9.96514 

5 
5 
5 
6 
5 
5 

29 
28 
27 
26 
25 
24 
23 

22 
21 

6 

I 

9 

19.2       18.6       18.0 

22.4          21.7           21.0 

25.6       24.8       24.0 
28.8      27.9       27.0 

40 

9-58588 

9.62  079 

36 

0-37921 

9-96  509 

5 

30 

41 

42 
43 
44 

8 

47 
48 
49 

9.58618 
9.58648 
9.58  678 
9.58  709 
9.58739 
9.58  769 

9.58  799 
9-58829 
9-58859 

3° 
30 
30 
31 
30 
30 
3° 
3° 
30 

9.62  114 
9.62  150 
9.62  185 

9.62  221 
9.62  256 
9.62  292 
9-62327 
9.62  362 
9-62  398 

36 

35 
36 
35 
36 
35 
35 
36 

0.37  886 
0.37  850 
0.37815 
0.37  779 
0-37  744 
0.37  708 
0.37673 
0.37638 
0.37  602 

9.96  504 
9.96  498 
9.96  493 
9.96  488 
9.96  483 
9.96477 
9-96472 
9.96467 
9.96  461 

5 
6 
5 
5 
5 
6 
5 

19 
18 
17 
16 
IS 
14 
13 

12 
TT 

i 

2 

3 
4 
5 
6 

29           6           5 

2.9        0.6        0.5 

5.8             1.2             1.0 

8.7         1.8         1.5 

II.  6            2.4            2.0 

14.5         3.0         2.5 
17.4         3.6         3.0 

50 

9-58889 

30 

9-62  433 

35 

o.37  567 

9.96456 

5 

10 

7 

20.3         4.2         3.5 

51 

52 
53 
54 
55 
56 
57 
58 
59 

9.58919 
9-58949 
9-58979 
9.59009 
9-59  039 
9.59069 

9.59098 
9.59128 
9.59158 

30 
30 
30 
30 
30 
30 
29 
30 
30 

9.62  468 
9-62  504 
9-62  539 
9.62  574 
9.62  609 
9-62  645 
9.62  680 
9-62  715 
9-62  750 

35 
36 
35 
35 
35 
36 
35 
35 
35 

0.37532 
0.37  496 
0.37  461 
0.37  426 
0.37  391 
0-37355 
0.37320 
0.37  285 
0.37  250 

9.96451 
9.96445 
9.96  440 

9.96435 
9-96429 
9-96424 
9.96419 
9.96413 
9.96  408 

6 

5 
5 
6 
5 
5 
6 
5 

9 

8 
7 
6 
5 
4 
3 

2 

I 

8 
9 

23.2         4.8         4.0 
26.1         5-4         4-5 

60 

9-59  188 

9-62  785 

0.37  215 

9.96  403 

0 

LCos 

d 

LCot 

cd 

LTan 

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112C 


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LTan 

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2 

3 

4 

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7 
8 
9 
10 
ii 

12 
13 
14 
15 

16 

3 

19 
20 

21 

22 
23 
24 
25 
26 

3 

29 
30 

31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 
43 
44 
45 
46 

8 

49 
50 

5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 

9-59188 

30 
29 
30 
30 
29 
30 
30 
29 
30 
29 
30 
29 
30 
29 
30 
29 
29 
30 
29 
29 

30 
29 
29 
29 
29 
30 
29 
29 
29 
29 
29 
29 
29 
29 

29 
29 
29 
29 
29 
28 

29 
29 
29 
28 
29 
29 
29 
28 
29 
28 

29 

29 
28 
29 
28 
29 
28 

ll 

28 

9-62  785 

35 
35 
35 
36 
35 
35 
35 
35 
35 
34 
35 
35 
35 
35 
35 
35 
34 
35 
35 
35 
35 
34 
35 
35 
34 
35 
34 
35 
35 
34 
35 
34 
35 
34 
35 
34 
35 
34 
34 
35 
34 
34 
35 
34 
34 
35 
34 
34 
34 
34 
35 
34 
34 
34 
34 
34 
34 
34 
34 
34 

cd 

0.37  215 

9-96  403 

6 

5 
5 
6 

I 

5 

1 

5 
6 
5 

I 

5 
6 
5 
6 

5 

5 
6 

I 

5 
6 
5 
6 

I 

5 
6 
5 
6 

I 

5 

6 

5 
6 
6 

5 
6 
5 
6 

I 

6 

5 
6 
5 
6 
6 
5 
6 
5 
6 

60 

59 
58 
57 
56 
55 
54 
53 
52 
5i 
50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
3i 
30 

29 

28 
27 
26 
25 
24 
23 

22 
21 

20 

19 
18 
17 
16 
15 
14 
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12 
II 

10 

1 

7 
6 
5 
4 
3 

2 

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0 

36         35         34 

i       3-6         3-5         3-4 
2       7.2         7.0        6.8 
3     10.8       10.5       10.2 
4     14.4       14.0       13.6 
5     18.0       17.5       17.0 
6     21.6       21.0      20.4 
7     25.2       24.5       23.8 
8     28.8      28.0      27.2 
9     32.4      31-5       30.6 

30         29         28 

i       3.0        2.9        2.8 

2          6.0            5.8            5.6 

3       9-0         8.7         8.4 

4       12.0         II.6         II.  2 

5     15.0      14.5       14.0 
6     18.0      17.4      16.8 
7     2  i.o      20.3       19.6 
8     24.0       23.2       22.4 
9     27.0      26.1       25.2 

6           5 

i     0.6        0.5 

2       1.2            I.O 

3     1.8        1.5 
4     2.4         2.0 
5     3-0         2.5 
6     3.6        3.0 
7     4-2         3-5 
8     4.8        4.0 
9     5-4        4-5 

9.59218 
9.59247 
9-59277 
9-59307 
9.59336 
9-59366 
9-59396 
9-59425 

9-59455 

9.62  820 
9-62855 
9.62  890 
9.62926 
9.62  961 
9.62  996 

9-63  031 
9.63  066 

9.63  ioi 

0.37  180 
o.37  145 
0.37  no 
0.37074 
0.37  039 
0.37  004 
0.36  969 

0.36  934 
0.36  899 

9-96397 
9-96392 
9.96  387 
9.96381 
9-96376 
9-96370 
9-96  365 
9-96  360 
9.96354 

9-59  484 

9.63  135 

0.36  865 

9.96  349 

9-5*)  514 
9-59  543 
9-59573 
9.59602 
9-59632 
9.59661 
9-59  690 
9-59  720 
9-59  749 

9.63  170 
9.63  205 
9.63  240 
9.63  275 
9-63310 

9-63  345 
9-63  379 
9-63  414 
9.63  449 

0.36830 
0.36  795 
0.36  760 
0.36725 
0.36  690 
0.36655 
0.36621 
0.36  586 
0.36551 

9.96  343 
9.96338 
9-96  333 
9-96327 
9-96322 
9-96316 
9.963" 
9.96  305 
9.96  300 

9.59778 

9.63  484 

0.36  516 

9.96  294 

9.598o8 
9.59837 
9-59  866 
9.59895 
9.59924 
9-59954 
9.59983 
9.60012 
9.60  041 

9.63  519 
9-63  553 
9-63  588 
9-63  623 
9-63  657 
9-63  692 
9-63  726 
9-63  761 
9.63  796 

0.36  481 
0.36  447 
0.36412 
0.36377 
0.36343 
0.36  308 
0.36  274 
0.36  239 
0.36  204 

9.96  289 
9.96  284 
9.96  278 
9.96  273 
9.96  267 
9.96262 
9-96256 
9.96  251 
9.96  245 

9.60070 

9.63  830 

0.36170 

9.96  240 

9.60  099 
9.60  128 
9-60157 
9.60  186 
9.60215 
9.60  244 
9-6o  273 
9.60302 
9-60331 

9-63  865 
9-63  899 
9-63  934 
9-63  968 
9-64  003 
9-64037 
9.64072 
9.64  106 
9.64  140 

0.36  135 
0.36  ioi 
0.36  066 
0.36032 
0-35  997 
0-35  963 
0.35928 
0-35  894 
0.35  860 

9.96  234 
9.96229 
9-96223 
9.96218 

9.96  212 
9.96  207 
9.96  2OI 
9.96  196 
9.96  190 

9-60359 

9-64  175 

0-35825 

9.96  185 

9.60  388 
9.60417 
9.60  446 
9.60474 
9-6o  503 
9-60532 
9.60561 
9-6o  589 
9.60618 

9.64  209 
9.64  243 
9.64278 
9-64312 
9-64  346 
9-64381 
9.64415 
9.64  449 
9.64  483 

0-35  79i 
o.35  757 
0.35  722 
0.35  688 
0.35654 
0.35619 

0-35  585 
0-35551 
0.35517 

9.96  179 

9.96  174 
9.96  168 
9.96  162 
9.96157 
9.96151 
9.96  146 
9.96  140 
9-96I35 

9.60  646 

9-645I7 

0.35  483 

9.96129 

9-60675 
9.60  704 
9-60732 
9.60  761 
9.60  789 
9.60  818 
9.60  846 
9-60875 
9.60  903 

9-64552 
9-64  586 
9.64620 
9.64  654 
9.64  688 
9.64722 
9-64756 
9.64  790 
9.64824 

0.35  448 
0.354H 
0.35  380 

0-35  346 
0-35312 
0.35  278 
0-35  244 

0.35  210 
0.35  176 

9-96123 
9.96  118 
9.96112 
9.96  107 
9.96  ioi 
9.96  095 
9.96  090 
9.96  084 
9.96  079 

9-6o  931 

9.64858 

0-35  142 

9.96073 

LCos 

d 

LCot 

LTan 

LSin 

d 

t 

P  P 

113° 


(36i) 


66° 


155 


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LCos 

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3 

4 
5 
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9 
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12 
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14 

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16 

17 
18 
19 
20 

21 
22 
23 
24 
25 
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29 
30 

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32 
33 
34 
35 
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9-60931 

29 

28 
28 
29 
28 
28 
28 
29 
28 
28 
28 
28 
28 
28 
28 
28 
29 
27 
28 
28 
28 
28 
28 
28 
28 
28 
27 
28 
28 
28 
27 
28 
28 
27 
28 
28 
27 
28 
27 
28 

27 
28 
27 
28 

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27 

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27 
27 
27 
28 
27 
27 
27 
27 
28 
27 
27 

9-64858 

34 
34 
34 
34 
34 
34 
34 
34 
34 
33 
34 
34 
34 
34 
33 
34 
34 
33 
34 
34 
33 
34 
34 
33 
34 
33 
34 
33 
34 
33 
34 
33 
34 
33 
34 
33 
33 
34 
33 
33 
34 
33 
33 
33 
34 
33 
33 
33 
33 
34 
33 
33 
33 
33 
33 
33 
33 
33 
33 
33 

0.35  142 

9.96073 

6 

5 
6 
6 

5 
6 
5 
6 
6 
5 
6 
6 
5 
6 
6 
6 
5 
6 
6 
5 
6 
6 
6 
5 
6 
6 
5 
6 
6 
6 

5 
6 
6 
6 
6 

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6 
6 
6 

5 
6 
6 
6 
6 

1 

6 
6 
6 
6 

6 
6 
6 
6 
6 
6 
5 

60 

56 
55 
54 
53 
52 
5i 
50 

49 
48 
47 
46 
45 
44 
43 
42 
4i 
40 

39 
38 
37 
36 
35 
34 
33 
32 
3i 
30 

2Q 

28 
27 
26 
25 
24 
23 

22 
21 

30 

19 
18 
17 
1  6 

15 
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13 

12 
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10 

7 
6 
5 
4 
3 

2 

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0 

34    33 

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2   6.8    6.6 
3  10.2     9.9 
4  13-6    13.  f 
5  17.0    16.5 
6  20.4    19.8 
7  23.8    23.1 
8  27.2    26.4 
9  30.6    29.7 

29    28    27 

i   2.9    2.8    2.7 
2   5.8    5.6    5-4 
3   8.7    8.4    8.1 
4  ii.  6   11.  2   10.8 
5  14.5   14.0   13.5 
6  17.4   16.8   16.2 
7  20.3   19.6   18.9 
8  23.2   22.4   21.6 
9  26.1   25.2   24.3 

6    5 

i  0.6   0.5 

2   1.2     I.O 

3  1.8    1.5 
4  2.4    2.0 
5  3-0    2.5 
6  3.6    3.0 
7  4-2    3-5 
8  4.8    4.0 
9  5-4    4-5 

9.60  960 
9.60  988 
9.61016 

9-6i  045 
9-6i  073 
9.61  101 
9.61  129 
9-6i  158 
9.61  186 

9.64892 
9.64926 
9.64  960 

9.64  994 
9.65028 
9.65  062 
9-65  096 
9.65  130 
9-65  164 

0.35  108 
0-35074 
0.35  040 
0.35  006 
0.34972 
0.34  938 
0.34  904 
0.34  870 
0.34  836 

9.96067 
9.96062 
9.96056 
9.96  050 
9.96  045 
9.96  039 
9.96  034 
9.96028 
9.96022 

9.61  214 

9.65  197 

0.34  803 

9.96017 

9.61  242 
9.61  270 
9.61  298 
9.61  326 
9-6i  354 
9.61  382 
9.61  411 
9-6i  438 
9.61  466 

9-65  231 
9-65  265 
9-65  299 

9-65  366 
9.65  400 
9-65  434 
9-65  467 
9-65  501 

0.34  769 
0-34735 
0.34  701 
0.34  667 
0.34  634 
0.34  600 
0.34  566 
0-34  533 
0-34  499 

9.96011 
9.96005 
9.96000 

9-95  994 
9-95  988 
9-95  982 
9-95  977 
9-95  97i 
9-95  965 

9.61  494 

9-65  535 

0.34  465 

9-95  96o 

9.61  522 
9-6i  550 
9.61  578 
9.61  606 
9-6i  634 
9.61  662 
9.61  689 
9.61  717 
9-6i  745 

9-65  568 
9.65  602 
9.65  636 
9-65  669 
9-65  703 
9-65  736 
9.65  770 
9-65  803 
9-65  837 

0-34  432 
0.34398 
0.34364 
0.34331 
0.34  297 
0.34  264 
0.34  230 
0.34197 
0.34  163 

9-95  954 
9-95  948 
9-95  942 
9-95  937 
9-95  93i 
9.95925 
9-95920 
9-95  914 
9-95  9o8 

9.61  773 

9.65  870 

0.34  130 

9-95  902 

9.61  800 
9.61  828 
9.61  856 
9.61  883 
9.61  911 
9.61  939 
9.61  966 
9.61  994 
9.62021 

9.65  904 
9.65  937 
9.65971 
9.66  004 
9.66  038 
9.66071 
9.66  104 
9.66  138 
9.66  171 

0.34096 
0.34063 
0.34029 
0.33  996 
0.33  962 
0.33  929 
0.33  896 
0.33  862 
0.33829 

9-95  897 
9-95  891 
9-95  885 
9-95  879 
9-95  873 
9-95  868 
9-95  862 
9-95  856 
9-95  850 

40 

41 

42 
43 
44 

If 
Ji 

49 
50 

5i 
52 
53 

54 

S 

57 
58 
59 
60 

9.62  049 

9.66  204 

0.33  796 

9.95  844 

9.62076 
9.62  104 
9.62  131 
9.62  159 
9.62  186 
9.62  214 
9.62  241 
9.62  268 
9.62  296 

9.66  238 
9.66  271 
9-66  304 
9.66337 
9.66371 
9.66  404 

9.66437 
9.66470 
9-66  503 

0.33  762 
0.33  729 
0.33  696 
0.33  663 
0.33  629 
0-33  596 
0.33  563 
0-33  530 
0.33  497 

9-95  839 
9-95  833 
9-95827 
9.95821 
9.95815 
9.95  810 
9-95  804 
9-95  798 
9-95  792 

9-62323 

9-66537 

0-33  463 

9-95  786 

9-62350 
9-62377 
9-62  405 
9-62432 
9.62  459 
9.62  486 
9-62  513 
9.62  541 
9.62  568 

9-66570 
9.66  603 
9.66  636 
9.66  669 
9.66  702 
9-66  735 
9.66  768 
9.66  801 
9-66  834 

0-33  430 
0-33  397 
0-33  364 
0.33  331 
0.33  298 
0.33  265 
0.33  232 
0.33  199 
0.33  166 

9-95  78o 
9-95  775 
9-95  769 
9-95  763 
9-95  757 
9-95  75i 
9-95  745 
9-95  739 
9-95  733 

9-62  595 

9.66  867 

0.33  133 

9-95  728 

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cd 

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9.66867 

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9-95  728 

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60 

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2 

3 

4 
5 
6 

7 
8 
9 

9.62622 
9.62  649 
9.62  676 
9.62  703 
9-62  730 
9.62757 
9.62  784 
9.62811 
9.62  838 

27 
27 
27 
27 
27 
27 
27 
27 

9.66  900 

9.66  933 
9.66  966 
9.66  999 
9-67032 
9-67  065 
9.67  098 
9.67  131 
9-67  163 

33 

33 
33 
33 
33 
33 
33 
32 

0.33  loo 

0.33  067 
0.33  034 
0.33  ooi 

0.32  968 
0.32935 
0.32902 
0.32  869 
0.32837 

9-95  722 
9-95  7i6 
9-95  7io 
9-95  704 
9-95  698 
9-95  692 
9-95  686 
9.95  680 
9-95  674 

6 
6 
6 
6 
6 
6 
6 
6 
g 

59 
58 
57 
56 
55 
54 
53 
52 
Si 

33    32 

10 

9.62865 

9.67  196 

0.32  804 

9-95  668 

50 

I 

3.3    3.2 

ii 

12 
13 
14 

S 

17 

18 
19 

9.62  892 
9.62  918 
9.62  945 
9.62972 
9.62  999 
9.63  026 
9-63052 
9.63079 
9.63  106 

27 
26 
27 
27 
27 
27 
26 
27 
27 

9.67  229 
9.67  262 
9.67  295 

9.67327 
9.67  360 
9.67  393 
9.67426 
9.67  458 
9.67  491 

33 
33 
33 
32 
33 
33 
33 
32 
33 

0.32  771 
0.32  738 
0.32  705 
0.32  673 
0.32  640 
0.32  607 
0.32  574 
0.32  542 
0.32  509 

9-95  663 
9-95  657 
9-95  651 
9-95  645 
9-95  639 
9-95  633 
9-95  627 
9-95621 
9-956i5 

6 
6 
6 
6 
6 
6 
6 
6 
5 

49 

48 
47 
46 
45 
44 
43 
42 
41 

2 

3 

4 

I 

7 
8 
9 

6.6    6.4 
9-9    9-6 
13.2    12.8 
16.5    16.0 
19.8    19.2 
23.1    22.4 
26.4    25.6 
29.7    28.8 

20 

9-63  133 

9.67  524 

0.32  476 

9-95  609 

g 

40 

21 
22 
23 
24 

11 

27 
28 
29 

9-63  159 
9.63  186 
9-63  213 
9-63  239 
9.63  266 
9-63  292 
9-633I9 
9-63  345 
9.63372 

27 
27 
26 

27 
26 
27 
26 
27 
26 

9.67  556 
9.67  589 
9.67  622 

9.67  654 
9.67  687 
9.67  719 
9.67  752 
9.67  785 
9.67817 

32 

33 
33 
32 
33 
32 
33 
33 
32 

0.32  444 
0.32411 
0.32378 
0.32  346 
0.32  313 
0.32  281 
0.32  248 
0.32215 
0.32  183 

9-95  603 
9-95  597 
9-95  59i 
9-95  585 
9-95  579 
9-95  573 
9-95  567 
9-95  56i 
9-95  555 

6 
6 
6 
6 
6 
6 
6 
6 
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39 
38 
37 
36 
35 
34 
33 
32 
31 

i 

2 
3 

27     26 

2.7    2.6 
5-4     5-2 
8.1     7-8 

30 

9.63  398 

9.67  850 

0.32  150 

9-95  549 

6 

30 

4 

10.8    10.4 

3i 

32 
33 
34 

Jl 

37 
38 
39 

9.63425 
9-63  45i 
9.63  478 
9.63  504 
9-63  531 
9-63  557 
9-63  583 
9.63  610 
9.63  636 

26 
27 
26 

3 

26 
27 
26 
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9.67  882 
9.67915 
9.67  947 
9.67  980 
9.68012 
9.68  044 
9.68  077 
9.68  109 
9.68  142 

33 
32 
33 
32 
32 
33 
32 
33 

0.32  118 
0.32  085 
0.32  053 
0.32  020 
0.31  988 
0.31  956 
0.31  923 
0.31  891 
0.31  858 

9-95  543 
9-95  537 
9-95  53i 
9-95  525 
9-95  519 
9-95  513 
9-95  507 
9-95  5oo 
9-95  494 

6 
6 
6 
6 
6 
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7 
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29 

28 
27 
26 
25 
24 
23 

22 
21 

5 
6 
7 
8 
9 

13-5    13-0 
16.2    15.6 
18.9    18.2 

21.6     2O.8 

24.3   23.4 

40 

9.63  662 

9.68174 

0.31  826 

9-95  488 

20 

4i 
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43 
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11 
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49 

9-63  689 
9-637I5 
9-63  741 
9-63  767 
9-63  794 
9.63  820 
9.63  846 
9-63  872 
9-63  898 

26 
26 
26 

27 
26 
26 
26 
26 
26 

9.68  206 
9-68  239 
9.68271 
9-68  303 
9-68  336 
9.68368 
9.68  400 
9-68432 
9-68  465 

33 
32 
32 
33 
32 
32 
32 
33 

0.31  794 
0.31  761 
0.31  729 
0.31  697 
0.31  664 
0.31  632 
0.31  600 
0.31  568 
0.31  535 

9-95  482 
9-95  476 
9-95  470 
9-95  464 
9-95  458 
9-95  452 
9-95  446 
9-95  440 
9-95  434 

6 
6 
6 
6 
6 
6 
6 
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19 
18 
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16 
15 
14 
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12 
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7 

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3   2. 
4   2. 
5  3- 
6  4. 

6     5 

7    0.6    0.5 
4    1.2    i.o 
i    1.8    1.5 
8    2.4    2.0 
5    3-o    2.5 
2    3.6    3.0 

50 

9.63  924 

26 

9-68  497 

0.31  503 

9-95  427 

10 

7  4- 

8   s 

9    4-2    3-5 
6    48    40 

5i 

52 
53 
54 
55 
56 

3 

59 

9-63  950 
9-63  976 
9.64002 
9.64028 
9.64054 
9.64080 
9.64  106 
9-64132 
9-64158 

26 
26 
26 
26 
26 
26 
26 
26 
26 

9-68529 
9.68561 
9-68  593 
9.68626 
9.68  658 
9.68  690 
9.68722 
9-68  754 
9.68  786 

32 
32 
33 
32 
32 
32 
32 
32 

0.31471 
0-31  439 
0.31  407 
0.31  374 
0-31  342 
0.31  310 
0.31  278 
0.31  246 
0.31  214 

9-95  42i 
9-95  415 
9-95  409 
9-95  403 
9-95  397 
9-95391 
9-95  384 
9.95378 
9-95372 

6 
6 
6 
6 
6 
7 
6 
6 
g 

1 

7 
6 
5 
4 
3 

2 

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9  6. 

3    5-4    4-5 

60 

9.64  184 

9.68818 

0.31  182 

9-95  366 

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LCos 

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9.64  184 

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9.68818 

0.31  18 

9-95  36 

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9.64210 
9.64  236 
9.64  262 

26 
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9.68  850 
9.68  882 
9.68  914 

32 

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0.31  150 
0.31  118 
0.31  086 

9-95  360 
9-95  354 
9-95  348 

6 

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59 
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9.64  288 

9.68  946 

32 

0.31  054 

9-95  34i 

7 

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9.64313 
9-64339 

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9.68  978 

9.69  oio 

32 
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0.31  022 
0.30  990 

9-95  335 
9-95329 

6 
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9-64365 
9.64391 
9.64417 

26 
26 

9.69  042 
9.69074 
9.69  106 

32 
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0.30958 
0.30926 
0-30  894 

9.95323 
9.95317 
9-95310 

6 
6 
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53 

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32           31 

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9.64  442 

26 

9-69  138 

32 

0.30862 

9-95  304 

50 

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2           64                62 

II 

12 

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9.64  468 

9.64  494 
9.64519 

26 

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9-69170 

9.69  202 
9.69  234 

32 
32 

0-30  830 
0.30  798 
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9-95  298 
9-95  292 
9-95  286 

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3       9-6           9.3 
4     12.8         12.4 
5      16.0         15.5 

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9.64  545 
9.6457I 

26 

9.69  266 
9.69  298 

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0.30  734 
0.30  702 

9-95  279 
9-95  273 

7 
6 

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6     19.2         18.6 
7     22.4         21.7 

16 

9.64  596 

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9.69329 

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9-95  254 

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9.69  520 
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9.69615 
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9-95  211 
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9.69  679 
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9-95  198 
9-95  192 

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9.64927 

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3        7.8         7-5         7-2 

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6     15.6       15.0       14.4 
7     18.2       17.5       16.8 
8     20.  8       20.0       19  2 

9.64  978 
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9-95  173 
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22 
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9-65  705 

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31 
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31 
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31 
30 
31 
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30 
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0.29  283 

9-94  988 

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39 
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37 
36 
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29 
28 
27 
26 
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24 
23 

22 
21 

20 

19 
18 
17 
16 
15 
14 
13 

12 
II 

10 

9 

8 
7 
6 
5 
4 
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2 

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0 

32         31         30 

I       3-2         3-1         3-0 
2       6.4         6.2         6.0 
3      9-6         9-3         9-o 
4     12.8       12.4       12.0 
5     16.0       15.5       15.0 
6    19.2       18.6       18.0 
7     22.4       21.7       21.0 
8    25.6       24.8       24.0 
9     28.8       27.9       27.0 

25         24       23 

i       2.5        2.4        2.3 

2         5.0            4.8            4.6 

3       7-5         7-2         6.9 
4     10.0         9.6         9.2 
S     12.5       12.0       ii.  5 
6     15.0       14.4       13.8 
7     17.5       16.8       16.1 
8     20.0       19.2       18.4 
9     22.5       21.6       20.7 

7             6 

i    0.7           0.6 

2       1.4                1.2 

3     2.1            1.8 
4     2.8            2.4 
5     3-5            3-0 
6     4.2            3.6 
7     4-9            4-2 
8     5.6            4.8 
9     6.3            5.4 

9.65  729 

9.65  754 
9-65  779 
9.65  804 
9.65828 
9.6s  853 
9-65  878 
9-65  902 
9-65927 

9.70  748 
9-70779 
9.70810 
9.70841 
9.70873 
9.70  904 

9-70935 
9.70966 
9.70997 

0.29252 

0.29  221 
O.29  190 
0.29159 
0.29  127 
0.29096 
0.29065 
0.29034 
0.29003 

9-94982 

9-94975 
9-94  969 
9.94962 
9.94956 
9-94  949 
9-94  943 
9-94936 
9.94  930 

9-65952 

9.71  028 

0.28  972 

9-94923 

9-65  976 
9.66001 
9.66025 
9.66050 
9.66075 
9.66  099 
9.66  124 
9.66  148 
9-66173 

9.71059 
9.71090 
9.71121 
9-71  153 
9.71  184 
9.71  215 
9.71  246 
9.71  277 
9.71  308 

0.28941 
0.28910 
0.28879 
0.28847 
0.288l6 
0.28  785 
0.28754 
0.28723 
O.28  692 

9.94917 
9.94911 
9-94  904 
9-94  898 
9.94891 
9-94  885 
9.94878 
9.94871 
9-94865 

9.66  197 

9-71339 

0.28661 

9-94  858 

9.66  221 
9.66  246 
9.66  270 

9-66  295 
9-66319 
9-66  343 
9.66  368 
9-66392 
9.66416 

9.71370 
9.71401 
9-71431 
9.71462 
9.71493 
9-71  524 
9.71555 
9.71  586 
9.71617 

O.28  630 

0.28  599 
0.28569 
0.28538 
0.28  507 
0.28476 
0.28445 
0.28414 
0.28383 

9-94852 
9-94  845 
9-94  839 
9.94832 
9.94826 
9.94819 
9.94813 
9.94  806 
9-94  799 

9.66  441 

9.71  648 

0.28352 

9-94  793 

9.66  465 
9.66489 
9-66513 

9-66537 
9.66562 
9.66  586 
9.66610 
9-66  634 
9.66658 

9.71  679 
9.71  709 
9.71  740 
9.71  771 
9.71  802 
9-71  833 
9-71  863 
9.71  894 
9.71925 

0.28321 
0.28  291 
0.28  260 
0.28  229 
0.28  198 
0.28  167 
0.28  137 
0.28  106 
0.28075 

9-94  786 
9-94  78o 
9-94773 
9-94  767 
9-94  76o 
9-94  753 
9-94  747 
9-94  740 
9-94  734 

9.66682 

9-71  955 

0.28045 

9.94727 

4i 
42 
43 
44 

8 

47 
48 
49 
50 

5i 

52 
53 

54 

II 

57 
58 
59 
60 

9.66  706 
9-66731 
9.66755 
9-66779 
9.66  803 
9.66827 
9.66851 
9-66875 
9.66  899 

9.71  986 
9.72017 
9.72  048 
9.72078 
9.72  109 
9.72  140 
9.72  170 

9.72  201 
9-72  23I 

0.28014 
0.27  983 
0.27952 
0.27  922 
0.27891 
0.27  860 
0.27  830 
0.27  799 
0.27  769 

9-94720 
9.94714 
9-94  707 
9.94  700 
9.94  694 
9.94687 
9-94  680 
9-94  674 
9-94  667 

9.66922 

9.72262 

0.27  738 

9-94  660 

9.66  946 
9-66  970 
9-66  994 
9.67018 
9.67  042 
9.67  066 
9.67  090 
9.67  113 
9.67  137 

9.72  293 
9.72323 
9-72354 
9-72  384 
9.72415 

9-72  445 
9.72476 
9-72  506 
9.72537 

0.27  707 
0.27677 
0.27  646 
0.27  616 
0.27585 
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0.27  524 
0.27  494 
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9-94654 
9.94  647 
9.94  640 

9.94634 
9.94627 
9.94620 

9.94614 
9.94  607 
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9.67  161 

9.72567 

0.24433 

9-94  593 

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9.67  185 
9.67  208 
9-67  232 
9.67  256 
9.67  280 
9-6?  303 
9.67327 
9.67  350 
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23 

24 
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9.72  598 
9.72628 
9.72659 
9.72  689 
9.72720 
9.72750 
9.72  780 
9.72811 
9.72841 

30 
31 
30 
31 
30 
30 
31 
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0.27  402 
0.27372 
0.27341 
0.27311 
0.27  280 
0.27  250 

0.27  220 
0.27  189 
0.27159 

9-94  587 
9-94  58o 
9-94573 
9-94  567 
9-94  56o 
9-94553 
9-94  546 
9.94  540 
9-94  533 

7 
7 
6 

7 
7 
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59 
58 
57 
56 
55 
54 
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SI 

31         30         29 

10 

9.67  398 

9.72872 

0.27  128 

9.94526 

7 

50 

1       3-1         3-0         2.9 

ii 

13 

14 
15 
16 

17 
18 
19 

9.67421 
9.67  445 
9.67  468 

9.67  492 
9.67515 
9.67  539 
9-67  562 
9.67  586 
9.67  609 

23 
24 
23 
24 
23 
24 
23 
24 
23 

9.72902 
9.72932 
9.72  963 

9-72  993 
9-73  023 
9.73054 
9-73  084 
9.73H4 
9-73  144 

30 
31 
30 
30 
31 
30 
30 
30 

0.27  098 
0.27068 
0.27037 
0.27007 
0.26977 
O.26  946 
0.26916 
0.26886 
0.26856 

9-94  519 
9-94513 
9-94  506 
9.94  499 
9-94  492 
9-94  485 
9-94479 
9.94472 
9-94  465 

7 
6 
7 
7 
7 
7 
6 

7 

7 

49 
48 
47 
46 
45 
44 
43 
42 
4i 

3       9-3         9-0         8.7 
4     12.4       12.0       n.6 
5     15-5       15-0       14-5 
6     18.6       18.0       17.4 
7     21.7       21.0       20.3 
8     24.8       24.0       23.2 
9     27.9       27.0       26.1 

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9.67  633 

24 

9-73  175 

0.26825 

9.94458 

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9-67  656 
9.67  680 
9.67  703 
9.67  726 
9.67  750 
9-67  773 
9-67  796 
9.67820 
9.67  843 

23 

24 
23 
23 
24 
23 
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9-73  205 
9-73  235 
9-73  265 
9-73  295 
9.73326 
9.73356 
9.73386 
9.73416 
9-73  446 

30 
30 
30 
31 
30 
30 
30 
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0.26795 
0.26765 
0.26735 
0.26  70S 
0.26674 
0.26644 
0.26614 
0.26584 
0.26554 

9-94451 
9-94  445 
9-94438 
9-94431 
9.94424 
9.94417 
9.94410 
9-94  404 
9-94397 

6 

7 
7 
7 
7 
7 
6 
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39 
38 
37 
36 
35 
34 
33 
32 
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24         23         22 

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2         4.8            4.6            4.4 

3       7-2         6.9         6.6 

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9.67  866 

23 

9.73476 

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9-94  390 

30 

4      9-6         9.2         8.8 

31 

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35 
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9.67  890 
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9-67  959 
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9.68  006 
9.68029 
9.68052 
9-68075 

23 
23 
23 
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9-73  507 
9-73537 
9-73  567 
9-73  597 
9-73  627 
9.73657 
9-73  687 
9.73717 
9-73  747 

30 
30 
30 
30 
30 
30 
30 
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0.26493 
0.26463 
0.26433 
0.26403 
0.26373 
0.26343 

0.26313 
0.26  283 
0.26253 

9-94  383 
9-94376 
9-94  369 
9.94362 
9-94355 
9-94  349 
9-94342 
9-94335 
9.94328 

7 
7 
7 
7 
6 
7 
7 
7 

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27 
26 

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24 
23 
22 
21 

6     14.4       13.8       13.2 
7     16.8       16.1       15.4 
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9     21.6       20.7       19.8 

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9.68  098 

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9-73777 

0.26  223 

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47 
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9.68121 
9-68  144 
9.68  167 
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9.68213 
9-68  237 
9.68  260 
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9.68  305 

23 
23 
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9-73  807 
9-73  837 
9.73867 

9-73  897 
9.73927 
9-73957 
9-73987 
9  74017 
9.74047 

30 
30 
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30 
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0.26  193 
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0.25  983 
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9-94314 
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9-94  293 
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9.94  266 
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4     2.8            2.4 
5     3-5            3-0 
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9.68328 

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9.74077 

0.25923 

9.94252 

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7     4-9            4-2 

51 
52 
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9.68  397 
9.68420 
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9.68  466 
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0.68512 
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23 
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9.74107 
9.74137 
9-74  166 
9-74  196 
9.74226 
9.74256 
9.74286 
9.74316 
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30 
29 
30 
30 
30 
30 
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0.25  893 
0.25  863 

0.25  834 

0.25  804 

0.25774 

0.25  744 

0.25714 
0.25  684 
0.25655 

9-94  245 
9-94  238 
9.94231 
9-94  224 
9.94217 
9.94  210 
9-94  203 
9.94  196 
9.94  189 

7 
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8 
9 
10 

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12 
13 
14 

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16 

17 
18 
i9 
20 

21 
22 
23 

24 
25 
26 
27 
28 
29 

30 

31 
32 
33 
34 

11 

37 
38 
39 
40 

4i 
42 
43 
44 
45 
46 

47 
48 
49 
50 

Si 

52 
53 
54 
55 
56 

11 

59 
60 

9-68557 

23 
23 

22 
23 
23 
23 
22 

23 
23 
22 

23 
22 
23 
23 
22 
23 
22 

23 
22 
23 
22 

23 
22 
23 
22 
22 
23 
22 
23 
22 

22 

23 
22 
22 
22 
23 
22 
22 
22 
22 

23 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 
22 

9-74375 

30 
30 
30 
29 
30 
30 
29 
30 
30 
30 

29 
30 
30 
29 
30 
30 
29 
30 
29 
30 
29 
30 
30 
29 
30 
29 
30 
29 
30 
29 

30 

29 
30 
29 
29 
30 
29 
30 
29 
29 
30 
29 
30 
29 

29 
30 
29 
29 
29 
30 
29 

29 
29 
30 
29 
29 
29 
30 
29 
29 

0.25  625 

9.94  182 

7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 

7 
8 
7 
7 
7 
7 
7 
7 
7 
7 
7 
7 
8 
7 
7 
7 
7 
7 
7 
7 
8 
7 
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8 
7 
7 
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7 
7 

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7 
7 
7 
7 
8 
7 
7 
8 
7 
7 
7 
8 
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30         29         23 

i       3-0         2.9         2.3 
2       6.0         5.8         4.6 
3       9.0         8.7         6.9 
4     12.0       n.6         9.2 
5     15.0       14.5       11.5 
6     18.0       17.4       13.8 
7     21.0       20.3       16.1 
8     24.0       23.2       18.4 
9     27.0       26.1       20.7 

22           8           7 

I          2.2            0.8            O.7 

2       4.4         1.6         1.4 
3       6.6         2.4         2.1 
4       8.8         3-2         2.8 
5     n.o         4-0        3-5 
6     13.2        4.8        4.2 
7     15.4         5-6         4-9 
8     17.6        6.4        5.6 
9     19.8         7.2         6.3 

9.68  580 
9.68  603 
9.68  625 
9.68  648 
9.68671 
9.68  694 
9.68716 

9.68  739 
9.68  762 

9.74405 
9-74435 
9-74465 
9-74494 
9.74524 
9-74554 
9.74583 
9-746I3 
9.74643 

0.25  595 
0.25  565 
0-25535 
0.25  506 
0.25  476 
0.25  446 
0.25417 
0.25387 
0.25357 

9-94175 

9.94  168 
9.94  161 
9-94  154 
9-94  147 
9-94  140 
9-94  133 
9.94126 
9.94119 

9.68  784 

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0.25327 

9.94"2 

9.68  807 
9.68829 
9.68852 

9-68875 
9.68897 
9.68920 
9.68  942 
9-68  965 
9.68  987 

9-74702 
9-74732 
9.74762 

9-74791 
9.74821 
9-74851 
9.74880 
9.74910 
9-74939 

0.25  298 
0.25  268 
0.25  238 
0.25  209 
0.25  179 
0.25  149 

0.25  120 
0.25090 
0.25061 

9-94  105 
9-94  098 
9.94090 
9.94  083 
9-94076 
9-94  069 
9.94062 
9.94055 
9.94  048. 

9.69010 

9.74969 

0.25031 

9.94041 

9-69032 
9-69055 
9.69077 
9.69  loo 

9.69  122 
9.69  144 
9.69  167 
9.69  189 
9.69212 

9.74998 
9.75028 
9.75058 
9-75087 
9-75  H7 
9-75  146 
9.75176 
9-75  205 
9-75  235 

0.25  O02 
0.24972 
0.24942 
0.24913 
0.24883 
0.24854 
0.24824 
0.24795 
0.24  765 

9.94034 
9.94027 
9.94020 
9.94012 
9-94  005 
9-93  998 
9-93  991 
9-93  984 
9-93977 

9.69  234 

9-75  264 

0.24736 

9-93  970 

9.69  256 
9.69279 
9.69301 
9.69323 
9.69345 
9.69368 
9.69390 
9.69412 

9-69  434 

9-75  294 
9.75323 
9-75353 
9.75382 
9-754II 
9-75441 
9-75  470 
9-75  500 
9.75529 

O.24  706 
0.24677 
0.24647 
0.24618 
0.24589 
0.24559 
0.24530 
0.24500 
0.24471 

9-93  963 
9-93  955 
9-93  948 
9-93  941 
9-93  934 
9.93927 
9-93  920 
9.93912 
9-93  90S 

9.69456 

9.75558 

0.24442 

9-93  898 

9.69479 
9-69  SOi 
9-69523 
9-69  545 
9.69  567 
9.69  589 
9.69611 
9.69  633 
9-69655 

9-75  588 
9.75617 
9-75  647 
9.75676 
9-75  70S 
9-75  735 
9-75  764 
9-75  793 
9.75822 

0.24412 
0.24383 
0.24353 
0.24324 
0.24  295 
0.24  265 
O.24  236 
0.24  2O7 
0.24  178 

9-93  891 
9-93  884 
9-93  876 
9-93  869 
9-93  862 
9-93  855 
9-93  847 
9-93  840 
9-93  833 

9-69677 

9.75852 

0.24  148 

9-93  826 

9.69  699 
9.69721 
9.69  743 
9.69  765 
9.69  787 
9.69  809 

9-69831 
9-69853 
9.69875 

9.75881 
9-75910 
9-75  939 
9.75969 
9.75998 
9.76027 
9.76056 
9.76086 
9.76  115 

O.24  119 
0.24090 
0.24061 
0.24031 
O.24OO2 
0-23973 

0.23  944 
0.23914 
0.23885 

9.93  819 
9.938ii 
9-93  804 
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9-93  789 
9.93  782 

9-93  775 
9-93  768 
9-93  76o 

9.69  897 

9.76  144 

0.23  856 

9-93  753 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

t 

P  P 

119° 


(367) 


60° 


30° 


149C 


r 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

60 

59 
58 
57 
56 
55 
54 
53 
52 

50 

48 
47 
46 
45 
44 
43 
42 

40 

39 
38 
37 
36 
35 
34 
33 
32 

30 

29 
28 
27 
26 
25 
24 
23 

22 
21 

20 

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16 
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14 
13 

12 
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10 

9 
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6 

5 
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2 
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9 
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12 

13 
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19 

20 

21 

22 

23 

24 
25 
26 

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29 

30 

32 

33 
34 

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11 

39 
40 

41 

42 
43 
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3 
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49 
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59 
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9.69  897 

22 
22 
22 
21 
22 
22 
22 
22 
21 
22 
22 
22 
21 
22 
22 
21 
22 
21 
22 
22 
21 
22 
21 
22 
21 
22 
21 
22 
21 
22 
21 
22 
21 
22 
21 
21 
22 
21 
21 
22 
21 
21 
21 
22 
21 
21 
21 
22 
21 
21 
21 
21 
21 
22 
21 
21 
21 
21 
21 
21 

9.76  144 

OOO  O  OOO  OOOOO  OOOOOOOOO  OOO  OOO  OOO  O  O  O  O  OOO  O  OOOOOOOOO  O  OOO  O  OOOOOO  O  OOOOOO  OOO  O 

0.23856 

9-93  753 

7 
8 
7 
7 
7 
8 
7 
7 
8 
7 
7 
8 

1 

7 
7 
8 
7 

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7 
8 

7 
7 
8 
7 
8 

7 
8 
7 
7 
8 
7 
8 
7 
8 
7 
8 
7 
8 

7 
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7 
8 
7 
8 
7 
8 

7 

8 

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8 
7 
8 

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7 

3 

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2          6 

3       9 

4       12 

5     15 
6     18 
7     21 
8     24 
9     27 

i 

2 

3 

4 

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9 

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2 
3 
4 

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7 
8 
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)         29         28 

.0        2.9        2.8 
.0         5.8         5.6 
.0        8.7         8.4 

.0          II.  6          II.  2 

.0       14.5       14.0 
.0       17.4       16.8 
.0       20.3       19.6 
.0       23.2       22.4 
.0      26.1       25.2 

22           21 

2.2               2.1 

4.4               4.2 

6.6           6.3 
8.8           8.4 
n.o         10.5 
13.2        12.6 

15.4      14.7 

17.6        16.8 
19.8        18.9 

8             7 

0.8            0.7 
1.6           1.4 

2.4            2.1 

3.2                  2.8 

4-0           3-5 
4.8            4-2 
5-6           4-9 
6.4           5-6 
7-2           6.3 

9.69919 
9-69  941 
9.69  963 
9.69  984 
9.70006 
9.70028 
9.70050 
9.70072 
9.70  093 

9.76  173 

9.76  202 
9.76231 
9.76  26l 
9.76  290 
9.76319 
9.76348 
9.76377 
9.76  406 

0.23827 
0.23  798 
0.23  769 

0.23  739 
0.23710 
0.23681 
0.23652 
0.23  623 
0.23594 

9-93  746 
9-93  738 
9-93  73i 
9-93  724 
9.93717 
9-93  709 
9-93  702 
9-93  695 
9-93  687 

9.70115 

9.76435 

0.23565 

9.93  680 

9.70  137 
9-70159 

9.70  180 
9.70202 
9.70224 
9.70  245 
9.70267 
9.70  288 
9.70310 

9.76  464 

9.76  493 
9-76522 

9.7655I 
9.76  580 
9.76  609 
9.76639 
9.76668 
9.76697 

0.23536 
0.23  507 
0.23478 
0.23  449 
0.23  420 
0.23391 
0.23361 
0.23332 
0.23  303 

9-93  673 
9-93  665 
9-93  658 
9-93  650 
9-93  643 
9.93  636 
9-93  628 
9-93  621 
9-93  614 

9-70332 

9.76725 

0.23275 

9-93  606 

9.70353 
9.70375 
9-70396 
9.70418 
9-70439 
9.70461 
9.70482 
9.70  504 
9-70525 

9.76  754 
9-76783 
9.76812 
9.76841 
9.76870 
9.76899 
9.76928 
9.76957 
9.76986 

0.23  246 
0.23  217 
0.23  188 
0.23  159 
0.23  130 
0.23  101 
0.23072 
0.23043 
0.23014 

9-93  599 
9-93  59i 
9-93  584 
9-93  577 
9-93  569 
9-93  562 
9-93  554 
9-93  547 
9-93  539 

9.70547 

9.77015 

0.22  985 

9-93  532 

9-70568 
9.70590 
9.70611 
9-70633 
9.70654 
9.70675 
9-70697 
9.70718 
9-70  739 

9-77  044 
9.77073 
9.77  101 
9-77  130 
9-77  159 
9.77188 

9.77217 
9-77  246 
9.77274 

0.22  956 
0.22927 
0.22  899 
O.22  870 
0.22  841 
O.22  8l2 
0.22  783 

0.22  754 

0.22  726 

9-93  525 
9.93517 
9-93  5io 
9-93  502 
9-93  495 
9-93  487 
9.93  480 
9-93  472 
9-93  465 

9.70761 

9-77  303 

0.22697 

9-93  457 

9.70782 
9-70803 
9.70824 
9.70  846 
9.70867 
9.70  888 
9.70909 
9.70931 
9.70952 

9-77332 
9.77361 
9-77  390 
9.77418 
9-77  447 
9.77476 

9-77  505 
9-77533 
9.77562 

0.22  668 

0.22  639 
O.22  6lO 
0.22  582 

0.22  553 

0.22  524 

0.22495 
0.22  467 
0.22438 

9-93  450 
9-93  442 
9-93  435 
9-93  427 
9-93  420 
9.93412 

9-93  405 
9-93  397 
9-93  390 

9.70973 

9-77  59i 

O.22  409 

9-93  382 

9.70994 
9.71015 
9-71  036 
9-7i  058 
9.71079 
9.71  100 
9.71121 
9.71  142 
9-71  163 

9.77619 
9-77  648 
9.77677 
9-77  7o6 
9-77  734 
9-77  763 
9-77791 
9.77820 
9-77  849 

0.22  381 
0.22352 
0.22323 
0.22  294 
0.22  266 
0.22  237 
0.22  209 
0.22  l8o 
0.22  151 

9-93  375 
9-93  367 
9-93  360 
9-93352 
9-93  344 
9-93  337 
9-93  329 
9.93322 
9-93  314 

9.71  184 

9.77877 

0.22  123 

9-93  307 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

t 

P  P 

120° 


(368) 


sr 


148° 


t 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

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0 

9.71  184 

9-77877 

0.22  123 

9-93  307 

g 

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2 

3 
4 

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9 

9-71  205 
9.71  226 
9.71  247 
9.71  268 
9.71  289 
9.71  31° 
9-71331 
9-71352 
9-71373 

21 
21 
21 
21 
21 
21 
21 
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9.77  906 
9-77935 

9-77  963 
9-77  992 
9.78020 
9.78  049 
9.78077 
9.78  106 
9.78135 

29 
28 
29 
28 
29 
28 
29 
29 
28 

0.22094 
0.22065 
O.22037 
0.22O08 
0.21  980 
O.2I  951 
0.21  923 
O.2I  894 
0.21  865 

9.93  299 
9-93  291 
9.93  284 
9.93  276 
9-93  269 
9-93  261 
9-93  253 
9-93  246 
9-93  238 

8 

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7 
8 
8 
7 
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g 

59 
58 
57 
56 
55 
54 
53 
52 
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29           28 

10 

9-71393 

9.78  163 

0.21  837 

9-93  230 

50 

2 

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12 
13 
14 
15 

16 
17 
18 
19 

9.71414 
9-71  435 
9-7i  456 
9.71  477 
9.71  498 
9-71  519 
9-71  539 
9-71  56o 
9-71  58: 

21 
21 

21 
21 
21 
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21 
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9.78  192 
9.78  220 
9.78  249 
9.78277 
9-78306 
9.78334 
9-78363 
9.78391 
9.78419 

28 
29 
28 

29 
28 
29 

28 
28 

0.2l8o8 
O.2I  780 
0.21  751 
0.21  723 
O.2I  694 
O.2I  666 
0.21637 
O.2I  609 
0.21  581 

9-93  223 
9-93  215 
9-93  207 
9-93  200 
9-93  192 
9.93  184 

9-93  177 
9-93  169 
9-93  161 

8 

8 
7 
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8 
7 
8 
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49 

48 
47 
46 
45 
44 
43 
42 
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3 

4 

7 
8 
9 

8.7           8.4 

II.6            II.  2 

14.5         14.0 
17.4         16.8 
20.3         19.6 
23.2         22.4 
26.1         25.2 

20 

9.71  602 

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9.78  448 

28 

0.21552 

9-93  154 

g 

40 

21 

22 
23 

24 
25 
26 

27 
28 
29 

9.71  622 
9-71  643 
9.71  664 
9.71  685 
9-71  70S 
9.71  726 

9.71  747 
9.71  767 
9.71  788 

21 
21 
21 
20 
21 
21 
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21 

9.78476 
9.78  505 
9.78533 
9-78562 
9.78  590 
9.78618 
9.78647 
9-78675 
9.78  704 

2 

29 
28 
28 
29 
28 
29 

0.21  524 
0.21495 
0.21  467 
0.21  438 
O.2I  410 
O.2I  382 

0.21  353 

0.21325 
O.2I  296 

9-93  146 
9-93  138 
9-93  131 
9-93  123 
9-93  "5 
9-93  108 
9-93  ioo 
9-93  092 
9-93  084 

8 

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8 
7 
8 
8 
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39 
38 
37 
36 
35 
34 
33 
32 
31 

2 

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21           20 

2.1               2.0 

4.2               4.0 

6.3           6.0 

30 

9.71809 

9.78732 

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O.2I  268 

9.93077 

30 

4 

8.4           8.0 

3i 
32 
33 
34 

31 

37 
38 
39 

9.71  829 
9.71  850 
9.71870 
9.71  891 
9.71911 
9.71932 
9.71952 
9.7I973 
9.71  994 

21 

20 
21 
20 
21 
20 
21 
21 

9.78760 
9.78  789 
9-78817 
9-78845 
9.78874 
9.78902 

9.78930 
9.78959 
9-78987 

29 

28 
28 
29 
28 
28 
29 
28 

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O.2I  240 
0.21  211 
0.21  183 
0.21  155 
O.2I  126 
O.2I  098 
O.2I  070 
O.2I  041 
O.2I  013 

9-93  069 
9-93  061 
9-93  053 
9.93  046 
9-93  038 
9-93  030 
9.93022 
9-93  014 
9.93  007 

8 
8 
7 
8 
8 
8 
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29 
28 
27 
26 
25 
24 

23 

22 
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6 
7 
8 
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12.6            I2.O 

14.7      14.0 

16.8        16.0 
18.9        18.0 

40 

9.72014 

9-79015 

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0.20985 

9-92  999 

20 

4i 
42 
43 
44 
45 
46 

47 
48 
49 

9.72034 
9-72055 
9.72075 
9.72096 
9.72  116 
9.72137 
9.72157 
9.72  177 
9.72  198 

21 
2O 
21 
20 
21 
20 
20 
21 

9-79043 
9.79072 
9.79100 
9.79128 
9.79156 
9.79i85 
9.79213 
9.79  241 
9-79  269 

29 
28 
28 
28 

3 

28 
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0.20957 
O.20928 
O.2O  9OO 
O.2O872 
O.2O  844 
0.20815 
0.20787 
0.20759 
0.20731 

9-92  99i 
9-92  983 
9-92  976 
9.92  968 
9.92  960 
9.92  952 
9.92  944 
9-92  936 
9-92  929 

8 

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8 
8 

8 
8 

7 

19 
18 
17 
16 
15 
14 
13 

12 
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2 

3 

4 
5 
6 

8             7 

0.8           0.7 
1.6           1.4 

2.4                2.1 
3-2                 2.8 

4-0            3-5 
4.8            4.2 

50 

9.72  218 

9-79  297 

O.20703 

9.92921 

10 

7 

5-6            4-9 

Si 
52 
53 
54 
55 
56 

11 

59 

9-72  238 
9-72259 
9.72  279 
9.72  299 
9-72320 
9.72340 
9-72  360 
9.72381 
9.72401 

21 
2O 
2O 
21 
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20 
21 
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9.79326 
9-79354 
9.79382 
9.79410 
9.79438 
9.79466 
9-79495 
9-79523 
9-79551 

28 
28 
28 
28 
28 
29 
28 
28 

28 

0.20674 
0.20646 
0.2o6l8 
0.2O59O 
0.20562 

0.20  534 

0.20  5O5 

0.20477 
0.20449 

9.92913 
9.92  905 
9-92  897 
9.92  889 
9.92881 
9.92874 
9.92  866 
9.92858 
9.92  850 

8 
8 
8 
8 

I 

8 
8 
g 

I 

7 
6 
5 
4 
3 
2 

8 
9 

6.4            5-6 
7.2            6.3 

60 

9.72421 

9-79579 

0.20421 

9.92  842 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

/ 

P  P 

121C 


(369) 


58C 


32° 


147C 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

u 

9.72421 

9-79579 

28 

0.20421 

9.92  842 

g 

60 

I 

2 

3 

4 

I 

7 
8 
9 

9.72441 
9.72  461 
9.72  482 
9.72  502 
9-72522 
9.72  542 
9-72562 
9-72582 
9.72  602 

20 

21 
2O 
2O 
2O 
2O 
2O 
2O 

9.79607 
9-79635 
9-79  663 
9.79691 
9.79719 
9-79  747 
9.79776 
9-79  804 
9-79832 

28 
28 
28 
28 
28 
29 
28 
28 
28 

0.20393 
0.20365 
0.20337 
0.20309 

O.20  28l 
O.2O  253 
0.20  224 
O.20  196 
O.20  1  68 

9.92  834 
9.92826 
9.92818 

9.92  810 
9-92  803 
9-92  795 
9-92  787 
9.92  779 
9.92  771 

8 
8 
8 

7 
8 
8 
8 
8 

59 
58 
57 
56 
55 
54 
53 
52 
5i 

29         28         27 

10 

9.72622 

9.79860 

28 

O.2O  140 

9.92  763 

50 

2 

5-8         5.6         5.4 

ii 

12 
13 
14 
15 

16 

17 
18 
19 

9-72  643 
9-72  663 
9-72683 
9-72  703 
9.72723 
9-72743 
9-72  763 
9.72  783 
9.72  803 

2O 
2O 
2O 
2O 
2O 
2O 
20 
2O 

9-79888 
9.79916 
9.79  944 
9-79972 
9.80000 
9.80028 
9.80  056 
9.80  084 

9.8O  112 

28 
28 
28 
28 
28 
28 
28 
28 
28 

0.  20  112 
0.20084 
0.20056 
O.2O  O28 
O.20000 
0.19972 
0.19944 
O.I99I6 
0.19888 

9-92  755 
9-92  747 
9-92  739 
9.92  731 
9.92723 
9.92  715 

9-92  707 
9.92  699 
9.92  691 

8 
8 
8 
8 
8 
8 
8 
8 

49 

48 
47 
46 
45 
44 
43 
42 
41 

3 

4 
5 
6 

I 

9 

8.7         8.4         8.1 
ii.  6       ii.  2       10.8 
14.5       14.0       13.5 
17.4       16.8       16.2 
20.3       19.6       18.9 
23.2       22.4       21.6 
26.1       25.2       24.3 

20 

9-72823 

9O 

9.80  140 

28 

O.I9860 

9-92  683 

g 

40 

21 

22 
23 
24 
25 
26 
27 
28 
29 

9.72843 
9-72863 
9-72883 
9.72902 
9.72922 
9.72  942 
9.72962 
9.72982 
9.73002 

2O 

20 
19 
20 
20 
20 
2O 
20 

9.80  1  68 
9-8o  195 
9.80223 
9.80251 
9.80279 
9-8o  307 
9-80335 
9-80363 
9-80391 

27 
28 
28 
28 
28 
28 
28 
28 
28 

0.19832 
O.I9805 
0.19777 

0.19  749 
0.19  721 
0.19693 
0.19665 
0.19637 
0.19609 

9-92675 
9.92  667 
9.92  659 
9-92651 
9.92  643 
9-92635 
9.92  627 
9.92  619 
9.92  6n 

8 
8 
8 
8 
8 
8 
8 
8 
g 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

i 

2 

3 

21         20         19 

2.1             2.0             1-9 

4-2         4.0         3-8 
6.3         6.0         5.7 

30 

9.73022 

9.80419 

28 

0.19  581 

9-92  603 

g 

30 

4 

8.4         8.0         7.6 

31 
32 
33 
34 
35 
36 

8 

39 

9.73041 
9-73  061 
9-73  081 
9-73  ioi 
9.73121 
9-73  140 
9-73  160 
9-73  180 
9-73  200 

20 
2O 
2O 
2O 
19 
2O 
2O 
2O 

9.80  447 
9.80  474 
9.80  502 
9.8o  530 
9-8o  558 
9.80  586 
9.80614 
9.80  642 
9.80  669 

3 

28 
28 
28 
28 
28 
27 
28 

0.19553 
0.19526 
0.19498 
0.19470 
0.19442 
0.19414 
0.19386 
0.19358 
O.I933I 

9-92  595 
9-92  587 
9-92  579 
9.92571 
9-92  563 
9-92555 
9-92  546 
9-92  538 
9-92  530 

8 
8 
8 
8 
8 
9 
8 
8 
g 

29 

28 
27 
26 
25 
24 
23 

22 
21 

6 
7 
8 
9 

12.6          12.0          II.4 

14.7     14.0     13.3 

16.8       16.0       15.2 
18.9       18.0       17.1 

40 

9-73219 

9.80  697 

28 

0.19303 

9-92522 

g 

20 

41 

42 
43 
44 

3 

% 

49 

9-73  239 
9-73  259 
9-73  278 
9-73  298 
9.73318 
9-73337 
9-73357 
9-73377 
9-73  396 

2O 
19 
2O 
20 
19 
2O 
2O 
19 

9-80725 
9-8o  753 
9.80  781 
9.80  808 
9.80  836 
9.80  864 
9.80892 
9.80  919 
9.80  947 

28 
28 
27 
28 
28 
28 

3 

28 

0.19275 
0.19247 
0.19  219 
0.19  192 
0.19  164 
0.19  136 
0.19  108 
0.19081 
0.19053 

9-925I4 
9.92  506 
9.92  498 
9.92  490 
9.92  482 
9-92  473 
9-92  465 
9.92457 
9-92  449 

8 
8 
8 
8 
9 
8 
8 
8 

iQ 
18 
i? 
16 
IS 
14 
13 

12 
II 

i 

2 

3 

4 
5 
6 

987 

0.9         0.8         0.7 
1.8         1.6         1.4 

2.7            2.4            2.1 

3-6         3-2         2.8 
4-5         4-0         3-5 
5.4         4.8         4.2 

50 

9.73416 

*° 

9-80975 

28 

0.19025 

9.92  441 

10 

7 

6.3         5.6         4.9 

5i 
52 

53 

54 

11 

57 
58 
59 

9-73435 
9-73  455 
9-73  474 
9-73  494 
9-73  513 
9-73  533 
9-73552 
9-73572 
9-73  591 

20 

19 
20 

19 
20 
19 

20 
19 

9.81  003 
9.81  030 
9.81  058 
9.81  086 
9-8i  113 
9.81  141 
9.81  169 
9.81  196 
9.81  224 

27 
28 
28 

3 

28 
27 
28 
28 

0.18997 
0.18970 
0.18942 
0.18914 
0.18887 
0.18859 
0.18831 
0.18804 
0.18  776 

9-92  433 
9.92425 
9.92416 
9.92  408 
9.92  400 
9.92392 
9.92  384 
9.92376 
9-92  367 

8 

! 

g 
8 

8 
8 

9 
g 

9 

8 
7 
6 
5 
4 
3 

2 

I 

8 
9 

7.2         6.4         5.6 
8.1         7-2         6.3 

60 

9-736ii 

9.81  252 

0.18  748 

9-92359 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

/ 

P  P 

122° 


(370) 


146° 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9.73611 

9.81  252 

0.18748 

9.92359 

g 

60 

I 

2 
3 
4 
5 
6 

I 

9 

9-73  630 
9-73650 
9-73  669 
9-73  689 
9-73  708 
9-73  727 
9-73  747 
9-73  766 
9.73785 

20 
19 
20 

19 
19 

20 

19 
19 

9.81  279 
9.81  307 

9-8i  335 
9.81362 
9-8i  390 
9.81  418 

9-8i  445 
9-8i  473 
9.81  500 

28 
28 
27 
28 
28 
27 
28 

11 

0.18  721 
0.18693 
0.18665 
0.18638 
0.18610 
0.18582 
0.18555 
0.18  527 
0.18  500 

9.92351 

9-92  343 
9.92335 
9-92  326 
9-92318 
9.92310 
9-92  302 
9.92  293 
9-92  285 

8 
8 
9 
8 
8 
8 

9 

8 
8 

59 

58 
57 
56 
55 
54 
53 
52 
Si 

28           27 

10 

9-73  805 

M 

9.81  528 

28 

0.18472 

9-92  277 

g 

50 

I          2.8               2.7 

ii 

12 
13 
14 

!i 
3 

19 

9.73824 
9-73843 
9-73  863 
9.73882 
9-73  9oi 
9-73921 
9-73  940 
9-73959 
9.73978 

19 

20 
19 
19 
20 
19 
19 
19 

9-8i  556 
9.8i  583 
9.81  611 
9.81  638 
9.81  666 
9-8i  693 
9.81  721 
9.81  748 
9.81  776 

27 
28 
27 
28 
27 
28 
27 
28 

0.18444 
0.18417 
0.18389 
0.18362 
0.18334 
0.18  307 
0.18  279 
0.18  252 
0.18  224 

9-92  269 
9.92  260 
9-92252 
9.92  244 
9-92  235 
9.92  227 
9.92  219 

9.92  211 
9.92  2O2 

I 

8 

! 

8 
8 

8 

49 

48 
47 
46 
45 
44 
43 
42 
4i 

3       8.4           8.1 
4     ii.  2         10.8 
5     14.0         13.5 
6     16.8         16.2 
7     19.6         18.9 
8    22.4        21.6 
9     25.2         24.3 

30 

9-73  997 

9.81  803 

28 

0.18  197 

9-92  194 

g 

40 

21 
22 
23 
24 
25 
26 

27 
28 
29 

9.74017 
9.74036 
9.74055 
9.74074 
9.74093 
9.74II3 
9-74I32 
9-74JC5I 
9.74  170 

19 
19 
19 

19 

20 

19 
19 
19 

9.81  831 
9.81  858 
9.81  886 
9.81  913 
9-81  941 
9.81  968 
9.81  996 
9.82  023 
9-82051 

27 
28 
27 
28 
27 
28 
27 
28 

0.18  169 
0.18  142 
0.18  114 
0.18087 
0.18059 
0.18032 
0.18004 
0.17977 
0.17949 

9.92  186 

9.92  177 
9.92  169 
9.92  161 
9-92152 
9.92  144 
9-92  136 
9.92  127 
9.92  119 

9 

8 
8 

9 

8 
8 

I 

g 

39 

38 
37 
36 

35 
34 

33 

32 
31 

20         19         18 

I           2.0             1.9             1.8 

2       4.0        3-8        3-6 
3       6.0         5.7         5-4 

30 

9-74  189 

9-82078 

28 

0.17  922 

9.92  in 

30 

4       8.0         7-6         7-2 

3i 

32 
33 
34 
35 
36 

3 

39 

9.74  208 
9.74227 
9.74  246 
9-74  265 
9.74284 
9-74  303 
9-74322 
9-74341 
9.74360 

19 
19 
19 
19 
19 
19 
19 
19 

9.82  106 
9-82  133 
9.82  161 
9.82  188 
9-82215 
9-82  243 
9.82  270 
9.82  298 
9.82325 

27 
28 
27 

27 
28 
27 
28 
27 

0.17  894 
0.17867 
0.17839 
0.17  812 
0.17785 
0.17  757 
0.17  730 
0.17  702 
0.17  675 

9.92  IO2 
9.92  094 
9.92  086 
9.92077 
9.92  069 
9.92  060 
9.92052 
9.92  044 
9.92035 

8 
8 
9 
8 
9 
8 
8 

jj 

29 
28 
27 
26 
25 
24 
23 

22 
21 

S     10.0         9-5         9-o 
6     12.0       11.4       10.8 
7     14.0       13-3       I2-6 
8     16.0       15.2       14-4 
9     18.0      17.1       16.2 

40 

9-74379 

9.82352 

28 

0.17  648 

9.92027 

20 

41 
42 
43 
44 
45 
46 
47 
48 
49 

9-74398 
9.74417 
9.74436 
9-74455 
9-74474 
9-74493 
9-74512 
9-74531 
9-74549 

19 
19 
19 
19 
19 
19 
19 
18 

9.82  380 
9.82  407 
9-82  435 
9.82  462 
9.82  489 
9-82517 
9.82  544 
9.82571 
9.82  599 

ll 

27 
27 
28 

27 
27 
28 

0.17  620 
0.17593 
0.17  565 
0.17538 
0.17  511 
0.17483 
0.17456 
0.17429 
0.17  401 

9.92  018 
9.92  oio 
9.92  002 
9-91  993 
9-91  985 
9.91  976 
9.91  968 
9-9i  959 
9-91  951 

8 
8 
9 
8 

I 

19 
18 
i7 
16 

15 

14 
13 

12 
II 

9             8 

I     0.9           0.8 
2     1.8           1.6 

3     2.7            2.4 
4     3-6            3-2 
S     4-5            4-0 

50 

9.74568 

9.82626 

0.17374 

9.91  942 

g 

10 

5-4            4-» 
7     6.3            5-6 

Si 

52 
53 
54 
55 
56 

11 

59 

9.74587 
9.74  606 
9-74625 
9.74644 
9.74662 
9.74681 
9-74700 
9.74719 
9-74737 

19 
19 
19 
18 
i9 
19 
19 
18 

9-82  653 
9.82681 
9.82  708 
9-82735 
9.82  762 
9.82  790 
9.82817 
9-82  844 
9.82871 

28 
27 
27 
27 
28 
27 
27 
27 
28 

0.17347 
0.17319 
0.17  292 
0.17  265 
0.17  238 

O.I7  2IO 
0.17  183 
O.I7  156 
0.17  129 

9-91  934 
9.91  925 
9.91917 
9.91  908 
9.91  900 
9.91  891 
9-91  883 
9.91  874 
9.91  866 

9 
8 
9 
8 

! 

I 

7 
6 
5 
4 
3 

2 
I 

8     7.2            6.4 
9     8.1            7-2 

60 

9.74756 

9.82  899 

0.17  ioi 

9-91  857 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

r 

P  P 

123 


(37i) 


66C 


145C 


1 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9-74756 

9.82  899 

0.17  ioi 

9-91  857 

60 

I 

2 

3 

4 

I 

7 
8 
9 

9-74775 
9-74  794 
9-74812 

9-74831 
9-74850 
9-74868 
9.74887 
9.74906 
9.74924 

19 

18 
19 

:i 

19 
19 

18 

9.82926 
9-82953 
9.82  980 
9.83  008 
9-83  035 
9.83  062 
9.83  089 
9.83  117 
9.83  144 

27 

27 
28 

27 
27 
27 
28 
27 

0.17074 
0.17047 

0.17020 
0.16992 
0.16965 
0.16938 
0.16911 
0.16883 
0.16856 

9.91  849 
9.91  840 
9.91  832 
9-91  823 
9.91815 
9.91  806 
9.91  798 
9.91  789 
9.91  781 

1 

9 
8 
9 
8 

1 

59 

58 
57 
56 
55 
54 
53 
52 
Si 

2 

8         27         26 

10 

9-74943 

18 

9.83171 

0.16829 

9-91772 

9 

50 

I          2 

.8        2.7         2.6 

ii 

12 
13 
14 

15 

16 

3 

19 

9.74961 
9.74980 
9-74999 
9-75017 
9.75036 
9.75054 
9.75073 
9.75091 
9-75  no 

19 
19 
18 

19 
18 
19 
18 
19 
18 

9.83  198 
9-83  225 
9-83  252 
9.83  280 
9-83  307 

9-83  334 
9-83  36l 
9.83  388 
9.834I5 

27 
27 
28 
27 
27 
27 
27 
27 

0.16802 
0.16775 
0.16748 
0.16  720 
0.16693 
0.16666 
0.16639 
0.16612 
0.16585 

9-91  763 

9-91  755 
9.91  746 
9-91  738 
9.91  729 
9.91  720 
9.91712 
9.91  703 
9-9i  695 

9 

8 

1 

9 

9 
8 

4Q 
48 
47 
46 
45 
44 
43 
42 
4i 

2         < 

3       * 
4     I] 
5     i/ 
6     if. 
7     I? 

8      22 

9     25 

•6        5.4        5.2 
.4        8.1         7.8 
.2       10.8       10.4 
^.o       13.5       13.0 
.8       16.2       15.6 
.6       18.9       18.2 
.4       21.6       20.8 

.2         24.3         23.4 

20 

9.75128 

9.83  442 

28 

0.16558 

9.91  686 

40 

21 

22 
23 
24 
25 
26 

27 
28 
29 

9-75  147 
9-75  165 
9-75  184 
9-75  202 
9-75  221 
9-75  239 
9-75  258 
9-75  276 
9-75  294 

18 
19 
18 

19 
18 
19 
18 
18 

9.83  470 
9-83  497 
9-83  524 
9.83551 
9-83  578 
9-83  605 
9-83  632 
9-83  659 
9.83  686 

27 
27 
27 
27 
27 
27 
27 
27 

0.16530 
0.16  503 
0.16476 
0.16  449 
0.16422 
0.16395 
0.16368 
0.16341 
0.16314 

9.91  677 
9.91  669 
9.91  660 
9-91651 
9.91  643 
9.91  634 
9-91  625 
9.91  617 
9.91  608 

8 
9 
9 
8 
9 
9 
8 
9 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

I 

2 
3 

19           18 

1.9          1.8 

3-8           3-6 
5-7           5-4 

30 

9.75313 

To 

9-83  713 

0.16  287 

9-91  599 

30 

4 

7.6           7.2 

3i 

32 
33 
34 
35 
36 
37 
38 
39 

9.75  33i 
9-75350 
9.75368 
9-75  386 
9.75405 
9.75423 
9-75  44i 
9-75  459 
9.75478 

19 

18 
18 

19 
18 
18 
18 

11 

9.83  740 
9-83  768 
9-83  795 
9.83822 
9-83  849 
9-83  876 
9-83  903 
9-83  930 
9.83957 

27 
28 
27 
27 
27 
27 
27 
27 
27 

0.16  260 
0.16  232 
0.16  205 
0.16  178 
0.16  151 
0.16  124 
0.16097 
0.16070 
0.16043 

9-91  59i 
9-91  582 
9-91  573 
9-91  565 
9-91  556 
9-91  547 
9-91  538 
9-91  530 
9.91521 

9 
9 
8 

9 
9 
9 
8 
9 

29 
28 
27 
26 
25 
24 
23 

22 
21 

5 
6 
7 
8 
9 

9-5           9-o 
11.4         10.8 

13-3            12.6 

15-2         14-4 
17.1         16.2 

40 

9-75  496 

18 

9-83  984 

27 

0.16016 

9.91512 

9 
g 

20 

41 
42 
43 
44 
45 
46 

47 
48 

49 

9.75514 
9-75  533 
9-75551 
9-75  569 
9-75  587 
9-75  605 
9.75624 
9-75642 
9-75  660 

19 
18 
18 
18 
18 
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18 
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9.84011 
9-84038 
9-84  065 
9.84092 
9.84119 
9.84  146 

9-84173 

9.84  200 
9.84227 

27 
27 
27 
27 
27 
27 
27 
27 

0.15  989 
0.15  962 
0.15935 
0.15908 
0.15881 
0.15854 
0.15827 
0.15  800 
0.15773 

9.91  504 
9-91  495 
9.91  486 
9.91  477 
9.91  469 
9.91  460 

9-91  451 
9.91  442 
9-91  433 

9 
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9 
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9 
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19 
18 
17 
16 
15 
14 
13 

12 
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4 
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9              8 

0.9           0.8 
1.8            1.6 
2.7            2.4 
3-6            3-2 
4-5            4-o 

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9-75  678 

18 

9.84  254 

27 

0.15  746 

9-91  425 

10 

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5-4            4-8 
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51 
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57 
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9-75  696 
9.757I4 
9-75  733 
9-75751 
9-75  769 
9-75  787 
9-75  805 
9-75823 
9-75  841 

18 
19 
18 
18 
18 
18 
18 
18 
18 

9.84  280 
9.84307 
9.84334 
9.84361 
9.84388 
9.84415 
9.84  442 
9.84469 
9.84  496 

27 
27 
27 

27 
27 
27 
27 
27 

0.15  720 
0.15  693 
0.15666 

0.15639 
0.15612 
0.15  585 
0.15558 
O.I553I 
0.15504 

9.91  416 
9.91  407 
9.91  398 
9.91  389 
9.91  381 
9.91  372 
9-91  363 
9.91354 
9-91  345 

9 
9 
9 
9 
8 
9 
9 
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7 
6 
5 
4 
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8 
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7.2            6.4 
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9-75  859 

9.84523 

0.15477 

9-91  336 

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13 
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17 
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21 
22 
23 
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25 
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32 
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17 
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27 
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26 
27 
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27 
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0.15477 

9-91  336 

8 

9 
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9 
9 
9 
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9 
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57 
56 
55 
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49 
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47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 

32 

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30 

29 
28 

27 
26 

25 
24 
23 

22 
21 

20 

19 
18 
17 
16 
15 
14 
13 

12 
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10 

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7 
6 
5 
4 
3 

2 

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0 

27           26 

i       2.7          2.6 
2       5-4           5-2 
3       8.1           7.8 
4     10.8         10.4 
5     13.5         13.0 
6     16.2         15.6 
7     18.9         18.2 
8     21.6        20.8 
9     24.3        23.4 

18           17 

i       1.8          1.7 
2       3-6           3-4 
3       5-4           5-1 
4       7-2           6.8 
5       9-0          8.5 
6     10.8        10.2 
7     12.6        11.9 
8     14.4        13.6 
9     16.2        15.3 

10         9          8 

i     i.o        0.9        0.8 

2        2.0             1.8             1.6 

3     3.0         2.7         2.4 
4     4.0         3.6         3.2 
5     5.0        4.5         4.0 
6     6.0        5.4        4.8 
7     7-0        6.3         5.6 
8     8.0         7.2         6.4 
9     9.0    .    8.1         7.2 

9-75877 

9-75  895 
9.759I3 
9-75931 
9-75  949 
9-75  967 
9.75985 
9.76003 
9.76021 

9-84550 
9.84576 
9.84  603 
9.84  630 
9.84657 
9.84  684 
9.84711 
9.84  738 
9.84  764 

0.15450 
0.15424 
0.15397 
0.15370 
0.15343 
0.15  316 
0.15  289 
0.15  262 
0.15  236 

9.91  328 
9.91519 
9.91310 
9.91  301 
9.91  292 
9-91  283 
9.91  274 
9.91  266 
9.91  257 

9.76039 

9.84  791 

0.15  209 

9.91  248 

9-76057 
9-76075 
9-76  093 
9.76  in 
9.76129 
9.76  146 
9.76164 
9.76182 

9.76  200 

9.84818 
9.84  845 
9.84872 
9.84899 
9.84925 
9.84952 
9.84979 
9.85  006 
9-85  033 

0.15  182 
0.15  155 
0.15  128 

0.15  ioi 
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0.15  048 
0.15021 

0.14994 
0.14967 

9.91  239 
9-91  230 

9.91  221 
9.91  212 
9-91  203 
9.91  194 

9-91  185 
9.91  176 
9.91  167 

9.76  218 

9-85  059 

0.14941 

9.91  158 

9-76  236 
9.76253 
9.76271 
9.76  289 
9.76307 
9.76324 
9-76342 
9.76  360 
9.76378 

9.85  086 
9-85  113 
9-85  140 

9.85  166 
9-85  193 

9.85  220 
9.85  247 

9-85  273 

9.85  300 

0.14914 
0.14887 
0.14860 
0.14834 
0.14807 
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0.14753 
0.14727 
0.14  700 

9.91  149 
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9-91  132 
9-91  123 
9.91  114 
9.91  105 
9.91  096 
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9.91  078 

9.76395 

9.85327 

0.14673 

9.91  069 

9.76413 
9.76431 
9.76  448 
9.76  466 
9.76484 
9.76  501 
9.76519 
9.76537 
9.76554 

9.85  354 
9-85  380 
9.85  407 
9.85434 
9-85  460 
9.85  487 
9-855I4 
9-85  540 
9.85  567 

0.14  646 
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0.14566 
0.14540 
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9.91  O6O 
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9-91  033 
9-91  023 
9.91  014 
9-91  005 
9.90  996 
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9-85  594 

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9.76590 
9.76607 
9.76625 
9.76642 
9.76  660 
9.76677 
9.76695 
9.76712 
9.76730 

9.85  620 
9-85  647 
9-85  674 
9.85  700 
9.85727 
9-85  754 
9-85  78o 
9-85  807 
9-85  834 

0.14380 
0.14353 
0.14326 
0.14300 
0.14273 
0.14  246 

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0.14  166 

9.90969 
9.90  960 
9.90951 
9-90  942 

9-90  933 
9.90  924 

9.90915 
9.90  906 
9.90  896 

9.76747 

9.85  860 

0.14  140 

9.90887 

9.76765 
9.76782 
9.76800 
9.76817 
9.76835 
9.76852 
9.76870 
9.76887 
9.76  904 

9-85  887 
9-859I3 
9.85  940 
9.85967 
9-85  993 
9.86020 
9.86  046 
9.86073 
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0.14113 
0.14087 
0.14060 
0.14033 
0.14007 
0.13  980 

0.13954 
0.13927 
0.13900 

9-90878 
9.90  869 
9.90  860 
9-90851 
9.90  842 
9-90832 
9-90823 
9.90814 
9-90  805 

9.76922 

9.86126 

0.13874 

9.90  796 

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12 
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16 
17 
18 
19 
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33 
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24 
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22 
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9.76922 

9.86126 

27 
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9.90  796 

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27          26 

i       2.7          2.6 
2       5-4           5-2 
3       8.1           7.8 
4     10.8         10.4 
5     13-5         13-0 
6     16.2         15.6 
7     18.9         18.2 
8     21.6        20.8 
9     24.3        23.4 

18         17         16 

i       1.8        1.7         1.6 
2       3-6         3-4         3-2 
3       5.4         5.1         4.8 
4       7.2         6.8         6.4 
5       9.0         8.5         8.0 
6     10.8       10.2         9.6 
7     12.6       11.9       ii.  2 
8     14.4       13.6       12.8 
9     16.2       15.3       14.4 

10            9 

i     i.o           0.9 

2       2.0                1.8 

3     3-0            2.7 
4     4-o            3-6 
5     5-0            4-5 
6     6.0            5.4 
7     7-o            6.3 
8     8.0            7.2 
9    9.0            8.1 

9-76939 
9-76957 
9.76974 
9.76991 
9.77009 
9.77026 

9-77  043 
9.77061 
9.77078 

9-86153 
9.86  179 
9.86  206 
9.86232 
9.86  259 
9.86  285 
9.86312 
9.86338 

9-86  365 

0.13  847 
0.13821 

0.13  794 
0,13  768 
0.13  741 
O.I37I5 
0.13688 
0.13  662 
0.13635 

9.90  787 
9.90777 
9-90  768 

9-90759 
9.90  750 
9-90  741 
9-90731 
9.90722 
9.90713 

9-77095 

9-86392 

0.13  608 

9.90  704 

9.77112 
9-77  130 
9-77  147 
9-77  164 
9.77181 
9.77  199 
9.77  216 
9-77  233 
9.77  250 

9.86418 
9-86  445 
9.86471 
9.86  498 
9-86  524 
9-86  551 
9-86577 
9.86  603 
9.86  630 

0.13  582 
0.13  555 
0.13  529 
0.13  502 
0.13476 
0-13  449 
0.13423 
0.13397 
0.13370 

9.90  694 
9-90  685 
9.90  676 
9.90  667 
9-90657 
9.90  648 
9.90  639 

9-90  630 
9.90620 

9.77  268 

9.86  656 

0.13  344 

9.90611 

9-77  285 

9-77  302 

9.773I9 
9.77336 
9-77353 
9-77370 
9.77387 
9-77  405 
9-77422 

9.86  683 
9.86  709 
9-86  736 
9.86762 
9.86  789 
9.86815 
9.86  842 
9.86  868 
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0.13  264 
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0.13  211 
0.13  185 
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9.90  602 
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9-90  574 
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9.90  546 
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9-77  439 

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0.13079 

9.90  518 

9.77456 
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9-77  490 
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9-77524 
9-77  541 
9.77558 
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9.86  947 
9-86  974 
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9.87  079 
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9-77  694 
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9.87  211 
9.87  238 
9.87  264 
9.87  290 
9.87317 

9.87  343 
9.87  369 
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0.12  789 
0.12  762 
0.12  736 
0.12  710 
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O.I2  657 
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9.90  349 
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0.12  552 

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9-77  846 
9.77  862 
9.77879 
9-77  896 
9.779I3 
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9-87  475 
9.87  501 
9.87  527 
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9.87  58o 
9.87  606 
9-87  633 
9.87  659 
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0.12  367 
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9-90311 
9-9030I 
9.90  292 
9.90  282 
9-90  273 
9-90  263 
9.90  254 
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9.90091 
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9-78  230 

9.88158 

o.ii  842 

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9.78  246 

9.88  184 

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9.78  445 

16 

9.88  498 

26 

o.n  502 

9-89  947 

30 

4 

6.8          6.4 

31 

9.78461 

9-88524 

o.n  476 

9-89  937 

?.q 

5 

8.5          8.0 

32 

9.78478 

i? 

9-88550 

26 

0.11450 

9.89927 

10 

28 

6 

10.2               9.6 

33 

9.78494 

9.88577 

27 

0.11423 

9.89918 

9 

27 

7 

II.9           II.  2 

34 

9.78510 

9.88  603 

0.11397 

9.89  908 

10 

8 

13.6        12.8 

35 

9.78527 

17 

9.88629 

26 

0.11371 

9.89  898 

IO 

2S 

9 

IS-3            14-4 

30 

9.78543 

16 

9-88655 

O.II345 

9.89  888 

10 

24 

g 

9-78560 
9.78576 

17 
16 

9.88681 
9.88  707 

26 

0.11319 
o.n  293 

9-89879 
9.89  869 

y 

10 

23 

7,7, 

39 

9.78592 

16 

9-88733 

26 

o.n  267 

9.89859 

10 

21 

40 

9.78  609 

16 

9-88  759 

o.ii  241 

9-89  849 

20 

41 

9-78625 

9.88  786 

o.ii  214 

9.89  840 

9 

TO 

42 

9.78642 

17 

9.88812 

26 

o.ii  188 

9.89  830 

10 

T« 

43 

9-78658 

9.88  838 

o.n  162 

9.89820 

IO 

T? 

44 
45 
46 

9.78674 
9-78691 
9.78  707 

11 

9.88  864 
9.88  890 
9.88916 

26 
26 

o.ii  136 
o.n  no 
o.n  084 

9.89810 
9.89  801 
9.89  791 

IO 

9 

10 

16 
15 
14 

i 

2 

10             9 

i.o            0.9 

2.0                1.8 

47 
48 

9-78723 
9.78  739 

16 

9.88  942 
9.88  968 

26 

0.11058 
o.n  032 

9.89  781 
9.89771 

IO 

IO 

13 

T? 

3 

4 

3-o            2.7 
4-0            3-6 

49 

9.78756 

11 

9-88  994 

26 

o.n  006 

9.89  761 

IO 

II 

5 

5-0            4-5 

50 

9.78772 

16 

9.89  020 

26 

0.10980 

9.89752 

9 

10 

6.0           5.4 
70           63 

Si 

9.78788 

9.89  046 

0.10954 

9.89  742 

g 

8 

8.0           7.2 

52 

9.78  805 

*7 

9.89  073 

*i 

0.10927 

9.89732 

IO 

i 

9 

Q.O               8.1 

53 

9.78821 

9-89  099 

26 

0.10901 

9.89722 

IO 

7 

54 
55 
56 

9-78837 
9-78853 
9-78869 

16 
16 

9-89  125 
9-89  151 
9.89177 

26 
26 

0.10875 
0.10849 
0.10823 

9.89712 
9.89  702 
9.89  693 

IO 
10 

9 

6 
5 
4 

57 
58 

9.78886 
9.78902 

16 

9-89  203 
9.89  229 

26 
26 

0.10797 
0.10771 

9-89  683 
9.89  673 

IO 
10 

3 

2 

59 

9.78918 

16 

9.89  255 

0.10745 

9.89  663 

10 

I 

60 

9.78  934 

9.89  281 

0.10719 

9-89  653 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

; 

P  P 

127 


(375) 


52° 


38C 


t 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

I 

2 

3 

4 

7 
8 
9 
10 

ii 

12 
13 

14 
15 

16 

17 
18 
19 
20 

21 
22 
23 
24 
25 
26 

27 
28 
29 

30 

3i 
32 
33 

34 

11 

il 

39 
40 

41 
42 
43 
44 
45 
46 

% 

49 
50 

5i 

52 
53 
54 

II 

11 

59 
60 

9.78  934 

16 

li 

16 
16 
16 
16 
16 
16 
16 
16 

11 

16 
16 
16 
16 
16 
16 
16 
16 
16 
16 
15 
16 
16 
16 
16 
16 
16 
16 
16 
16 

15 

16 
16 
16 
16 
16 
IS 
16 
16 
16 
IS 
16 
16 
16 

;i 

16 
IS 
16 
16 
IS 
16 
16 
IS 
16 
16 
15 

9.89  281 

26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 
26 

25 
26 
26 
26 
26 

iS 

26 
26 
26 
26 
26 
25 
26 
26 
26 
26 
26 
26 
26 
25 
26 
26 
26 
26 
26 
26 
25 
26 
26 
26 

c~d 

0.10719 

9-89653 

10 
IO 

9 

10 
10 
10 
10 
IO 
10 
10 
10 
IO 
IO 
10 
IO 

9 

IO 
IO 
10 
10 
10 
10 
IO 
10 
10 
IO 
10 
10 

II 

10 
10 
10 
10 
10 
IO 
10 
10 
10 
10 
10 
10 
II 

10 
IO 
IO 
IO 
IO 
IO 

II 

IO 
IO 
IO 
IO 

10 

II 

IO 
IO 
10 

II 

10 

60 

59 

58 

57 
56 
55 
54 
53 
52 
5i 
50 

49 
48 
47 
46 
45 
44 
43 
42 
4i 
40 

39 
38 
37 
36 
35 
34 
33 
32 
3i 
30 

20 
28 
27 
26 
25 
24 
23 
22 
21 

20 

19 
18 
17 
16 
15 
14 
13 

12 
II 

10 

9 
8 
7 
6 
5 
4 
3 

2 

I 
0 

26           25 

i       2.6          2.5 

2          5-2                5-0 

3       7-8           7-5 
4     10.4         10.0 
S     13-0         12.5 
6    15.6        15.0 
7     18.2         17.5 

8      20.8            2O.O 

9     23.4        22.5 

17         16         15 

i       1.7        1.6        1.5 
2      3.4        3.2        3.0 
3       5.1         4.8        4.5 
4       6.8         6.4         6.0 
5       8.5         8.0         7-5 
6     10.2        9.6        9.0 
7     11.9       ii.  2       10.5 
8     13.6       12.8      12.0 
9     15.3       14.4      13.5 

11         10         9 

i     i.i         i.o        0.9 

2       2.2             2.0             1.8 

3     3-3         3-0         2.7 
4     4.4         4.0         3.6 
5     5-5         5-o         4-5 
6     6.6         6.0         5.4 
7     7-7         7-o         6.3 
8     8.8         8.0         7-2 
9    9.9        9.0        8.1 

9.78950 
9.78  967 
9.78  983 
9.78  999 
9.79015 
9.79031 
9.79047 
9.79063 
9.79079 

9-89  307 

9.89  333 
9-89359 
9.89385 
9.89411 
9.89  437 
9.89  463 
9.89  489 
9.89515 

0.10693 
0.10667 
0.10641 
0.10615 
0.10589 

o.io  563 
0.10537 
0.10511 
0.10485 

9.89  643 
9-89633 
9.89624 
9.89614 
9.89  604 

9-89  594 
9.89  584 
9.89  574 
9.89  564 

9.79095 

9.89  541 

0.10459 

9.89554 

9.79111 
9.79128 
9.79  144 
9.79  160 
9.79176 
9.79192 
9.79  208 
9.79224 
9-79  240 

9.89567 
9.89  593 
9.89619 
9.89  645 
9.89671 
9-89  697 
9.89  723 
9.89  749 
9.89775 

0.10433 
0.10407 
0.10381 
0.10355 
0.10329 
0.10303 
0.10277 
0.10251 
o.io  225 

9.89  544 
9.89  534 
9.89  524 
9.89514 
9.89  504 
9-89  495 
9.89  485 
9-89475 
9.89  465 

9.79256 

9.89  801 

o.io  199 

9.89455 

9.79272 
9-79  288 
9.79304 
9-79319 
9-79335 
9-79351 
9.79367 
9.79383 
9-79399 

9.89827 
9-89853 
9-89879 
9.89  905 
9.89931 
9-89957 
9.89  983 
9.90  009 
9-90035 

0.10173 
o.io  147 

O.IO  121 

0.10095 
0.10069 
0.10043 
0.10017 
0.09  991 
0.09  965 

9.89  445 
9.89435 
9.89425 
9.89415 
9.89  405 
9.89395 
9.89385 
9.89375 
9.89  364 

9-79415 

9.90061 

0.09  939 

9-89354 

9-79431 
9-79447 
9-79  463 
9.79478 
9-79494 
9.79510 
9.79526 
9-79542 
9.79558 

9.90  086 

9.90  112 
9-90  138 
9-90  164 
9.90  190 

9.90  216 
9.90  242 
9.90  268 
9.90  294 

0.09  914 
0.09  888 
0.09  862 
0.09  836 
0.09810 
0.09  784 
0.09  758 
0.09  732 
0.09  706 

9.89  344 
9.89334 
9.89324 
9.89314 
9.89  304 
9.89  294 
9.89  284 
9.89  274 
9.89  264 

9-79573 

9.90320 

0.09  680 

9.89  254 

9-79589 
9-79  605 
9.79621 
9.79636 
9.79652 
9.79  668 
9-79  684 
9-79699 
9-79715 

9.90  346 
9.90371 

9.90  397 
9.90423 
9.90  449 
9-90475 
9-90  501 
9.90527 
9.90553 

0.09  654 
0.09  629 
0.09  603 
0.09  577 
0.09  551 
0.09525 
0.09  499 
0.09  473 
0.09  447 

9.89  244 
9-89  233 
9-89  223 
9-89213 
9-89  203 
9-89  193 
9-89  183 
9.89173 
9.89162 

9-79731 

9.90578 

0.09422 

9-89152 

9.79  746 
9.79762 
9.79778 
9-79  793 
9-79  809 
9.79825 
9.79  840 
9-79856 
9.79872 

9.90  604 
9.90  630 
9.90  656 
9.90682 
9.90  708 
9-90  734 
9-90759 
9-90  785 
9.90811 

0.09  396 
0.09  370 
0.09  344 
0.09318 
0.09  292 
0.09  266 
0.09  241 
0.09  215 
0.09  189 

9.89  142 
9-89132 

9.89  122 
9.89  112 

9.89  ioi 

9.89091 
9.89081 
9.89071 
9.89  060 

9.79887 

9-90  837 

0.09  163 

9.89050 

LCos 

d 

LCot 

LTan 

LSin 

d 

/ 

P  P 

128 


(376) 


51C 


39° 


140° 


f 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9-79887 

16 

9-90837 

26 

0.09  163 

9.89  050 

60 

I 

2 

3 
4 
5 
6 

7 
8 
9 

9-79  903 
9-799i8 
9-79934 
9-79950 
9-79965 
9.79981 
9.79996 
9.80012 
9.80027 

;i 

16 

15 
16 
15 
16 
15 
16 

9-90  863 
9.90  889 
9.90914 
9.90  940 
9.90966 
9.90  992 

9.91  018 
9.91  043 
9.91  069 

26 
25 
26 
26 
26 
26 

3 

26 

0.09  137 
0.09  in 
0.09  086 
0.09  060 
0.09  034 
0.09  008 
0.08  982 
0.08957 
0.08931 

9.89  040 
9.89030 
9.89020 
9.89  009 

9-88  999 
9.88  989 
9.88978 
9.88  968 
9-88958 

10 
IO 

II 

10 
IO 

II 

IO 
10 

59 

58 
57 
56 
55 
54 
53 
52 
5i 

26    25 

26    25 

10 

9.80  043 

9-91  095 

26 

0.08  905 

9.88  948 

50 

2 

5-2     S-o 

ii 

12 
13 

14 

S 

17 

18 
19 

9.80058 
9.80074 
9.80  089 
9.80  105 

9.80  120 
9.80  136 
9.80  151 

9.80  1  66 
9.80182 

16 
15 
16 

15 
16 
15 

11 

9.91  121 
9.91  147 
9.91  172 
9.91  198 
9.91  224 
9-91  250 
9.91  276 
9.91  301 
9-9I327 

26 
25 
26 
26 
26 
26 
25 
26 
26 

0.08  879 
0.08  853 
0.08  828 
0.08  802 
0.08  776 
0.08  750 
0.08  724 
0.08  699 
0.08  673 

9.88937 
9.88927 
9.88917 
9.88  906 
9.88  896 
9.88  886 

9-88875 
9.88  865 
9.88855 

10 
10 

II 

10 
IO 

II 

10 
10 

40 
48 
47 
46 
45 
44 
43 
42 
41 

3 
4 
5 
6 
7 
8 
9 

7-8     7-5 
10.4    10.0 
13.0    12.5 
15-6    15.0 
18.2    17.5 
20.  8    20.0 

23.4   22.5 

20 

9.80197 

16 

9-91  353 

26 

0.08  647 

9.88  844 

11 

40 

21 
22 
23 
24 
25 
26 
27 
28 
29 

9.80  213 
9.80228 
9.80  244 
9-8o  259 
9.80  274 
9.80  290 
9.80305 
9.80320 
9-80336 

11 

IS 
15 
16 

15 

15 
16 

9-91  379 
9.91  404 
9.91  430 
9.91  456 
9.91  482 
9.91  507 
9-91  533 
9-91  559 
9-91  585 

11 

26 

26 

% 

26 
26 

0.08621 
0.08  596 
0.08  570 

0.08  544 
0.08518 
0.08  493 
0.08  467 
0.08  441 
0.08415 

9-88  834 
9.88824 
9.88813 
9.88803 
9.88  793 
9.88  782 
9.88772 
9.88  761 
9.88751 

10 

II 

10 
10 

II 

10 

II 

10 

39 
38 

37 
36 
35 

34 

33 

32 
3i 

I 

2 

3 

16     15 

1.6    1.5 

3-2      3-0 

4-8    4-5 

30 

9-80351 

9.91  610 

26 

0.08  390 

9.88  741 

30 

4 

6.4    6.0 

3i 

32 
33 
34 
35 
36 

II 

39 

9.80366 
9.80382 
9-80397 
9.80412 
9.80428 
9.80  443 
9-80458 
9.80473 
9.80  489 

16 
IS 
15 
16 
15 

15 

IS 
16 

9-91  636 
9.91  662 
9.91  688 
9.9I7I3 
9-9i  739 
9-91  765 
9.91  791 
9.91  816 
9.91  842 

26 
26 
25 
26 
26 
26 
25 
26 

0.08  364 
0.08338 
0.08312 
0.08  287 
0.08  261 
0.08  235 
0.08  209 
0.08  184 
0.08  158 

9-88  730 
9.88720 
9.88  709 
9.88  699 
9.88  688 
9.88678 
9.88  668 
9.88657 
9.88  647 

IO 

II 

10 

II 

10 
IO 

II 

IO 

29 

28 
27 
26 
25 
24 
23 

22 
21 

6 
7 
8 
9 

9.6    9.0 

II.  2     IO.5 
12.8     I2.O 
14-4     I3-S 

40 

9-8o  504 

9.91  868 

0.08  132 

9.88636 

20 

41 
42 
43 

44 
45 
46 

47 
48 
49 

9-80519 
9-8o  534 
9-80550 
9-8o  565 
9.80  580 
9-8o  595 
9.80610 
9.80625 
9.80641 

15 
16 
IS 
IS 
IS 
IS 
IS' 
16 

9-91  893 
9.91919 
9-91  945 
9.91  971 
9.91  996 

9.92  022 
9.92  048 
9.92073 
9.92099 

26 
26 
26 

25 
26 
26 

25 
26 
26 

0.08  107 
0.08  081 
0.08055 
0.08  029 
0.08  004 
0.07  978 
0.07  952 
0.07927 
0.07  901 

9.88626 
9.88615 
9.88  605 
9-88  594 
9-88  584 
9.88573 
9-88  563 
9-88552 
9-88  542 

II 

IO 

II 

10 

II 

IO 

II 

IO 

iQ 

18 
17 
16 
15 
14 
13 

12 
II 

2 

3 

4 

| 

11     10 

I.I       I.O 

2.2       2.O 
3-3       3-0 
4-4       4-0 

5-5     5-0 

50 

9.80656 

9.92  125 

0.07  875 

9-88531 

10 

7 

7-7     7-0 

Si 

52 
53 
54 

II 
11 

59 

9.80671 
9.80  686 
9.80  701 
9.80  716 
9-8o  731 
9.80  746 
9.80  762 
9-80777 
9-80792 

IS 
IS 
IS 
IS 

;i 

IS 
IS 

9-92  ISO 
9.92  176 
9.92  2O2 
9-92  227 
9-92  253 
9.92  279 
9.92  304 
9-92  330 
9.92356 

26 
26 
25 
26 
26 
25 
26 
26 

0.07  850 
0.07  824 
0.07  798 
0.07  773 
0.07  747 
0.07  721 
0.07  696 
0.07  670 
0.07  644 

9.88521 
9.88510 
9-88  499 
9.88  489 
9.88478 
9.88  468 
9.88457 
9-88  447 
9.88436 

II 
II 

10 

II 

IO 

II 

IO 

II 

9 

8 
7 
6 
5 
4 
3 

2 

I 

8 
9 

8.8     8.0 
9-9     9-0 

60 

9.80  807 

9-92  38l 

0.07  619 

9-88425 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

r 

P  P 

129° 


(377) 


50° 


40° 


139C 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9.80  807 

9-92381 

26 

0.07  619 

9-88425 

60 

I 

2 

3 

4 

s 

7 
8 
9 

9.80822 
9-80837 
9.80852 
9.80867 
9.80882 
9.80  897 
9.80912 
9.80927 
9.80  942 

15 
15 
15 
15 
15 
15 
15 
15 

9.92  407 

9-92  433 
9.92  458 
9.92  484 
9-92  5io 
9-92  535 
9-92  561 
9.92  587 
9.92  612 

26 
25 
26 
26 

ll 

26 
11 

0-07  593 
0.07  567 
0.07  542 
0.07  516 
0.07  490 
0.07  465 
0.07  439 
0.07413 
0.07  388 

9-88415 
9.88  404 
9.88394 

9-88383 
9-88372 
9.88362 
9-88351 

9-88  340 
9-88330 

ii 

10 

II 
II 

IO 

II 
II 

10 

3 

57 
56 
55 
54 
53 
52 
51 

26    25 

10 

9.80957 

15 

9.92  638 

0.07  362 

9-88319 

11 

50 

I 

2.6    2.5 

ii 

12 
13 

14 
15 

16 

17 
18 
19 

9.80972 
9.80987 

9-8l  002 
9.8l  017 
9.8l  032 
9.8l  047 

9.81  061 
9.81076 
9.81  091 

IS 

15 
15 
15 
15 
15 
14 
IS 
15 

9-92  663 
9.92  689 
9.92715 
9-92  740 
9.92  766 
9-92  792 
9.92817 
9.92  843 
9.92  868 

26 
26 
25 
26 
26 
25 
26 
25 
26 

0.07  337 
0.07  311 
0.07  285 
0.07  260 
0.07  234 
0.07  208 
0.07  183 
0.07  157 
0.07  132 

9.88  308 
9.88  298 
9.88  287 
9.88276 
9.88  266 
9-88  255 
9.88  244 
9-88  234 
9.88  223 

10 

II 
II 

10 

II 
II 

10 

II 

49 

48 
47 
46 
45 
44 
43 
42 
4i 

3 

4 
5 
6 

I 

9 

5-2     5-o 
7-8     7-5 
10.4    10.0 
13.0   12.5 
15.6    15.0 
18.2    17.5 

20.8     20.0 

23.4   22.5 

20 

9.81  106 

9.92  §94 

0.07  106 

9.88212 

40 

21 
22 
23 
24 
25 
26 

27 
28 
29 

9.8l  121 
9-8l  136 
9-8l  151 

9.81  166 
9.81  180 
9.81  195 

9.8l  210 
9.8l  225 
9.8l  240 

IS 
15 
IS 
15 
14 
IS 

15 

IS 

IS 

9.92  920 
9-92  945 
9.92971 
9.92  996 
9.93022 
9.93  048 
9-93  073 
9-93  099 
9-93  124 

25 
26 
25 
26 
26 
25 
26 
25 

0.07  080 
0.07  055 
0.07  029 
0.07  004 
0.06978 
0.06952 
0.06927 
0.06  901 
0.06876 

9.88  201 
9.88  191 

9.88  180 
9.88  169 

9.88  158 

9.88  148 

9.88137 
9.88  126 
9.88115 

IO 

II 
II 
II 

10 

II 
II 
II 

39 
33 
37 
36 
35 
34 
33 
32 
31 

I 

2 

15     14 

i.S     i-4 

3.0    2.8 

30 

9.8l  254 

14 

9-93  ISO 

0.06  850 

9.88  105 

30 

3 

4-5     4-2 
6.0     5.6 

3i 

32 
33 
34 
35 
36 
37 
38 
39 

9.8l  269 
9-8l  284 
9.8l  299 

9-8I3I4 
9.8l  328 

9-8i  343 
9-8l  358 
9-81372 
9.81  387 

15 
IS 

15 

IS 
14 
IS 

15 
14 
IS 

9-93  175 
9-93  201 
9-93  227 
9-93  252 
9-93  278 
9-93  303 
9-93  329 
9-93  354 
9-93  38o 

26 
26 
25 
26 
25 
26 

il 

26 

0.06825 
0.06  799 
0.06  773 
0.06  748 
0.06  722 
0.06  697 
0.06  671 
0.06  646 
0.06  620 

9.88  094 
9.88  083 
9.88072 
9.88  061 
9.88051 
9.88  040 
9.88029 
9.88018 
9.88007 

II 
II 
II 

10 

II 
II 
II 
II 

29 
28 
27 
26 

25 
24 

23 

22 
21 

5 
6 
7 
8 
9 

7-5     7-0 
9.0     8.4 
10.5     9.8 

12.0     II.  2 
I3-S     12-6 

40 

9.81  402 

9.93  406 

0.06  594 

9.87  996 

20 

4i 
42 
43 
44 
45 
46 
47 
48 
49 

9.81  417 
9.81  431 
9.81  446 
9.81  461 
9-8i  475 
9.81  490 
9-8i  505 
9.81  519 
9-8i  534 

IS 

14 

IS 

15 
14 
15 

IS 
14 
IS 

9-93  43i 
9-93  457 
9-93  482 
9-93  5o8 
9-93  533 
9-93  559 
9-93  584 
9-93  610 
9-93  636 

26 

25 
26 

25 
26 
25 
26 
26 

0.06  569 
0.06  543 
0.06  518 
0.06  492 
0.06  467 
0.06  441 
0.06  416 
0.06  390 
0.06  364 

9.87  985 
9-87975 
9.87  964 

9.87  953 
9.87  942 
9.8793I 
9.87920 
9.87  909 
9.87  898 

10 

II 
II 
II 
II 
II 
II 
II 

19 
18 
i/ 
16 
15 
14 
13 

12 
II 

I 

2 

3 

4 
5 

11     10 

I.I       1.0 

2.2        2.0 

3-3     3-0 

4-4     4-0 
5-5     5-° 

50 

9.81  549 

9-93  661 

26 

0.06339 

9.87  887 

10 

6 

6.6     6.0 

5i 
52 
53 
54 
55 
56 

11 

59 

9-8i  563 
9-81578 
9-8i  592 
9.81  607 
9.81  622 
9.81  636 
9.81  651 
9.81  665 
9.81  680 

IS 

14 
IS 
IS 
14 
15 
14 
15 

9-93  687 
9-93  712 
9-93  738 
9-93  763 
9-93  789 
9-938i4 
9-93  840 
9-93  865 
9-93  891 

25 
26 
25 
26 
25 
26 

25 
26 

0.06313 
0.06  288 
0.06  262 
0.06  237 

0.06  211 

0.06  186 
0.06  1  60 
0.06  135 
0.06  109 

9-87877 
9.87  866 
9-87855 
9.87  844 
9-87833 
9.87  822 
9.87811 
9.87  800 
9.87  789 

II 
II 
II 
II 
II 
II 
II 
II 

7 
6 
5 
4 
3 

2 
I 

I 

9 

7-7     7-o 
8.8     8.0 
9-9     9-0 

60 

9.81  694 

14 

9.93916 

25 

0.06  084 

9.87778 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

t 

P  P 

130° 


(378) 


49° 


138C 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9.81  694 

9.93916 

26 

0.06  084 

9.87  778 

60 

I 

2 

3 

4 

I 

7 
8 
9 

9.81  709 
9.81  723 
9.81  738 
9.81  752 
9.81  767 
9.81  781 
9.81  796 
9.81810 
9.81825 

14 
15 
14 
15 
14 
15 
14 

IS 

9-93  942 
9-93  967 
9-93  993 
9.94018 
9.94  044 
9-94  069 
9-94  °95 
9.94120 
9-94  146 

25 
26 
25 
26 
25 
26 

25 
26 

0.06  058 
0.06  033 
0.06  007 
0.05  982 
0.05  956 
0.05931 
0.05  905 
0.05  880 
0.05  854 

9.87  767 
9-87756 

9-87  745 
9.87  734 
9-87  723 
9.87  712 
9.87  701 
9.87  690 
9-87679 

ii 
ii 
ii 
ii 
ii 
ii 
ii 
ii 

59 
58 
57 
56 
55 
54 
53 
52 
5i 

26    25 

26    25 

10 

9-81  839 

9-94  171 

26 

0.05  829 

9.87  668 

50 

2 

5-2      5-0 

ii 

12 
13 

14 

11 

17 

18 

19 

9-81  854 

9.81  868 
9.81882 
9.81  897 
9.81  911 
9.81  926 
9.81  940 
9-8i  955 
9.81  969 

14 
14 
IS 

14 

IS 

14 

IS 

14 

9.94  197 
9.94222 
9-94  248 
9-94  273 
9-94  299 
9.94324 
9-94350 
9-94375 
9-94  401 

25 
26 
25 
26 
25 
26 

3 

0.05  803 
0.05778 
0.05  752 
0.05  727 
0.05  701 
0.05  676 
0.05  650 
0.05  625 

0-05  599 

9-87657 
9.87  646 
9-87  635 
9.87624 
9-87613 
9.87  601 
9.87  590 
9-87  579 
9-87  568 

ii 
ii 
ii 
ii 

12 
II 
II 
II 

49 

48 
47 
46 
45 
44 
43 
42 
41 

3 

4 

s 

6 
7 
8 
9 

7-8     7-5 
10.4    10.0 

13.0   12.5 
15.6   15.0 
18.2    17.5 

20.8     20.O 

23.4   22.5 

20 

9.8i  983 

9-94  426 

26 

0.05  574 

9-87SS7 

40 

21 

22 
23 
24 
25 
26 

27 
28 
29 

9.81  998 
9.82012 
9.82  026 
9.82  041 
9.82055 
9.82  069 
9.82  084 
9.82  098 

9.82  112 

14 
14 
IS 

14 
14 

IS 
14 
14 

9-94452 
9-94477 
9-94  503 
9-94  528 
9-94  554 
9-94579 
9.94  604 
9-94  630 
9-94655 

25 
26 
25 
26 
25 
25 
26 
25 
26 

0.05  548 
0.05  523 
0.05  497 
0.05472 
0.05  446 
0.05  421 
0.05  396 
0.05  370 
0.05  345 

9.87  546 
9-87  535 
9.87  524 

9.87513 
9.87  501 
9.87  490 

9.87479 
9.87  468 
9-87457 

II 
II 
II 
12 
II 
II 
II 
II 

39 
38 
37 
36 
35 
34 
33 
32 
3i 

i 

2 
3 

15     14 

1.5     1.4 
3.0    2.8 

4-5      4-2 

30 

9.82  126 

9.94  681 

0.05  319 

9.87  446 

30 

4 

6.0    5.6 

3i 

32 
33 
34 
35 
36 

3 

39 

9.82  141 
9.82155 
9.82  169 
9.82  184 
9.82  198 
9.82  212 
9.82  226 
9.82  240 
9-82  255 

14 
14 
IS 

14 
14 

14 
14 
IS 

9-94  7o6 
9-94732 
9-94757 
9-94  783 
9-94  808 
9-94  834 
9.94859 
9.94  884 
9.94910 

26 
25 
26 

25 
26 
25 
25 
26 

0.05  294 
0.05  268 
0.05  243 
0.05  217 
0.05  192 
0.05  166 
0.05  141 
0.05  116 
0.05  090 

9.87434 
9-87423 
9.87412 
9.87  401 
9.87  390 
9.87378 
9-87367 
9-87356 
9.87  345 

II 
II 
II 
II 
12 
II 
II 
II 

29 
28 
27 
26 
25 
24 
23 

22 
21 

6 

1 
9 

9.0    8.4 
10.5    9.8 

I2.O     II.  2 
I3-S     12.6 

40 

9.82  269 

9-94935 

26 

0.05  065 

9-87334 

20 

4i 
42 
43 
44 

a 

47 
48 
49 

9.82  283 
9.82  297 
9.823II 
9.82326 
9.82  340 
9.82354 
9.82  368 
9.82382 
9-82  396 

14 
14 
IS 
14 
14 
14 
14 
14 

9.9496i 
9-94  986 
9.95012 

9-95  037 
9-95  062 
9-95  088 
9-95  H3 
9-95  139 
9.95  164 

25 
26 
25 

3 

25 
26 
25 
26 

0.05  039 
0.05  014 
0.04  988 
0.04  963 
0.04  938 
0.04912 
0.04  887 
0.04  861 
0.04  836 

9-87322 
9.873H 
9-87  300 
9.87  288 
9.87  277 
9.87  266 
9.87  255 
9.87  243 
9.87  232 

II 

II 
12 
II 
II 
II 
12 
II 

19 
18 
17 
16 
15 
14 
13 

12 
II 

z 

2 
3 

4 

I 

12     11 

1.2      I.I 

2.4      2.2 

3-6     3-3 
4.8     4-4 
6.0    5.5 
7.2    6.6 

50 

9.82  410 

9.95  190 

0.04  810 

9.87  221 

10 

I 

8.4     7-7 

51 

52 
53 
54 
55 
56 

11 

59 

9.82  424 

9.82  439 
9-82453 
9.82467 
9.82  481 
9.82  495 
9-82  509 
9-82  523 
9-82537 

IS 

14 
14 
14 
14 
14 
14 
14 

9-95  215 
9-95  240 
9-95  266 
9-95  291 
9-95317 
9-95342 
9-95368 
9-95  393 
9-95  4i8 

25 
26 
25 
26 

•A 

25 
25 

0.04  785 
0.04  760 
0.04  734 
0.04  709 
0.04  683 
0.04  658 
0.04632 
0.04  607 
0.04  582 

9.87  209 
9.87  198 
9.87  187 
9.87  175 
9.87  164 
9.87153 
9.87  141 
9-8?  130 
9.87  119 

II 
II 
12 
II 
II 
12 
II 
II 

9 
8 
7 
6 
5 
4 
3 

2 
I 

8 
9 

9.6    8.8 
10.8    9.9 

60 

9-82551 

9.95  444 

0.04  556 

9.87  107 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

f 

P  P 

131C 


(379) 


42° 


137C 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9-82551 

9-95  444 

0.04  556 

9.87  107 

60 

I 

2 

3 
4 

7 
8 
9 

9-82  565 

9-82  579 
9-82  593 
9.82  607 
9.82  621 
9-82  635 
9.82  649 
9.82  663 
9.82677 

14 
14 
14 
14 
14 
14 
14 
14 

9-95  469 
9-95  495 
9-95  520 
9-9S  545 
9-95571 
9-95  596 
9-95622 
9-95  647 
9-95  672 

26 
25 
25 
26 
25 
26 

25 

25 
26 

0.04531 
0.04  505 
0.04  480 

0.04  455 
0.04  429 
0.04  404 
0.04378 
0.04  353 
0.04328 

9.87  096 
9-87  085 
9.87073 
9.87  062 
9.87  050 
9.87  039 
9.87028 
9.87016 
9-87  005 

u 

12 
II 
12 
II 
II 
12 
II 

59 

58 
57 
56 
55 
54 
53 
52 
5i 

26     25 

10 

9.82  691 

9-95  698 

0.04  302 

9-86  993 

50 

I 

2.6     2.5 

ii 

12 
13 
14 
15 

16 

17 
18 
19 

9-82  705 
9.82719 
9-82  733 
9.82  747 
9.82  761 
9.82775 
9.82  788 
9.82  802 
9.82816 

14 
14 
14 
14 
14 
13 
14 
14 

9-95  723 
9-95  748 
9-95  774 
9-95  799 
9-95825 
9-95  850 
9-95  875 
9-95  9oi 
9.95926 

25 
26 
25 
26 
25 
25 
26 

*6 

0.04  277 
0.04  252 
0.04  226 
0.04  201 
0.04  175 
0.04  150 
0.04125 
0.04  099 
0.04  074 

9.86982 
9.86  970 
9-86  959 
9-86  947 
9-86  936 
9.86924 
9.86913 
9.86  902 
9.86  890 

12 
II 
12 
II 
12 
II 
II 
12 

40 
48 
47 
46 
45 
44 

43 

42 
4i 

3 
4 
5 
6 

I 

9 

7-8     7-5 
10.4    10.  o 
13.0   12.5 
15.6   15.0 
18.2    17.5 

20.8     20.0 
23-4     22.5 

20 

9.82  830 

9-95952 

0.04  048 

9.86879 

40 

21 
22 
23 
24 

y 

27 
28 
29 

9.82  844 
9.82  858 
9.82872 
9.82  885 
9.82  899 
9-82  913 
9.82927 
9.82  941 
9-82  955 

14 
14 
13 
14 
14 
14 
14 
u 

9-95  977 
9.96  002 
9.96028 
9-96053 
9.96078 
9.96  104 
9.96129 
9.96155 
9.96  180 

25 
26 
25 
25 
26 
25 
26 
25 

0.04023 
0.03  998 
0.03  972 
0.03  947 
0.03  922 
0.03  896 
0.03  871 
0.03  845 
0.03  820 

9.86  867 
9-86855 
9.86  844 
9.86832 
9.86821 
9.86  809 
9.86  798 
9.86  786 
9-86  775 

12 
II 
12 
II 
12 
II 
12 
II 

39 

38 
37 
36 
35 
34 
33 
32 
3i 

i 

2 

3 

14    13 

1.4    1.3 

2.8       2.6 

4-2     3-9 

30 

9.82  968 

9-96  205 

26 

0.03  795 

9-86  763 

12 

30 

4 

5-6     5-2 

3i 
32 
33 
34 
35 
36 

11 

39 

9.82982 
9.82  996 
9.83010 
9-83  023 
9-83  037 
9-83051 
9-83  065 
9-83078 
9-83  092 

14 
14 
13 
14 
14 
14 
13 
14 

9-96  231 
9-96  256 
9.96  281 
9.96  307 
9.96332 
9-96357 
9-96  383 
9.96  408 
9-96  433 

25 

11 

25 
25 
26 

25 
25 

0.03  769 
0.03  744 
0.03  719 
0.03  693 
0.03  668 
0.03  643 
0.03  617 
0.03  592 
0.03  567 

9-86752 
9.86  740 
9.86728 
9.86717 
9-86  705 
9.86  694 
9.86682 
9.86670 
9-86  659 

12 
12 
II 
12 
II 
12 
12 
II 

29 

28 
27 
26 
25 
24 
23 

22 
21 

6 
7 
8 
9 

8.4     7-8 
9.8    9-1 

1  1.  2      IO.4 

12.6    11.7 

40 

9.83  106 

*4 

9.96  459 

0.03  541 

9.86  647 

20 

4i 
42 
43 
44 
45 
46 

47 
48 
49 

9.83  120 

9-83  133 
9-83  147 

9-83  161 
9.83  174 
9.83  188 

9.83  202 

9-83  215 
9-83  229 

13 
14 
14 
13 
14 
14 
13 
14 

9.96  484 
9-96510 
9-96535 
9-96  56o 
9-96  586 
9.96611 
9.96  636 
9.96  662 
9.96  687 

25 
26 
25 
25 
26 
25 
25 
26 
25 

0.03  516 
0.03  490 
0.03  465 
0.03  440 
0.03  414 
0-03  389 
0.03  364 
0.03  338 
0.03  313 

0.86635 
9.86624 
9.86612 
9.86  600 
9-86  589 
9.86577 
9-86565 
9-86  554 
9-86  542 

II 
12 
12 
II 
12 
12 
II 
12 

19 
18 
17 
16 
15 
14 
13 

12 
II 

i 

2 

3 
4 
5 
6 

12     11 

1.2      I.I 

2.4       2.2 

3-6     3-3 
4.8     4-4 
6.0     5-5 
7.2     6.6 

50 

9.83  242 

9.96712 

tf\ 

0.03  288 

9-86  530 

12 

10 

7 
g 

8.4     7-7 

Si 
52 
53 

54 
55 
56 

§ 

59 

9-83  256 
9-83  270 
9.83  283 
9.83  297 
9-83  310 
9-83  324 
9.83  338 

9-83  351 
9-83  365 

14 
13 
14 
13 
U 
14 
13 
U 

9-96  738 
9.96  763 
9.96  788 
9.96814 
9-96  839 
9.96  864 
9.96  890 
9.96915 
9.96  940 

25 

3 

25 

\l 

25 
25 

0.03  262 
0.03  237 

0.03  212 

0.03  1  86 
0.03  161 
0.03  136 
0.03  no 
0.03  085 
0.03  060 

9-86518 
9-86  507 
9-86  495 
9-86  483 
9.86472 
9.86  460 
9.86  448 
9-86  436 
9-86425 

II 
12 
12 
II 
12 
12 
12 
II 

9 

8 
7 
6 

5 
4 
3 

2 

i 

9 

10.8     9.9 

60 

9.83378 

9.96  966 

0.03  034 

9-86413 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

r 

P  P 

132C 


(380) 


43C 


136° 


/ 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

0 

9-83378 

9.96  966 

0.03  034 

9-86413 

60 

I 

2 

3 
4 
5 
6 

7 
8 
9 

9-83  392 
9-83  405 
9.83  419 
9-83  432 
9.83  446 

9-83  459 
9-83  473 
9-83  486 
9-83  5oo 

13 
14 
13 
14 
13 
14 
13 
14 

9.96991 
9.97016 

9-97  042 
9-97  067 
9-97  092 
9.97118 

9-97  143 
9.97  168 
9-97  193 

3 

25 

2 

25 
25 
25 
26 

0.03  009 

O.02  984 
0.02  958 

0.02  933 

O.O2  908 
0.02  882 
O.O2  857 
0.02  832 
0.02  8O7 

9.86  401 

9-86  389 
9-86377 
9-86  366 
9-86  354 
9-86342 
9-86  330 
9-86318 
9.86  306 

12 
12 
II 
12 
12 
12 
12 
12 

59 
58 
57 
56 
55 
54 
S3 
52 
51 

26    25 

10 

9-835I3 

13 

9-97  219 

O.O2  781 

9-86  295 

50 

2.6    2.5 

ii 

12 
13 
14 

IS 
16 

17 
18 
19 

9-83527 
9-83  540 
9-83  554 
9-83  567 
9-83  58i 
9-83  594 
9-83  608 
9.83  621 
9-83  634 

14 
13 
14 
13 
14 
13 
14 
13 
13 

9-97  244 
9-97  269 
9-97  295 
9.97320 
9-97  345 
9-97371 
9-97  396 
9.97421 
9-97  447 

25 
26 
25 
25 
26 
25 
25 
26 

O.O2  756 
0.02  731 
O.O2  705 
O.O2  68O 
0.02  655 
0.02  629 
O.O2  604 

0.02  579 
0.02  553 

9.86  283 
9.86271 
9-86  259 
9.86  247 
9-86  235 
9.86  223 
9.86211 

9.86  200 

9.86  188 

12 
12 
12 
12 
12 
12 
II 
12 

49 

48 
47 
46 
45 
44 
43 
42 
41 

3 

4 
5 
6 

I 

9 

7-8    7-5 
10.4    10.0 
13.0   12.5 
15-6    15-0 
18.2    17.5 

20.8     2O.O 
23-4     22.5 

20 

9.83  648 

14 

9.97472 

25 

0.02  528 

9.86176 

40 

22 
23 

24 
25 
26 

27 
28 
29 

9-83  661 
9.83  674 
9.83  688 
9.83  701 
9-83  715 
9-83  728 
9.83  74i 
9-83  755 
9-83  768 

13 
13 
14 
13 
14 
13 
13 
14 
13 

9-97  497 
9-97  523 
9-97  548 
9-97  573 
9-97  598 
9-97  624 
9-97  649 
9-97  674 
9-97  7oo 

25 
26 
25 
25 
25 
26 
25 
25 
26 

0.02  503 

0.02  477 

0.02  452 

0.02427 

0.02  4O2 
0.02  376 

0.02351 

0.02  326 
0.02  30O 

9.86  164 
9.86152 
9.86  140 
9.86128 
9.86116 
9.86  104 
9.86  092 
9.86  080 
9.86  068 

12 
12 
12 
12 
12 
12 
12 
12 

39 

38 
37 
36 
35 
34 
33 
32 
3i 

2 

3 

14     13 

1.4    1.3 

2.8      2.6 

4-2     3-9 

30 

9-83  78i 

13 

9-97  725 

25 

0.02  275 

9.86056 

30 

4 

5-6     5-2 

31 

32 
33 
34 
35 
36 

11 

39 

9-83  795 
9.83  808 
9.83821 

9.83  834 
9-83  848 
9.83  861 
9-83  874 
9-83  887 
9-83  9oi 

14 
13 
13 
13 
14 
13 
13 
13 
14 

9-97  750 
9-97  776 
9.97  801 
9.97  826 
9-9785I 
9-97  877 
9-97  902 
9.97927 
9-97  953 

25 
26 
25 
25 
25 
26 
25 
25 
26 

O.O2  250 
0.02  224 
O.O2  199 
0.02  174 
0.02  149 
0.02  123 
O.O2  098 
0.02  073 
O.02  047 

9.86  044 
9.86032 
9.86020 
9.86  008 
9.85  996 
9.85  984 
9.85972 
9-85  96o 
9.85  948 

12 
12 
12 
12 
12 
12 
12 
12 

29 

28 
27 
26 

25 
24 
23 

22 
21 

6 
7 
8 
9 

8.4     7-8 
9-8     9.1 

II.  2      IO.4 

12.6    11.7 

40 

9.83  914 

*3 

9.97978 

0.02022 

9-85  936 

20 

4i 
42 
43 
44 
45 
46 

47 
48 
49 

9.83  927 
9.83  940 
9-83  954 
9-83  967 
9-83  98o 
9-83  993 
9.84  006 
9.84  020 
9-84033 

ij> 
13 
14 
13 

13 
13 
13 

14 
13 

9.98  003 
9.98  029 
9.98  054 
9.98079 
9.98  104 
9.98  130 

9-98i55 
9.98  180 
9.98  206 

25 
26 
25 
25 

3 

25 

\\ 

o.oi  997 
o.oi  971 
o.oi  946 
o.oi  921 
o.oi  896 
o.oi  870 
o.oi  845 
o.oi  820 
o.oi  794 

9.85  924 
9-85912 
9-85  9oo 
9.85  888 
9-85876 
9-85  864 
9-85851 
9-85  839 
9-85827 

12 
12 
12 
12 
12 
13 
12 
12 

i9 
18 
i7 
16 
15 
U 
13 

12 
II 

i 

2 

3 

4 

I 

12     11 

1.2      I.I 

2-4      2.2 

3-6     3-3 
4-8     4-4 
6.0     5.5 
7.2    6.6 

50 

9.84  046 

9-98  231 

25 

o.oi  769 

9-85815 

10 

7 
g 

8.4     7-7 

96     8.8 

Si 
52 
53 
54 
55 
56 

Si 

59 

9.84059 
9.84072 
9-84085 
9.84098 
9.84112 
9-84125 
9-84  138 
9-84151 
9.84  164 

13 
13 
13 
14 
13 
13 
13 
13 

9-98256 
9.98  281 
9.98  307 
9-98332 
9-98357 
9-98  383 
9-98  408 
9.98  433 
9-98  458 

25 
26 
25 
25 
26 
25 
25 
25 

o.oi  744 
o.oi  719 
o.oi  693 
o.oi  668 
o.oi  643 
o.oi  617 
o.oi  592 
o.oi  567 
o.oi  542 

9-85  803 
9-85  79i 
9-85  779 
9-85  766 
9-85  754 
9.85  742 

9-85  730 
9-85  7i8 
9-85  7o6 

12 
12 
13 
12 
12 
12 
12 
12 

1 

7 
6 
5 

4 
3 

I 

9 

10.8    9.9 

60 

9.84177 

9.98484 

o.oi  516 

9-85  693 

0 

LCos 

d 

LCot 

cd 

LTan 

LSin 

d 

I 

P  P 

(381) 


46° 


135° 


t 

T 

i 

2 

3 

4 
5 
6 

7 
8 
9 
10 

ii 

12 
13 

14 
15 

16 

17 
18 
19 
29 

21 

22 
23 

24 

11 

27 
28 
29 

30 

3i 
32 
33 

34 

51 

S 

39 
40 

4i 
42 
43 
44 

3 

a 

49 
50 

Si 
52 
53 
54 

II 

S 

59 
60 

LSin 

d 

LTan 

cd 

LCot 

LCos 

d 

P  P 

9-84177 

HHMMMMHHH  H  HHHHHHHHH  M  HHHHMMHHH  H  HHHHHMt-IHH  H  HHHHHHHHH  H  HHHHMHHHH  H 

9-98  484 

25 

25 
26 
25 
25 

II 

25 

11 

25 
25 
25 
26 

25 
25 
25 
26 
25 
25 
26 

25 
25 
25 
26 
25 
25 
25 
26 
25 
25 
26 
25 
25 
25 
26 
25 
25 
25 
26 

25 
25 
25 
26 

25 

11 

25 
25 
25 
26 

25 
25 
25 
26 
25 
25 
25 
26 
25 

o.oi  516 

9.85  693 

12 
12 
12 
12 

13 
12 
12 
12 
13 
12 

12 
12 
13 
12 
12 
13 
12 
12 
13 
12 

12 

13 
12 
12 

13 
12 
13 
12 
12 
13 
12 

13 
12 

13 
12 
12 
13 
12 
13 
12 

13 
12 
13 
12 

13 
12 
13 
12 
13 
13 
12 

13 
12 
13 
12 
13 
13 
12 
13 
12 

d 

60 

59 
58 
57 
56 
55 
54 
53 
52 
51 
50 

49 
48 
47 
46 
45 
44 
43 
42 
41 
40 

39 
38 
37 
36 
35 
34 
33 
32 
31 
30 

29 
28 
27 
26 

25 
24 
23 

22 
21 

20 

19 
18 
i7 
16 
15 
14 
13 

12 
II 

10 

9 
8 
7 
6 
5 
4 
3 

2 

I 
0 

26         25         14 

i        2.6         2.5         1.4 

2           5.2             5-0             2.8 

3       7-8         7-5         4-2 
4     10.4       10.0         5.6 
5     13.0       12.5         7.0 
6     15.6       15.0         8.4 
7     18.2       17.5         9.8 

8       2O.8         2O.O         1  1.  2 

9     23.4       22.5       12.6 
13           12 

I          1-3               1-2 
2          2.6               2.4 

3       3-9           3-6 
4       5-2           4-8 
5       6.5           6.0 
6       7-8           7-2 
7       9.1           8.4 
8     10.4           9.6 
9     11.7         10.8 

9.84  190 
9-84  203 
9.84  216 
9.84229 
9.84  242 
9-84255 
9.84269 
9.84282 
9.84  295 

9.98  509 

9.98  534 
9-98  560 
9-98  585 
9.98  610 
9-98635 
9.98  661 
9.98  686 
9.98711 

o.oi  491 
o.oi  466 
o.oi  440 
o.oi  415 
o.oi  390 
o.oi  365 
o.oi  339 
o.oi  314 
o.oi  289 

9.85  681 

9.85  669 

9-85  657 
9-85  645 
9.85632 

9.85  620 

9.85  608 
9-85  596 
9-85  583 

9-84308 

9-98  737 

o.oi  263 

9.85571 

9-84321 
9-84334 
9-84347 
9.84  360 
9-84373 
9-84  385 
9.84  398 
9.84411 
9.84424 

9.98  762 
9.98  787 
9.98812 
9.98  838 
9.98  863 
9.98  888 
9.98913 
9-98  939 
9.98  964 

o.oi  238 
o.oi  213 
o.oi  188 
o.oi  162 
o.oi  137 

O.OI  112 

o.oi  087 
o.oi  061 
o.oi  036 

9-85  559 
9-85  547 
9-85  534 
9-85522 
9.85510 
9-85  497 
9-85  485 
9-85473 
9-85  460 

9-84437 

9.98  989 

O.OI  Oil 

9-85  448 

9.84450 
9-84  463 
9.84476 

9-84  489 
9.84  502 
9-84515 
9-84528 
9.84  540 

9-84  553 

9.99015 
9.99  040 
9-99  065 
9.99090 
9.99116 
9-99  141 
9.99  166 
9-99  I9i 
9.99217 

o.oo  985 
o.oo  960 
0.00935 
o.oo  910 
o.oo  884 
0.00859 
o.oo  834 
o.oo  809 
o.oo  783 

9-85  436 
9-85423 
9.854" 
9-85  399 
9-85386 
9-85374 
9-85361 
9-85  349 
9-85337 

9.84  566 

9-99  242 

0.00758 

9-85324 

9.84579 
9-84  592 
9-84  605 
9.84618 
9.84  630 
9.84  643 
9-84656 
9.84669 
9.84  682 

9.99  267 
9-99  293 
9.99318 

9-99  343 
9-99  368 
9-99394 
9.99419 
9-99  444 
9-99  469 

o.oo  733 
o.oo  707 
o.oo  682 
0.00657 
o.oo  632 
o.oo  606 
o.oo  581 
o.oo  556 
o.oo  531 

9-853I2 
9.85  299 
9-85  287 
9-85274 
9.85  262 
9-85  250 
9-85  237 
9.85225 
9.85212 

9.84  694 

9-99  495 

o.oo  505 

9.85  200 

9.84  707 
9.84720 
9-84  733 
9-84  745 
9.84758 
9.84771 
9.84  784 
9.84  796 
9.84  809 

9-99  520 
9-99  545 
9-99  570 
9-99  596 
9.99621 
9.99  646 
9.99672 
9-99697 
9.99722 

o.oo  480 
0.00455 
o.oo  430 
o.oo  404 
0.00379 
0.00354 

0.00328 
o.oo  303 
o.oo  278 

9.85  187 

9.85  175 
9.85  162 

9-85  150 
9-85I37 
9-85125 

9.85  112 

9.85  ioo 

9.85  OS? 

9.84822 

9-99  747 

o.oo  253 

9.85074 

9-84835 
9.84847 
9.84  860 
9.84873 
9-84885 
9.84898 
9.84911 
9.84923 
9.84  936 

9-99773 
9-99  798 
9-99823 
9-99  848 
9.99874 
9-99  899 
9-99924 
9-99  949 
9-99975 

o.oo  227 

O.OO  202 

0.00177 
o.oo  152 
0.00126 

O.OO  IOI 

0.00076 
0.00051 
0.00025 

9.85062 
9.85  049 
9.85037 
9-85024 
9.85012 

9.84  999 
9.84986 
9.84974 
9.84961 

9-84  949 

o.oo  ooo 

0.00000 

9.84  949 

LCos 

d 

LCot 

cd 

LTan 

LSin 

/ 

P  P 

134C 


(382) 


45C 


TOPICAL   INDEX 


PAGE 

Adjustment  of  instruments 333 

Azimuth,  latitude,  and  time 305 

Barometric  elevations 328 

Compound  curves 8 

Curvature,  estimating 254 

Curve  resistance 250 

Distance,  estimating 252 

Elevation  of  outer  rail 287 

Estimating  elements  for  distance,  curvature,  etc 252 

Gage  on  curves 286 

Grade,  ruling,  estimating  for  changes  in 254 

Grades  for  unbalanced  traffic 251 

Latitude,  azimuth,  and  time 305 

Load  on  grade 250 

Loads  on  grades,  table 259 

Location  theories  and  tables 249 

Logarithms,  sines,  etc.,  use  of  table 96 

table 76 

table,  use  of 70 

versine  and  exsecants 189 

Metric  curves 314 

Miscellaneous  tables 320 

Momentum  grade "...  251 

Prismoidal  correction 267 

table 276 

Pusher  grade 250 

Pusher  grades  table 260 

Pusher  service,  cost  of 255 

383 


384  TOPICAL  INDEX 

PAGE 

Right  of  way  table 290 

Rise  and  fall,  estimating • 253 

Resistance,  train  and  curve 250 

Ruling  grade,  estimating  for  changes  in 254 

Simple  curves,  approximate  fundamental  relations 2 

fundamental  notations  and  equations I 

location  by  offsets  from  long  chord 4 

problems 5 

table  of  radii  and  tangent  offsets  and  middle  ordi- 

nates  for  100  foot  chords 12 

tangent  distances  for  i°  curve 20 

Sines,  etc.,  natural 234 

use  of  tables 96 

Spiral,  Chapter  II 39 

chord  spiral,  the 41 

compound  curve  spiraling 44 

deflection  coefficients 46 

general  functions,  table  of 47 

select  and  layout,  to 43 

tables,  special 55 

Spring  frogs,  leads 304 

Switches  and  frogs,  properties  of 302 

Tables,  ballast  estimates 296 

barometric  elevations 328 

bridge  masonry  quantities  in  abutments 292 

bridge  weights 296 

compound  interest 262 

convergence  of  meridians 313 

conversion,  English  and  metric  units 332 

minutes  and  seconds  to  decimals 248 

cost  curves,  timber  trestles 293 

culvert  estimates 295 

drainage  areas 291 

elevation  of  outer  rail 288 

external  distances  for  i  °  curve 34 

frogs  and  switches,  properties  of 302 

gage  on  curves 286 

grades  and  grade  angles 261 

latitude  and  longitude  length  0.01° 312 


TOPICAL   INDEX  385 

PAGE 

Tables,  level  section  volumes 278 

loads  hauled  on  grades 259 

logarithmic  versines  and  exsecants 189 

sexagesimal  system  . . .  337 

long  chords  and  actual  arcs 35 

metric  curves,  long  chords  and  actual  arcs 316 

middle  ordinates  of  long  chords 318 

radii    tangent    offsets    and    middle    ordi- 
nates, one  sta 315 

middle  ordinates  for  long  chords 37 

for  100  feet 12 

for  rails 286 

natural  sines,  etc 234 

natural  versines  and  exsecants 243 

polaris,  elongation  and  culmination 3IQ 

pole  distance 309 

prices,  relative,  for  articles  of  different  lives 262 

prismoidal  correction 276 

pusher  grades 260 

radii  of  simple  curves 12 

of  metric  curves 315 

refraction  correction  to  altitude 309 

relative  trains  on  different  grades 260 

right  of  way 290 

sexagesimal  logarithmic  functions 337 

spiral  deflection  coefficients 46 

spiral  functions,  general 47 

spiral,  special 55 

spring  frog  leads 304 

stadia  reduction 325 

switch  leads  practical 303 

tangent  distance  corrections 33 

tangent  distances  for  i°  curves 20 

tangent  offsets  for  100  feet 12 

track  material 289 

tractive  effort  of  locomotive 258 

train  resistance 257 

trigonometric  formulas 320 

velocity  heads 256 

volumes  triangular  prisms 268 


386  TOPICAL  INDEX 


Tables,  weir  volumes 

Time,  azimuth,  and  latitude  .............  ,  ...................  305 

Track  material  ............................................  289 

Tractive  effort  ............................................  249 

of  locomotive  .................................  25 

Trains,  relative  number  on  different  grades  ,  ..................  26c 

Train  resistance  .........................  ..................  2 

table  .......................................  25 

Trestles,  cost  curves  ........................................  29, 

Trigonometric  functions,  logarithmic  sines,  etc  .................       96 

sexagesimal  .........................  337 

Turnouts  and  crossovers  ....................................  297 


i 


Unbalanced  traffic,  grades  for '. 251 

Velocity  grade 256 

heads,  table 256 

Versines  and  external  secants,  natural 243 

and  exsecants,  table  of  logarithmic 189 

Vertical  curves IO 

Volumes,  level  section 267 

tables 278 

triangular  prisms 265 

tables 268 

Weir  volumes,  table 331 


Ul 


YB  53598 


/  ~£i   •  S08538 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


